Casio fx-5800P User Manual

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fx-5800P

User's Guide

http://world.casio.com/edu/

RJA516644-001V01

Remove the insulation sheet!

Your calculator comes with a special insulation sheet, which isolates the battery from the contacts in the battery compartment, to keep the battery from running down during storage and shipment. Be sure to remove the insulation sheet before trying to use the calculator for the ﬁ rst time.

To remove the insulation sheet

1. Pull the tab of the insulation sheet in the direction indicated by the arrow to remove it.

Pull to remove

引き抜いてください

2. After removing the insulation sheet, press the P button on the back of the calculator with a thin, pointed object to initialize the calculator.

Be sure to perform this step! Do not skip it!

Resetting the Calculator to Initial Defaults

Perform the operation below to return the calculator to its initial default settings. Note that resetting the calculator will also delete all data currently stored in its memory.

P button

To reset the calculator to initial defaults

1. Press

• This causes the “Reset All?” conﬁ rmation message to appear.

2. Press E(Yes).

• If you do not want to reset the calculator to initial defaults, press J(No) instead of

(Yes).

The following is what happens when you reset the calculator to initial defaults.

• The calculation mode and setup conﬁ guration return to the initial defaults described under “Clearing the Calculation Mode and Setup Settings (Reset Setup)” (page 13).

• Calculation history data, memory data, statistical calculation sample data, program data, and all other data input by you is deleted.

(SYSTEM)3(Reset All).

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About this Manual

• Most of the keys perform multiple functions. Pressing 1 orS and then another key will perform the alternate function of the other key. Alternate functions are marked above the keycap.

sin–1{D}

Keycap function

Alternate function operations are notated in this manual as shown below.

Example:

• The following shows the notation used in the manual for menu items that appear on the display.

Example: z – {PROG} – { /}

• The following shows the notation used in the manual for menu items that appear on the display (which are executed by pressing a number key).

Example: z – {MATH} 1(∫ dX)

• The displays and illustrations (such as key markings) shown in this User’s Guide are for illustrative purposes only, and may differ somewhat from the actual items they represent.

• The contents of this manual are subject to change without notice.

• In no event shall CASIO Computer Co., Ltd. be liable to anyone for special, collateral, incidental, or consequential damages in connection with or arising out of the purchase or use of this product and items that come with it. Moreover, CASIO Computer Co., Ltd. shall not be liable for any claim of any kind whatsoever by any other party arising out of the use of this product and the items that come with it.

• Company and product names used in this manual may be registered trademarks or trademarks of their respective owners.

Symbols Used in Examples

Var ious symbols are used in the examples of this manual to alert you to settings that need to be conﬁ gured in order to perform the example operation correctly.

• A mark like the ones shown below indicates that you need to change the calculator’s display format setting.

If you see this:

For details, see “Selecting the Display Format (MthIO, LineIO)” (page 11).

–1

(sin

)

The notation in parentheses indicates the function executed by the preceding key operation.

The notation in braces ({ }) indicates the menu item being selected.

The notation in parentheses indicates the menu item accessed by the preceding number key.

Change the display format setting to:

Natural Display

Alternate function

If you see this:

Change the display format setting to:

Linear Display

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• A mark like the ones shown below indicates that you need to change the calculator’s angle unit setting.

If you see this:

For details, see “Specifying the Angle Unit” (page 12).

Change the angle unit setting to:

Deg

If you see this:

Change the angle unit setting to:

Rad

Safety Precautions

Be sure to read the following safety precautions before using this calculator. Be sure to keep all user documentation handy for future reference.

Caution

This symbol is used to indicate information that can result in personal injury or material damage if ignored.

Battery

• After removing the battery from the calculator, put it in a safe place where it will not get into the hands of small children and accidentally swallowed.

• Keep batteries out of the reach of small children. If accidentally swallowed, consult with a physician immediately.

• Never charge the battery, try to take the battery apart, or allow the battery to become shorted. Never expose the battery to direct heat or dispose of it by incineration.

• Improperly using a battery can cause it to leak and damage nearby items, and can create the risk of ﬁ re and personal injury.

• Always make sure that the battery’s positive correctly when you load it into the calculator.

• Remove the battery if you do not plan to use the calculator for a long time.

• Use only the type of battery speciﬁ ed for this calculator in this manual.

Disposing of the Calculator

• Never dispose of the calculator by burning it. Doing so can cause certain components to suddenly burst, creating the risk of ﬁ re and personal injury.

and negative l ends are facing

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Operating Precautions

• Be sure to press the P button on the back of the calculator before using the calculator for the ﬁ rst time. See page 1 for information about the P button.

• Even if the calculator is operating normally, replace the battery at least once a year.

A dead batter y can leak, causing damage to and malfunction of the calculator. Never

leave a dead battery in the calculator.

• The battery that comes with this unit discharges slightly during shipment and storage. Because of this, it may require replacement sooner than the normal expected battery life.

• Do not use an oxyride battery or any other type of nickel-based primary battery with this product. Incompatibility between such batteries and product speciﬁ cations can result in shorter battery life and product malfunction.

• Low battery power can cause memory contents to become corrupted or lost completely. Always keep written records of all important data.

• Avoid use and storage of the calculator in areas subjected to temperature extremes.

Ve ry low temperatures can cause slow display response, total failure of the display,

and shortening of battery life. Also avoid leaving the calculator in direct sunlight, near a window, near a heater or anywhere else it might be exposed to very high temperatures. Heat can cause discoloration or deformation of the calculator’s case, and damage to internal circuitry.

• Avoid use and storage of the calculator in areas subjected to large amounts of humidity and dust.

Ta ke care never to leave the calculator where it might be splashed by water or exposed to

large amounts of humidity or dust. Such conditions can damage internal circuitry.

• Never drop the calculator or otherwise subject it to strong impact.

• Never twist or bend the calculator.

Avoid carrying the calculator in the pocket of your trousers or other tight-ﬁ tting clothing

where it might be subjected to twisting or bending.

• Never try to take the calculator apart.

• Never press the keys of the calculator with a ballpoint pen or other pointed object.

• Use a soft, dry cloth to clean the exterior of the calculator.

If the calculator becomes very dir ty, wipe it off with a cloth moistened in a weak solution

of water and a mild neutral household detergent. Wring out all excess liquid before wiping the calculator. Never use thinner, benzene or other volatile agents to clean the calculator. Doing so can remove printed markings and can damage the case.

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Contents

Remove the insulation sheet! ............................................................................................. 1

Resetting the Calculator to Initial Defaults.......................................................................... 1

About this Manual ............................................................................................................... 2

Symbols Used in Examples ................................................................................................ 2

Safety Precautions ...................................................................................3

Operating Precautions .............................................................................4

Before starting a calculation... ...............................................................9

Tu r ning On the Calculator ................................................................................................... 9

Key Markings ...................................................................................................................... 9

Reading the Display ...........................................................................................................9

Calculation Modes and Setup ...............................................................10

Selecting a Calculation Mode ........................................................................................... 10

Calculator Setup ...............................................................................................................11

Clearing the Calculation Mode and Setup Settings (Reset Setup) ................................... 13

Using the Function Menu ....................................................................... 14

Inputting Calculation Expressions and Values ....................................14

Inputting a Calculation Expression (Natural Input) ........................................................... 14

Using Natural Display ....................................................................................................... 16

Editing a Calculation ......................................................................................................... 19

Finding the Location of an Error ....................................................................................... 21

Displaying Decimal Results while Natural Display is Selected

as the Display Format ............................................................................21

Example Calculations ....................................................................................................... 22

Using thef Key (S-D Transformation) ............................................... 22

Examples of S-D Transformation ...................................................................................... 22

Basic Calculations .................................................................................. 23

Arithmetic Calculations ..................................................................................................... 23

Fractions ........................................................................................................................... 24

Percent Calculations ......................................................................................................... 26

Degree, Minute, Second (Sexagesimal) Calculations ...................................................... 27

Calculation History and Replay ............................................................. 28

Accessing Calculation History .......................................................................................... 29

Using Replay .................................................................................................................... 29

Using Multi-statements in Calculations ...............................................30

Calculator Memory Operations .............................................................31

Using Answer Memory (Ans) ............................................................................................ 32

Using Independent Memory ............................................................................................. 33

Using Variables ................................................................................................................ 34

Clearing All Memory Contents ......................................................................................... 35

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Reserving Variable Memory ...................................................................35

User Memory Area ........................................................................................................... 35

Using Extra Variables ....................................................................................................... 36

Using

and Scientiﬁ c Constants ..........................................................37

Pi ( π ) ................................................................................................................................. 37

Scientiﬁ c Constants ..........................................................................................................38

Scientiﬁ c Function Calculations ...........................................................40

Tr igonometric and Inverse Trigonometric Functions ......................................................... 40

Angle Unit Conversion ...................................................................................................... 41

Hyperbolic and Inverse Hyperbolic Functions .................................................................. 41

Exponential and Logarithmic Functions ........................................................................... 41

Power Functions and Power Root Functions .................................................................... 42

Integration Calculation ...................................................................................................... 43

Derivative.......................................................................................................................... 45

Second Derivative ............................................................................................................ 46

Calculation .................................................................................................................... 46

Coordinate Conversion (Rectangular ↔ Polar) ................................................................ 47

Random Number Functions ............................................................................................. 49

Other Functions ................................................................................................................50

Using Engineering Notation ..................................................................53

Using 10 3 Engineering Notation (ENG) ............................................................................ 53

ENG Conversion Examples .............................................................................................. 54

Using Engineering Symbols ............................................................................................. 54

Complex Number Calculations (COMP) ...............................................55

Inputting Complex Numbers ............................................................................................. 55

Complex Number Display Setting ..................................................................................... 56

Complex Number Calculation Result Display Examples .................................................. 56

Conjugate Complex Number (Conjg) ............................................................................... 57

Absolute Value and Argument (Abs, Arg) ......................................................................... 57

Extracting the Real Part (ReP) and Imaginary Part (ImP) of a Complex Number ............ 58

Overriding the Default Complex Number Display Format ................................................. 58

Matrix Calculations (COMP) ..................................................................59

Matrix Calculation Overview ............................................................................................. 59

About the Mat Ans Screen ............................................................................................... 59

Inputting and Editing Matrix Data ..................................................................................... 59

Performing Matrix Calculations ......................................................................................... 62

Sequence Calculations (RECUR) ..........................................................65

Sequence Calculation Overview ...................................................................................... 65

Creating a Sequence Table .............................................................................................. 68

Sequence Calculation Precautions ..................................................................................69

Equation Calculations (EQN) ................................................................. 69

Equation Calculation Overview ........................................................................................69

Selecting an Equation Type .............................................................................................. 71

Inputting Values for Coefﬁ cients ....................................................................................... 71

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Viewing Equation Solutions .............................................................................................. 72

Statistical Calculations (SD/REG) .........................................................72

Statistical Sample Data .................................................................................................... 72

Performing Single-variable Statistical Calculations .......................................................... 75

Performing Paired-variable Statistical Calculations .......................................................... 77

Statistical Calculation Examples ...................................................................................... 84

Base-n Calculations (BASE-N) ..............................................................86

Performing Base- n Calculations ....................................................................................... 86

Converting a Displayed Result to another Number Base ................................................. 87

Specifying a Number Base for a Particular Value ............................................................. 88

Performing Calculations Using Logical Operations and Negative Binary Values ............. 89

CALC........................................................................................................90

Using CALC ...................................................................................................................... 90

SOLVE ......................................................................................................92

Expressions Supported by SOLVE ................................................................................... 92

Using SOLVE .................................................................................................................... 92

Creating a Number Table from a Function (TABLE) ............................ 94

TABLE Mode Overview..................................................................................................... 94

Creating a Number Table .................................................................................................. 96

Number Table Creation Precautions ................................................................................. 97

Built-in Formulas ....................................................................................97

Using Built-in Formulas .................................................................................................... 97

Built-in Formula Names .................................................................................................... 99

User Formulas ................................................................................................................ 102

Program Mode (PROG).........................................................................104

Program Mode Overview ................................................................................................ 105

Creating a Program ........................................................................................................ 105

Running a Program ........................................................................................................ 109

File Screen Operations ................................................................................................... 111

Deleting a Program......................................................................................................... 112

Command Reference ............................................................................ 113

Program Commands ...................................................................................................... 113

Statistical Calculation Commands .................................................................................. 121

Other PROG Mode Commands...................................................................................... 122

Data Communication (LINK) ................................................................124

Connecting Two fx-5800P Calculators to Each Other .................................................... 124

Tr ansferring Data Between fx-5800P Calculators ........................................................... 124

Memory Manager (MEMORY)...............................................................126

Deletable Data Types and Supported Delete Operations ............................................... 127

Using Memory Manager ................................................................................................. 127

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Appendix ...............................................................................................128

Calculation Priority Sequence ........................................................................................ 128

Stack Limitations ............................................................................................................ 130

Calculation Ranges, Number of Digits, and Precision .................................................... 130

Error Messages .............................................................................................................. 132

Before assuming malfunction of the calculator... ........................................................... 135

Lower Battery Indicator ................................................................................................. 135

Power Requirements ............................................................................ 136

Speciﬁ cations ....................................................................................... 137

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Before starting a calculation...

Turning On the Calculator

Presso. This displays the same screen that was on the display when you last turned off the calculator.

Adjusting Display Contrast

If the ﬁ gures on the display become hard to read, try adjusting display contrast.

1. Press

• This displays the contrast adjustment screen.

2. Use d ande to adjust display contrast.

3. After the setting is the way you want, press J.

Note

You can also use d ande to adjust contrast while the calculation mode menu that appears when you press the N key is on the display.

Tur ning Off the Calculator

Press

Key Markings

ln Press the key.

[ Red PressS and then press the key.

BIN Green In the BASE-N Mode, press the key.

(SYSTEM)1(Contrast).

(OFF).

BIN [%BIN [

Function Key Marking Color To perform the function:

Orange Press1 and then press the key.

Reading the Display

Input Expressions and Calculation Results

This calculator can display both the expressions you input and calculation results on the same screen.

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Input expression

Calculation result

Display Symbols

The symbols described below appear on the display of the calculator to indicate the current calculation mode, the calculator setup, the progress of calculations, and more.

The nearby sample screen shows the 7 symbol. The7 symbol turns on when degrees (Deg) are selected for

the default angle unit (page 12).

Calculation Modes and Setup

Selecting a Calculation Mode

Your calculator has 11 “calculation modes”.

Selecting a Calculation Mode

1. Press N.

• This displays the calculation mode menu. Use c andf to switch between menu screen 1 and screen 2.

Screen 1 Screen 2

2. Perform one of the following operations to select the calculation mode you want.

To select this calculation mode: Go to this screen: And press this key:

COMP (Computation)

BASE-N (Base

SD (Single Variable Statistics)

REG (Paired Variable Statistics)

PROG (Programming)

RECUR (Recursion)

TABLE (Tables)

EQN (Equations)

)

Screen 1

(COMP)

(BASE-N)

(SD)

(REG)

(PROG)

(RECUR)

(TABLE)

(EQN)

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To select this calculation mode: Go to this screen: And press this key:

LINK (Communication)

MEMORY (Memory Management)

SYSTEM (Contrast Adjustment, Reset)

• To exit the calculation mode menu without changing the calculation mode, press N.

Calculator Setup

The calculator setup can be used to conﬁ gure input and output settings, calculation parameters, and other settings. The setup can be conﬁ gured using setup screens, which you access by pressing

andc to navigate between them.

Selecting the Display Format (MthIO, LineIO)

You can select either natural display (MthIO) or linear display (LineIO) for expressions you input and for calculation results.

(SETUP). There are two setup screens, and you can use

Screen 2

(LINK)

(MEMORY)

(SYSTEM)

Natural Display (MthIO)

Natural display displays fraction, square root, derivative, integral, exponential, logarithmic, and other mathematical expressions just as they are written. This format is applied both for input expressions and for calculation results. When natural display is selected, the result of a calculation is displayed using fraction, square root, or π notation whenever possible.

For example, the calculation 1 ÷ 2 produces the result

, whileπ ÷ 3 results in

Linear Display (LineIO)

With linear display, expressions and functions are input and displayed using a special format deﬁ ned by your calculator. For example,

input as log(2,4). When linear display is selected all calculation results, except for fractions, are displayed

using decimal values.

To select this display fomat: Perform this key operation:

Natural Display (MthIO)

Linear Display (LineIO)

Note

For information about the input procedures when using the natural display and linear display, see “Inputting Calculation Expressions and Values” on page 14 of this manual and the sections of this manual that explanation of each type of calculation.

would be input as 1 { 2, and log

(MthIO)

(LineIO)

4 would be

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Specifying the Angle Unit

To select this angle unit: Perform this key operation:

Degrees

Radians

Grads

Specifying the Display Digits

3 4 5

(Deg)

(Rad)

(Gra)

(90˚ =

radians = 100 grads)

To specify this display digit setting: Perform this key operation:

Number of Decimal Places

Signiﬁ cant Digits

Exponential Display Range

(Fix)0(0) to9(9)

(Sci)1(1) to9(9),0(10)

(Norm) 1(Norm1) or

(Norm2)

The following explains how calculation results are displayed in accordance with the setting you specify.

• From zero to nine decimal places are displayed in accordance with the number of decimal places (Fix) you specify. Calculation results are rounded off to the speciﬁ ed number of digits.

Example: 100 ÷ 7 = 14.286 (Fix = 3)

14.29 (Fix = 2)

• After you specify the number of signiﬁ cant digits with Sci, calculation results are displayed using the speciﬁ ed number of signiﬁ cant digits and 10 to the applicable power. Calculation results are rounded off to the speciﬁ ed number of digits.

Example: 1 ÷ 7 = 1.4286 × 10

1.429 × 10

–1

(Sci = 5)

–1

(Sci = 4)

• Selecting Norm1 or Norm2 causes the display to switch to exponential notation whenever the result is within the ranges deﬁ ned below.

Norm1: 10

Norm2: 10 –9 >

Example: 100 ÷ 7 = 14.28571429 (Norm1 or Norm2)

–2

 , x



, x

1 ÷ 200 = 5. × 10

–3

(Norm1)

0.005 (Norm2)

Specifying the Fraction Display Format

To specify this fraction format for display of calculation results:

Mixed Fractions

Improper Fractions

Perform this key operation:

(ab/c)

(d/c)

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Specifying the Engineering Symbol Setting

This setting lets you turn engineering symbols on and off. For more information, see “Using Engineering Symbols” on page 54.

To do this: Perform this key operation:

Tu rn engineering symbols on

Tu rn engineering symbols off

While engineering symbols are turned on (EngOn), engineering symbols are used when a calculation result is outside of the range of 1

Specifying the Complex Number Display Format

You can specify either rectangular coordinate format or polar coordinate format for complex number calculation results.

To specify this complex number format for display of calculation results:

Rectangular Coordinates

Polar Coordinates

ENG conversion (page 53) is not possible while polar coordinate format is selected.

Specifying the Statistical Frequency Setting

Use the key operations below to turn statistical frequency on or off during SD Mode and REG Mode calculations (page 72).

To select this frequency setting: Perform this key operation:

Frequency On

Frequency Off

Changing the BASE-N Mode Negative Value Setting

You can use the key operations below to enable or disable use of negative values in the BASE-N Mode.

To specify this setting: Perform this key operation:

Negative values enabled

Negative values disabled

< 1000.



Perform this key operation:

(ENG)1(EngOn)

(ENG)2(EngOff)

(COMPLX)1(

(COMPLX)2(

(STAT) 1(FreqOn)

(STAT) 2(FreqOff)

(BASE-N)1(Signed)

(BASE-N)2(Unsigned)

a+b

∠

)

Clearing the Calculation Mode and Setup Settings

(Reset Setup)

Perform the following key operation to reset the calculation mode and setup settings.

If you do not want to reset the calculator’s settings, press J(No) in place ofE(Yes) in the above operation.

(SYSTEM)2(Reset Setup) E(Yes)

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Calculation Mode ..................................... COMP

Setup Settings

Display Format ....................................MthIO

Angle Unit ............................................ Deg

Exponential Display ............................. Norm1

Fraction Format ..................................d/c

Complex Number Format ....................

Engineering Symbol ............................EngOff

Statistical Frequency ........................... FreqOff

BASE-N Negatives .............................. Signed

a+b

Using the Function Menu

The function menu provides you with access to various mathematical functions, commands, constants, symbols, and other special operations.

Displaying the Function Menu

Pressz. The function menu shown below will appear if you press z while in the COMP Mode for example.

Exiting the Function Menu

PressJ.

Inputting Calculation Expressions and Values

Inputting a Calculation Expression (Natural Input)

The natural input system of your calculator lets you input a calculation expression just as it is written and execute it by pressing E. The calculator determines the proper priority sequence for addition, subtraction, multiplication, division, fractions and parentheses automatically.

Example: 2 (5 + 4) – 2 × (–3) =

2(5+4)-

2*-3

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Inputting Scientiﬁ c Functions with Parentheses (sin, cos, ',

etc.)

Your calculator supports input of the scientiﬁ c functions with parentheses shown below. Note that after you input the argument, you need to press ) to close the parentheses.

sin(, cos(, tan(, sin e^(, 10^(,'(, ImP(, Not(, Neg(, Det(, Trn(, Rnd(, Int(, Frac(, Intg(, RanInt#(

Example: sin 30 =

Note

Some functions require a different input sequence when using natural input. For more information, see “Inputting Calculation Expressions Using Natural Display” on page 17.

Omitting the Multiplication Sign

You can omit the multiplication sign in the following cases.

• Immediately before an open parenthesis: 2 × (5 + 4)

• Immediately before a scientiﬁ c function with parentheses: 2 × sin(30), 2 ×'(3)

• Before a preﬁ x symbol (excluding the minus sign): 2 × h123

• Before a variable name, constant, or random number: 20 × A, 2 ×π , 2 ×

Final Closed Parenthesis

You can omit one or more closed parentheses that come at the end of a calculation, immediately before the w key is pressed.

Example: (2 + 3) (4 − 1) = 15

Calculation Expression Wrapping (Linear Display)

When using linear display, calculation expressions that are longer than 16 characters (numbers, letters, and operators) are wrapped automatically to the next line.

Example: 123456789 + 123456789 = 246913578

–1

(, cos –1(, tan –1(, sinh(, cosh(, tanh(, sinh –1(, cosh –1(, tanh –1(, log(, ln(,

(, Abs(, Pol(, Rec(, ∫ (,d/dx(,

(,Σ (, P(, Q(, R(, Arg(, Conjg(, ReP(,

30)

(2+3) (4-1

123456789+ 123456789

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Number of Input Characters (Bytes)

As you input a mathematical expression, it is stored in memory called an “input area,” which has a capacity of 127 bytes. This means you can input up to 127 bytes for a single mathematical expression. When linear display is selected as the display format, each function normally uses one or two bytes of memory. With the natural display format, each function use four or more bytes of memory. For more information, see “Inputting Calculation Expressions Using Natural Display” on page 17. Normally, the cursor that indicates the current input location on the display is either a ﬂ ashing vertical bar ( is 10 bytes or less, the cursor changes to a ﬂ ashing box ( If this happens, stop input of the current expression at some suitable location and calculate its result.

Using Natural Display

While natural display is selected as the display format (page 11), you can input fractions and some scientiﬁ c functions just as they are written.

Natural Display Basics

The table below lists the types of scientiﬁ c functions that you can input using natural display format.

• The *1 column shows the number of bytes of memory used up by each scientiﬁ c function. See “Number of Input Characters (Bytes)” (page 16) for more information.

• For information about the *2 column, see “Using Values and Expressions as Arguments” (page 18).

) or horizontal bar ( ). When the remaining capacity of the input area

Scientiﬁ c Functions that Support Natural Display

Function Key Operation *1 *2

Improper Fraction

Mixed Fraction

log(a,b)

10^

e ^x

Square Root ( ')

Cube Root (

Square

Reciprocal

Power

Power Root

Absolute Value (Abs)

Integral

)

)14No

'((

– {MATH}

(

)4Yes

(

(#)9Yes

(

–1

)5No

(

)

(

– {MATH}

– {MATH} 1(∫ dX) 8 Yes

(logab) 7 Yes

)4Yes

)9Yes

(Abs) 4 Yes

9Yes

4Yes

4No

4Yes

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Function Key Operation *1 *2

Derivative

Second Derivative

Calculation

– {MATH} 2(d/dX) 7 Yes

– {MATH} 3(d

– {MATH} 4(Σ () 11 Yes

/dX2)7Yes

Note

If you include values or expressions in parentheses ( ( and)) while using natural display, the height of the parentheses will adjust automatically depending on whether they enclose one line or two lines. Regardless of their height, opening and closing parentheses take up one byte of memory each.

Inputting Calculation Expressions Using Natural Display

1. To input a speciﬁ c function, perform the operation in the “Key Operation” column of the “Scientiﬁ c Functions that Support Natural Display” table.

2. At the input ﬁ elds indicated by  , input the required values and expressions.

• Use the cursor keys to move between the input ﬁ elds of the expression.

Example: To input

Specify fraction input:

Important!

• Certain types of expressions can cause the height of a calculation formula to be greater than one display line. The maximum allowable height of a calculation formula is two display screens (31 dots × 2). Further input will become impossible if the height of the calculation you are inputting exceeds the allowable limit.

• Nesting of functions and parentheses is allowed. Further input will become impossible if you nest too many functions and/or parentheses. If this happens, divide the calculation into multiple parts and calculate each part separately.

1 + 2 2 × 3

Input the numerator: Move the cursor to the denominator: Input the denominator: Execute the calculation:

1+2

2*3

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Scrolling the Screen Left and Right

The screen will show up to 14 characters when inputting with natural display. When you input more than 14 characters, the screen will scroll automatically. If this happens, the symbol will turn on to let you know that the expression runs off the left side of the display.

Displayed expression

• While the ] symbol is turned on, you can use the d key to move the cursor to the left and scroll the screen.

• Scrolling to the left causes part of the expression to run off the right side of the display, which is indicated by the ' symbol on the right. While the ' symbol is on the screen, you can use thee key to move the cursor to the right and scroll the screen.

Using Values and Expressions as Arguments

When inputting with natural display, in certain cases you can use a value or an expression that is enclosed in parentheses that you have already input as the argument of a scientiﬁ c function (such as'), the numerator of a fraction, etc. For the sake of explanation here, a natural display function that supports the use of previously input values or parenthetical expressions is called an “insertable natural display function”.

Example: To insert the natural display function ' into the parenthetical expression in the

the parenthetical expression.)

following calculation: 1 + (2 + 3) + 4

(Move the cursor immediately to the left of

Input expression 1111 + 2222 + 3333 + 444

Cursor

(INS)

]

Note

• Not all natural display functions are insertable. Only the scientiﬁ c functions for which “Yes” appears in the column of the table under “Scientiﬁ c Functions that Support Natural Display” (page 16) are insertable.

• The cursor can be immediately to the left of a parenthetical expression, a numeric value, or a fraction. Inserting an insertable function will make the parenthetical expression, value, or fraction the argument of the inserted function.

• If the cursor is located immediately to the left of a scientiﬁ c function, the entire function becomes the argument of the inserted function.

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Editing a Calculation

Insert Mode and Overwrite Mode

The calculator has two input modes. The insert mode inserts your input at the cursor location, shifting anything to the right of the cursor to make room. The overwrite mode replaces the key operation at the cursor location with your input. Only the insert mode is available when natural display is selected as the display format. You cannot change to the overwrite mode. When linear display is selected as the display format, you can choose either the insert mode or overwrite mode for input.

Original Expression Pressing

Insert Mode

Overwrite Mode

A vertical cursor ( |) indicates the insert mode, while a horizontal cursor ( ) indicates the overwrite mode.

Cursor

Selecting an Input Mode

The initial default input mode setting is insert mode. If you have linear display selected as the display format and want to change to the overwrite mode, press:

Editing a Key Operation You Just Input

When the cursor is located at the end of the input, pressY to delete the last key operation you performed.

Example: To correct 369 × 13 so it becomes 369 × 12

369*13

(INS).

Deleting a Key Operation

With the insert mode, use d ande to move the cursor to the right of the key operation you want to delete and then press Y. With the overwrite mode, move the cursor to the key operation you want to delete and then press Y. Each press of Y deletes one key operation.

Example: To correct 369 × × 12 so it becomes 369 × 12

Insert Mode

369**12

E-19

Overwrite Mode

Editing a Key Operation within an Expression

With the insert mode, use d ande to move the cursor to the right of the key operation you want to edit, press Y to delete it, and then perform the correct key operation. With the overwrite mode, move the cursor to the key operation you want to correct and then perform the correct key operation.

Example: To correct cos(60) so it becomes sin(60)

Insert Mode

Overwrite Mode

Inserting Key Operations into an Expression

Be sure to select the insert mode whenever you want to insert key operations into an expression. Use d ande to move the cursor to the location where you want to insert the key operations and then perform them.

369**12

ddd

60)

ddd

60)

dddd

E-20

Finding the Location of an Error

If your calculation expression is incorrect, an error message will appear on the display when you press E to execute it. Pressing the J,d, ore key after an error message appears will cause the cursor to jump to the location in your calculation that caused the error so you can correct it.

Example: When you input 14 ÷ 0 × 2 = instead of 14 ÷ 5 × 2 =

(The following examples use the insert mode.)

14/0*2

• Instead of pressing J,e ord while an error message is displayed to ﬁ nd the location of the error, you could also press o to clear the calculation.

(ore,d)

Location of Error

Displaying Decimal Results while Natural Display is Selected as the Display Format

PressingE to execute a calculation while natural display is selected will display the result in natural format. Pressing decimal format.

To display the result in this format: Perform this key operation:

Natural Format

Decimal Format

Note

When linear display is selected as the display format, execution of a calculation is always displayed in linear (decimal) format, regardless of whether you press E or

will execute the calculation and display the result in

E-21

Example Calculations

Example:'2 + '8 = 3 '2

Produce the result in decimal format:

2e+!8

Using the

Key

(S-D Transformation)

You can use the f key to transform a value between its decimal (D) form and its standard (S) form (fraction, ',π ).

Important!

• Depending on the type of calculation result that is on the display when you press the key, the conversion process may take some time to perform.

• With certain calculation results, pressing the f key will not convert the displayed value.

Examples of S-D Transformation

Example 1: While linear display is selected as the display format, to perform the calculation

111 ÷ 33, and then convert the result to fraction format

111/33

E-22

Note

• Each press of the f key toggles the displayed result between the two forms.

• The format of the fraction depends on which fraction display format (improper or mixed) is currently selected (page 12).

Example 2: While natural display is selected as the display format, to perform the

calculation 111 ÷ 33, and then convert the result to decimal format

111/33

Example 3: While natural display is selected as the display format, to perform the

calculation shown below, and then convert the result to decimal format

(

)

*'2c5

Basic Calculations

Unless otherwise noted, the calculations in this section can be performed in any of the calculator’s calculation mode, except for the BASE-N Mode.

Arithmetic Calculations

Arithmetic calculations can be used to perform addition ( +), subtraction ( -), multiplication ( *), and division ( /).

E-23

Example 1: 2.5 + 1 − 2 = 1.5

2.5+1-2

Example 2: 7 × 8 − 4 × 5 = 36

7*8-4*5

• The calculator determines the proper priority sequence for addition, subtraction, multiplication, and division automatically. See “Calculation Priority Sequence” on page 128 for more information.

Fractions

Keep in mind when inputting fractions on your calculator that the input procedure you need to use depends on whether natural display or linear display is selected as the display format (page 11), as shown below.

Natural Display:

Key Operation Display

Improper Fraction

Mixed Fraction

7c3

'((

)

2e1c3

7 3

Linear Display:

Key Operation Display

Improper Fraction

Mixed Fraction

As you can see above, natural display lets you input fractions as they appear in your textbook, while linear display requires input of a special symbol ( {).

7'3

2'1'3

Integer Numerator Denominator

Note

• Under initial default settings, fractions are displayed as improper fractions.

• Fraction calculation results are always reduced automatically before being displayed. Executing 2 { 4 =, for example, will display the result 1 { 2.

7{ 3

Numerator Denominator

2{ 1{ 3

E-24

Fraction Calculation Examples

Example 1:

2c3

1c2

Example 2: 3

2'3+1'2

+ 1

= 4

(Fraction Display Format: ab/c)

1 2

'((

)

3'1'4+ 1'2'3

3e1c4e+

)

1e2c3

E-25

Note

• If the total number of elements (integer digits + numerator digits + denominator digits + separator symbols) that make up a mixed fraction expression is greater than 10, the calculation result will be displayed in decimal form.

• If an input calculation includes a mixture of fraction and decimal values, the result will be displayed in decimal format.

• You can input integers only for the elements of a fraction.

Switching between Improper Fraction and Mixed Fraction

Format

To convert an improper fraction to a mixed fraction (or a mixed fraction to an improper fraction), press

Switching between Fraction and Decimal Format

Use the procedure below to toggle a displayed calculation result between fraction and decimal format.

Example: 1.5 =

The current fraction display format setting determines if an improper or mixed fraction is displayed.

Note

The calculator cannot switch from decimal to fraction format if the total number of elements (integer digits + numerator digits + denominator digits + separator symbols) that make up a mixed fraction is greater than 10.

bcd

(

= 1.5

a— ⇔ —

1.5

Percent Calculations

Inputting a value and with a percent (%) sign makes the value a percent. The percent (%) sign uses the value immediately before it as the argument, which is simply divided by 100 to get the percentage value.

Percent Calculation Examples

All of the following examples are performed using linear display ( b).

E-26

Example 1: 2% = 0.02 (

1 00

)

21,

(%)

Example 2: 150 × 20% = 30 (150 ×

Example 3: What percent of 880 is 660?

Example 4: Increase 2500 by 15%.

Example 5: Reduce 3500 by 25%.

Degree, Minute, Second (Sexagesimal) Calculations

You can perform calculations using sexagesimal values, and you can convert between sexagesimal and decimal.

Inputting Sexagesimal Values

The following is basic syntax for inputting a sexagesimal value.

{Degrees} ${Minutes} ${Seconds}

Example: To input 2°30´30˝

2 0

)

1 0 0

(%)

150*201,

660/880

2500+2500*

151,

3500-3500*

251,

2e30e30

• Note that you must always input something for the degrees and minutes, even if they are zero.

Example: To input 0°00´30˝, press

0$0$30

E-27

Sexagesimal Calculation Examples

• The following types of sexagesimal calculations will produce sexagesimal results.

- Addition or subtraction of two sexagesimal values

- Multiplication or division of a sexagesimal value and a decimal value

Example 1: 2°20´30˝ + 39´30˝ = 3°00´00˝

Example 2: 2°20´00˝ × 3.5 = 8°10´00˝

Performing a Decimal Calculation to Obtain a Sexagesimal

2e20e30e+ 0e39e30

2e20e*

3.5

Result

You can use the “ 'DMS” command to execute a decimal calculation and obtain a sexagesimal result. The “ 'DMS” command can be used in the COMP Mode only.

Example: Perform the calculation 100 ÷ 3 so it produces a sexagesimal result

100/3

– {ANGLE} 4('DMS)

Converting between Sexagesimal and Decimal

Pressing$ while a calculation result is displayed will toggle the value between sexagesimal and decimal.

Example: To convert 2.255 to sexagesimal

2.255

E E

Calculation History and Replay

You can use calculation history in the COMP and BASE-N Modes.

E-28

Accessing Calculation History

The` symbol in the upper right corner of the display indicates that there is data stored in calculation history. To view the data in calculation history, press f. Each press of f will scroll upwards (back) one calculation, displaying both the calculation expression and its result.

Example:

While scrolling through calculation history records, the $ symbol will appear on the display, which indicates that there are records below (newer than) the current one. When this symbol is turned on, press c to scroll downwards (forward) through calculation history records.

1+1E2+2

3+3

E E

Important!

• Calculation history records are all cleared when you change to a different calculation mode, or when you change the display format.

• Calculation history capacity is limited. Whenever you perform a new calculation while calculation history is full, the oldest record in calculation history is deleted automatically to make room for the new one.

Note

A calculation that contains any of the following functions is not stored in calculation history when it is executed. CALC, SOLVE, Built-in Formulas, User Formulas

Using Replay

While a calculation history record is on the display, press d ore to display the cursor and enter the editing mode. Pressing e displays the cursor at the beginning of the calculation expression, while d displays it at the end. After you make the changes you want, press E to execute the calculation.

Example: 4 × 3 + 2.5 = 14.5 4 × 3 – 7.1 = 4.9

4*3+2.5

E-29

YYYY

-7.1

Using Multi-statements in Calculations

A multi-statement is a statement that is made up of multiple calculation expressions separated by special separator codes (: and ^). The following examples show how the two separator codes differ from each other.

{expression 1} : {expression 2} : .... : {expression

PressingE executes each expression in sequence, starting with {expression 1} and ending with the ﬁ nal expression in the series. After that, the result of the ﬁ nal expression appears on the display.

Example: To perform the calculation 123 + 456, and then subtract its result from 1000

123+456

1000-

{expression 1} ^ {expression 2} ^ .... ^ {expression

In this case, pressing E starts execution starting with {expression 1}. When execution reaches a^ separator, execution pauses and the calculation result up to that point appears on the display. Pressing E again will resume execution from the expression below the separator.

Example: To display the result of the calculation 123 + 456, and then subtract it from 1000

123+456

1000-

E-30

}

x(^

(Ans)

}

(Ans)

(:)

)

Note

• The Q symbol turns on in the upper right corner of the display when execution of a multi-statement calculation has been paused by a ^ separator.

• When performing a multi-statement calculation, Ans (Answer Memory) (page 32) is updated each time any of the statements that makes up a multi-statement produces a result.

• You can mix “ ^” and “:” separators within the same calculation.

Calculator Memory Operations

Your calculator includes the types of memory described below, which you can use for storage and recall of values.

Memory Name Description

Answer Memory

Independent Memory

Var iables

Extra Variables

Formula Variables

The types of memory described above are not cleared when you press the o key, change to another mode, or turn off the calculator.

Answer Memory contains the result of the last calculation you performed.

Independent memory comes in handy when adding or subtracting multiple calculation results.

The letters A through Z can be assigned different values individually and used in calculations. Note that variable M is also used for storing independent memory values.

You can create extra variables when you need storage for more values than provided by the 26 letters from A through Z. You can reserve up to 2372 extra variables, which are named Z[1], Z[2], etc.

The following literal variables are used by the calculator’s built-in formulas or user formulas.

• Lower-cast alphabetic characters: a through z

• Greek characters: α throughω ,Α through

• Subscripted alphabetic and Greek characters: A For details about built-in formulas and formula variables, see “Built-in Formulas” (page 97).

Ω

, a 0,

, etc.

∆

E-31

Using Answer Memory (Ans)

The result of any new calculation you perform on the calculator is stored automatically in Answer Memory (Ans).

Automatic Insertion of Ans in Consecutive Calculations

If you start a new calculation while the result of a previous calculation is still on the display, the calculator will insert Ans into the applicable location of the new calculation automatically.

Example 1: To divide the result of 3 × 4 by 30

3*4

(Next)

/30

Pressing/ inputs Ans automatically.

Example 2: To determine the square root of the result of 3 2 + 4

3x+4

Note

• As in the above examples, the calculator automatically inserts Ans as the argument of any calculation operator or scientiﬁ c function you input while a calculation result is on the display.

• In the case of a function with a parenthetical argument (page 15), Ans automatically becomes the argument only in the case that you input the function alone and then pressE. Note, however, that with natural display Ans may not become the argument automatically when using a function with a parenthetical argument.

• Basically, Ans is inserted automatically only when the result of the previous calculation is still on the display, immediately after you executed the calculation that produced it. If you want to insert Ans after clearing the display by pressing o, press

(Ans).

E-32

Inserting Ans into a Calculation Manually

Yo u can insert Ans into a calculation at the current cursor location by pressing

Example 1: To use the result of 123 + 456 in another calculation as shown below

123 + 456 = 579 789 – 579 = 210

123+456

(Ans).

789-

Example 2: To determine the square root of 3

(Ans)

+ 4 2 and then add 5 to the result

3x+4

(Ans)

Using Independent Memory

Independent memory (M) is used mainly for calculating cumulative totals.

Adding to Independent Memory

While a value you input or the result of a calculation is on the display, press l to add it to independent memory (M).

Example: To add the result of 105 ÷ 3 to independent memory (M)

)+5

105/3l

Subtracting from Independent Memory

While a value you input or the result of a calculation is on the display, press subtract it from independent memory (M).

(M–) to

E-33

Example: To subtract the result of 3 × 2 from independent memory (M)

3*21l

(M–)

Note

Pressingl or subtract it from independent memory.

(M–) while a calculation result is on the display will add it to or

Important!

The value that appears on the display when you press l or calculation in place ofE is the result of the calculation (which is added to or subtracted from independent memory). It is not the current contents of independent memory.

Viewing Independent Memory Contents

Press

Press following operation.

Example: 23 + 9 = 32

53 – 6 = 47

−) 45 × 2 = 90

99 ÷ 3 = 33

(Total) 22

Your calculator supports the use of 26 variables, named A through Z.

Use the procedure shown below to assign a value or a calculation expression to a variable.

Example: To assign 3 + 5 to variable A

To view the value assigned to a variable, press ~ and then specify the variable name. You could also pressS, specify the variable name, and then press E.

Example: To view the value assigned to variable A

(M).

Clearing Independent Memory Contents (to 0)

(STO)9(M)

Calculation Example Using Independent Memory

(STO)9(M) to clear independent memory contents before performing the

(Recalls value of M.)

Using Variables

Assigning a Value or Calculation Result to a Variable

3+5

Viewing the Value Assigned to a Variable

(A) or

(STO) 0(A)

(A)

(M–) at the end of a

23+9 53-6

45*2

99/3

(M–)

(M)

E-34

Using a Variable in a Calculation

You can use variables in calculations the same way you use values.

Example: To calculate 5 + A

Clearing the Value Assigned to a Variable (to 0)

Example: To clear variable A

Clearing All Variables (to 0)

Use the MEMORY Mode screen to clear the contents of all the variables. See “Memory Manager (MEMORY)” on page 126 for more information.

Clearing All Memory Contents

Perform the operation below when you want to clear all variables (including variable M) and Answer Memory (Ans) to zero.

– {CLR} – {Memory}

(STO) 0(A)

(A)

Reserving Variable Memory

If you ﬁ nd that the calculator’s default variables (A through Z) are not enough for your purposes, you can reserve variable memory and create “extra variables” for storage of value. Extra variables work like array variables of an array named “Z” when assigning or recalling their values. An extra variable name consists of the letter “Z” followed by a value in brackets, like Z[5].

User Memory Area

Your calculator has a 28500-byte user memory area that you can use to reserve variable memory and add extra variables.

Important!

• You can perform the procedure to reserve variable memory in the COMP Mode or in a COMP Mode program. All of the sample operations in this section are performed in the COMP Mode (

• The 28500-byte user memory is used for storage of extra variables and programs. This means that increasing the number of extra variables reduces the amount of memory available for storing programs. So also, storing programs in memory reduces the amount of memory available for storing extra variables.

E-35

Adding Extra Variables

Example: To increase the number of variables by 10

• When “Done” appears on the display, it means that the number of extra variables you speciﬁ ed has been added. At this point, zero is assigned to all of the extra variables.

(To check the value of Z[10])

– {PROG} – { /}

([)

(Dim Z)

(])

(Z)

Note

Reserving variable memory uses up a basic 26 bytes, plus 12 bytes for each of the extra variables that you add. Note that storing a complex number of an extra variable uses up 22 bytes. Adding 10 extra variables as shown above, for example, uses up 26 + (12 × 10) = 146 bytes of the user memory area. Since user memory has a total capacity of 28500 bytes, the limit on the number of extra variables you can add is 2372 (assuming you do not have any complex numbers assigned to the extra variables).

Using Extra Variables

After creating extra variables, you can assign values to them and insert them into calculations just as you do with the default valuables (from A through Z). Just remember that extra variable names consist of the letter “Z” followed by a value in brackets, like Z[5].

Note

• The closing bracket ( ] ) of the extra variable name can be omitted.

• In place of a value inside the brackets of an extra variable name, you can use a calculation expression or a default array name (A to Z).

• Note that the value in the brackets of an extra variable name must be in the range of 1 and the number of extra variables that have been added. Trying to use a value that exceeds the number of extra variables will cause an error.

Assigning a Value or Calculation Result to an Extra Variable

You can assign a value to an extra variable using the following command syntax: {value or expression} / Z[{extra variable value}] E.

Example: To assign 3 + 5 to variable Z[5]

3+5

(Z)

– {PROG} – { /}

([)

(])

E-36

Important!

You can write data to extra variables in the COMP Mode or in a COMP Mode program.

Recalling the Contents of an Extra Variable

Input the name (Z[ n]) of the extra variable whose contents you want to recall, and then pressE.

Example: To recall the contents of extra variable Z[5]

Using an Extra Variable in a Calculation

You can use extra variables in calculations the same way you use values.

Example: To calculate 5 + Z[5]

Clearing Extra Variable Contents (to 0)

Example: To clear extra variable Z[5]

– {PROG} – { /}

Clearing All Extra Variables

Perform the operation below when you want delete all extra variables that are currently in calculator memory.

– {PROG} – { /}

Note

You can also use the MEMORY Mode screen to delete all the extra variables. See “Memory Manager (MEMORY)” on page 126 for more information.

(Z)

(Dim Z)

([)

(])

Using

Pi ( π )

Your calculator supports input of pi ( π ) into calculations. Pi ( π ) is supported in all modes, except for the BASE-N Mode. The following is the value that the calculator uses for π .

= 3.14159265358980 (

and Scientiﬁ c Constants

(π ))

E-37

Scientiﬁ c Constants

Yo ur calculator has 40 often-used scientiﬁ c constants built in. Like π , each scientiﬁ c constant has a unique display symbol. Scientiﬁ c constants are supported in all modes, except for the BASE-N Mode.

Inputting a Scientiﬁ c Constant

1. Press z to display the function menu.

2. On the menu, select “CONST”.

• This displays page 1 of the scientiﬁ c constant menu.

• There are ﬁ ve scientiﬁ c command menu screens, and you can use c andf to navigate between them. For more information about scientiﬁ c constants, see “List of Scientiﬁ c Constants” on page 39.

3. Use c andf to scroll through the pages and display the one that contains the scientiﬁ c constant you want.

4. Press the number key (from 1 to8) that corresponds to the scientiﬁ c constant you want to select.

• This will input the scientiﬁ c constant symbol that corresponds to the number key you

press.

• Pressing E here will display the value of the scientiﬁ c constant whose symbol is

currently on the screen.

Example Calculations Using Scientiﬁ c Constants

Example: To calculate the constant for the speed of light in a vacuum (

– {CONST}

ccc

)

(

E-38

= 1/ 0

)

– {CONST}

List of Scientiﬁ c Constants

The numbers in the “No.” column show the scientiﬁ c constant menu page number on the left and the number key you need to press to select the constant when the proper menu page is displayed.

No. Scientiﬁ c Constant No. Scientiﬁ c Constant

1-1 Proton mass 3-5 Muon magnetic moment

1-2 Neutron mass 3-6 Faraday constant

1-3 Electron mass 3-7 Elementary charge

1-4 Muon mass 3-8 Avogadro constant

1-5 Bohr radius 4-1 Boltzmann constant

1-6 Planck constant 4-2 Molar volume of ideal gas

1-7 Nuclear magneton 4-3 Molar gas constant

1-8 Bohr magneton 4-4 Speed of light in vacuum

2-1 Planck constant, rationalized 4-5 First radiation constant

2-2 Fine-structure constant 4-6 Second radiation constant

2-3 Classical electron radius 4-7 Stefan-Boltzmann constant

2-4 Compton wavelength 4-8 Electric constant

2-5 Proton gyromagnetic ratio 5-1 Magnetic constant

2-6 Proton Compton wavelength 5-2 Magnetic ﬂ ux quantum

2-7 Neutron Compton wavelength 5-3 Standard acceleration of gravity

2-8 Rydberg constant 5-4 Conductance quantum

3-1 Atomic mass constant 5-5 Characteristic impedance of vacuum

3-2 Proton magnetic moment

3-3 Electron magnetic moment 5-7 Newtonian constant of gravitation

3-4 Neutron magnetic moment 5-8 Standard atmosphere

• The values are based on CODATA Recommended Values (2000). For details, see <#01> in the separate Supplement.

cccc

5-6 Celsius temperature

)

(

)

E-39

Scientiﬁ c Function Calculations

Unless otherwise noted, the functions in this section can be used in any of the calculator’s calculation modes, except for the BASE-N Mode.

Scientiﬁ c Function Calculation Precautions

• When performing a calculation that includes a built-in scientiﬁ c function, it may take some time before the calculation result appears. Do not perform any key operation on the calculator until the calculation result appears.

• To interrupt an on-going calculation operation, press @.

Interpreting Scientiﬁ c Function Syntax

• Text that represents a function’s argument is enclosed in braces ({ }). Arguments are normally {value} or {expression}.

• When braces ({ }) are enclosed within parentheses, it means that input of everything inside the parentheses is mandatory.

Trigonometric and Inverse Trigonometric Functions

sin(, cos(, tan(, sin –1(, cos –1(, tan –1(

Syntax and Input

sin({n}) (Other functions may be used in argument.)

Example: sin 30 = 0.5, sin

Remarks

The angle unit you need to use in a calculation is the one that is currently selected as the default angle unit.

–1

0.5 = 30

(sin

–1

30)

)

0.5)

E-40

Angle Unit Conversion

You can convert a value that was input using one angle unit to another angle unit. After you input a value, select z – {ANGLE} to display the menu screen shown below.

(°): Degrees

(r): Radians

(g): Grads

Example: To convert

Hyperbolic and Inverse Hyperbolic Functions

Syntax and Input

sinh({n}) (Other functions may be used in argument.)

Example: sinh 1 = 1.175201194

Remarks

To input a hyperbolic or inverse hyperbolic function, perform the following operation to display a menu of functions: z – {MATH} cc.

Exponential and Logarithmic Functions

Syntax and Input

10^({n}) .......................... 10

}) ........................... log 10{n} (Common Logarithm)

log({

},{n}) ..................... log

}) ............................. log e{n} (Natural Logarithm)

ln({

radians to degrees

sinh(, cosh(, tanh(, sinh –1(, cosh –1(, tanh –1(

(

– {MATH}

10^(,e^(, log(, ln(

{n}

(Same as e^()

{n} (Base { m} Logarithm)

{m}

(

)

– {ANGLE} 2(r)

(sinh)

/2)

E-41

Example 1 : log 216 = 4, log16 = 1.204119983

2,16)

Base 10 (common logarithm) is assumed when no base is speciﬁ ed.

16)

Example 2 : ln 90 (= log

90) = 4.49980967

– {MATH}

(logab)

2e16

90)

Power Functions and Power Root Functions

–1

Syntax and Input

{n}

............................... { n}2 (Square)

–1

n}x

............................. { n}–1 (Reciprocal)

{

)}^({n}) ....................... { m}

{(

({

}) .......................... { n} (Square Root)

({n}) ......................... 3 { n} (Cube Root)

})

({n}) ..................

({

{n}

(Power)

{m}

{ n} (Power Root)

Example 1: ( '2 + 1) ( '2 – 1) = 1, (1 + 1)

, ^(,'(,

2+2

= 16

(

(!2)+1)

(!2)-1)

E-42

(1+1)62+2)

(!2e+1)

(!2e-1)

Example 2: (–2)

2 3

= 1.587401052

(1+1)62+2

(-2)6(2'3)

Integration Calculation

Your calculator performs integration using Gauss-Kronrod integration for approximation. The calculator uses the following function for integration.

(

∫

Syntax and Input

f(x),a,b,tol

(

∫

• All variables other than X are viewed as constants.

tol

• This parameter can be omitted. In that case, a tolerance of 1 × 10 –5 is used.

Example:∫ (ln(

)

f(x

): Function of x (Input the function used by variable X.)

: Lower limit of region of integration

: Upper limit of region of integration

: Error tolerance range (Can be input only when linear display is being used.)

), 1,e) = 1 (

tol

value not input)

(X)

)c1

– {MATH} 1(

(%)

∫

dX)

E-43

– {MATH} 1(

(X)

Remarks

• Use of ∫ ( is supported in the COMP, SD, REG, and EQN Modes only.

• The following functions cannot be input for the

(,Σ (. In addition, the Pol( and Rec( functions, and the random number functions

cannot be input for the

• The integration result will be negative when the limit of region of integration parameters are within the range

Example: ∫ (0.5X

• In the case of integration of a trigonometric function, select Rad for the angle unit.

• Integration calculations can take a long time to complete.

• Specifying a smaller value for the causes the calculation to take more time. Specify a

• You will not be able to input a

• The type of function being integrated, positive and negative values within the region of integration, and the region of integration being used can cause large error in integration values and errors.

• You can interrupt an ongoing integration calculation operation by pressing o.

Tips to for Successful Integration Calculations

• For periodic functions, and for positive and negative f(x) values due to the region of integration being used

Divide the integration into parts for each period, or between positive and negative

parts, obtain integration values for each, and then add the values.

Positive Part Negative Part (

• For widely ﬂ uctuating integration values due to a minutely shifting region of integration

Divide the integration interval into multiple parts (in a way that breaks areas of wide

ﬂ uctuation into small par ts), perform integration on each part, and then combine the results.

),1,

f(x

) parameter.

a<x<b

– 2, –2, 2) = –5.333333333

andf(x) < 0.

tol

value while using natural display.

f(x)dx =

∫∫ ∫

(%)

f(x),a,b

parameter tends to improve precision, but it also

Positive

f(x)dx + (–

Positive) ( S Negative)

dX)

∫

1))

tol

, and

parameters: ∫ (,d/dx(,

tol

value greater than 1 × 10

Negative

f(x)dx)

–14

E-44

f(x)dx =

∫∫∫

Derivative

Your calculator performs differential calculations by approximating the derivative based on centered difference approximation. Calculation is performed using the function shown below.

d /dx

Syntax and Input

d /dx(f(x),a,tol

• All variables other than X are viewed as constants.

• This parameter can be omitted. In that case, a tolerance of 1 × 10

Example: To obtain the differential coefﬁ cient at point

(Continuing from 1, above)

)

f(x

): Function of x (Input the function used by variable X.)

: Value of point (derivative point) of desired derivative coefﬁ cient

tol

: Error tolerance range (Can be input only when linear display is being used.)

tol

value not input)

(

– {MATH} 2(d/dX)

(X)).....

(

)

f(x)dx +

for the function

.....+

–10

= sin( x)

f(x)dx

∫

is used.

Remarks

• Use of d/dx( is supported in the COMP, SD, REG, and EQN Modes only.

• The following functions cannot be input for the

(. In addition, the Pol( and Rec( functions, and the random number functions cannot be

input for the

• In the case of differentiation of a trigonometric function, select Rad for the angle unit.

• Specifying a smaller value for the causes the calculation to take more time. Specify a

• You will not be able to input a

• Non-consecutive points, abrupt ﬂ uctuation, extremely large or small points, inﬂ ection points, and the inclusion of points that cannot be differentiated, or a differential point or

f(x

) parameter.

(Continuing from 1, above)

tol

value while using natural display.

(

)

parameter tends to improve precision, but it also

f(x),a

tol

, and

parameters: ∫ (,d/dx(,

tol

value greater than 1 × 10

–14

E-45

differential calculation result that approaches zero can cause poor precision or error.

• You can interrupt an ongoing differential calculation operation by pressing o.

Second Derivative

Your calculator lets you calculate the second derivative coefﬁ cient (

x =a

where equation of the Newton interpolation polynomial. Calculation is performed using the function shown below.

Example 1: To obtain the second derivative coefﬁ cient for the function

. Your calculator uses approximation based on the second order value differential

(

Syntax and Input

• All variables other than X are viewed as constants.

coefﬁ cient

• This parameter can be omitted. In that case, a tolerance of 1 × 10

tol

(f(x),a,

f(x

: Value of point (second derivative point) of desired second derivative

tol

)

): Function of x (Input the function used by variable X.)

: Error tolerance range (Can be input only when linear display is being used.)

= 3

when

– {MATH} 3(d

+4S0

(X)

+S0

/dX2)

(X)

-6e3

(X)

(f(x))|x=a) for f(x)

y =x

+ 4

–10

is used.

+x – 6

= 1 × 10

–12

Example 2: To perform the same procedure as Example 1, specifying

Since you want to specify a value for linear display.

Remarks

See the remarks for derivative on page 45.

This function determines the sum of an input f(x) for a speciﬁ ed range. Calculation is performed using the function shown below.

– {MATH} 3(d

(X)

+S0

Calculation

tol

, you will need to perform this calculation using

/dX2)

(X)

-6,3,1

(

3)+4

12)

Z-

tol

E-46

The following shows the calculation formula used for Σ calculations.

f(x),x,a,b

(

Syntax and Input

f(x),x,a,b

(

• If the variable name you specify here does not match the variable name

•

• The step for this calculation is ﬁ xed as 1.

Example:Σ ( X + 1, X, 1, 5) = 20

)

f(x

): Function of x (parameter variable speciﬁ ed below)

: Par ameter variable (Any letter from A through Z)

used within the function of constant.

: Start point of calculation range

: End point of calculation range

andb are integers in the range of –1 × 10 10<

) =f(a) +f(a+1) + .... + f(b)

, the variable in the function will be treated as a

– {MATH} 4(

(X)

e1e

a<b

< 1 × 10 10.

()

(X)

– {MATH} 4(

+1,a0

Remarks

• Use of Σ ( is supported in the COMP, SD, REG, and EQN Modes only.

• The following functions cannot be input for the

(. In addition, the Pol( and Rec( functions, and the random number functions cannot be

input for the

• You can interrupt an ongoing Σ calculation operation by pressing o.

Coordinate Conversion (Rectangular ↔ Polar)

Your calculator can convert between rectangular coordinates and polar coordinates.

f(x

) parameter.

(X)

Pol(, Rec(

()

,1,5)

f(x),a

, andb parameters: ∫ (,d/dx(,

(X)

Rectangular Coordinates (Rec) Polar Coordinates (Pol)

E-47

Syntax and Input

Rectangular-to-Polar Coordinate Conversion (Pol)

x,y

Pol(

)

: Rectangular coordinate x-value

: Rectangular coordinate y-value

Polar-to-Rectangular Coordinate Conversion (Rec)

r,Ƨ

)

Rec(

: Polar coordinate r-value

: Polar coordinate Ƨ-value

Example 1: To convert the rectangular coordinates (

2 ) to polar coordinates

'2,'

(Pol)

,!2))

(Pol)

,!2e)

Example 2: To convert the polar coordinates (2, 30˚) to rectangular coordinates

(Rec)

Remarks

• These functions can be used in the COMP Mode.

• The

-value or x-value produced by the calculation is assigned to variable I, while the

-value or y-value is assigned to variable J (page 34).

• The values obtained for coordinates is within the range –180° <

• When executing a coordinate conversion function inside of a calculation expression, the calculation is performed using the ﬁ rst coordinate that the conversion produces (

-value).

Example: Pol (

2 ) + 5 = 2 + 5 = 7

'2,'

when converting from rectangular coordinates to polar

180°.

30)

-value or

E-48

Random Number Functions

Your calculator comes with functions for generating ten-digit non-sequential random numbers, ten-digit sequential random numbers, or random integers within a speciﬁ c range. The following are the random number generation functions.

Ran#, RanInt#(

Non-sequential Random Numbers (Decimal Values)

The following generates ten-digit non-sequential fractional numbers in the range of 0 to 1.

Syntax: Ran#

Example: To generate ten-digit non-sequential random numbers

– {MATH} 6(Ran#)

The above values are provided for example only. The actual values produced

Sequential Random Numbers (Decimal Values)

In this case, ten-digit sequential random numbers are generated in the range of 0 to 1 in accordance with nine sequences numbered from 1 through 9. The sequence is speciﬁ ed by the integer argument (1 through 9) of Ran#. The random numbers generated in accordance with the argument are generated in a ﬁ xed sequence.

Syntax: Ran#{

Example: To generate sequential random numbers

Initialize the sequence:

} ( n is an integer from 1 to 9.)

– {MATH} 6(Ran#)

by your calculator for this function will be different.

E-49

– {MATH} 6(Ran#)

Random Integers

This function generates random integers within a speciﬁ c range.

Syntax: RanInt#({

Example: To generate random integers in the range of 0 to 5

}, { n}) ( m andn are integers. m <n;

– {MATH}

(RanInt)

0,5)

| ,| n|

< 1

10; n –m < 1 E10)

Other Functions

The above values are provided for example only. The actual values produced

!, Abs(,nPr,nCr, Rnd(, Int(, Frac(, Intg(

by your calculator for this function will be different.

E-50

Factorial (!)

Syntax: { n}! ({ n} must be a natural number or 0.)

Example: (5 + 3)!

(5+3)

– {MATH} 5(X!)

Absolute Value (Abs)

Syntax: Abs({n})

Example: Abs (2 – 7) = 5

– {MATH}

(Abs)

2-7

– {MATH}

Permutation ( nPr)/Combination ( nCr)

Syntax: { n}P{m}, { n}C{m}

Example: How many four-person permutations and combinations are possible for a group

of 10 people?

(Abs)

2-7)

– {MATH} 7(nPr)

Rounding Function (Rnd)

Yo u can use the rounding function (Rnd) to round the value, expression, or calculation result speciﬁ ed by the argument. Rounding is performed to the number of signiﬁ cant digits in accordance with the number of display digits setting.

– {MATH} 8(

nCr

)

E-51

Display Digit Setting: Norm1 or Norm2

The mantissa is rounded off to 10 digits.

Display Digit Setting: Fix or Sci

The value is rounded to the speciﬁ ed number of digits.

Example: 200 ÷ 7 × 14 = 400

200/7*14

(3 decimal places)

(Internal calculation uses 15 digits.)

Now perform the same calculation using the rounding (Rnd) function.

(Calculation uses rounded value.)

(Rounded result)

Integer Part Extraction (Int)

The Int( function extracts the integer part of the real number input as its argument.

(SETUP)6(Fix)

200/7

*14

200/7

*14

(Rnd)

E-52

Syntax: Int({n})

Example: To extract the integer part of –1.5

Fractional Part Extraction (Frac)

The Frac( function extracts the fractional part of the real number input as its argument.

Syntax: Frac( {

Example: To extract the fractional part of –1.5

Largest Integer (Intg)

The Intg( function determines the largest integer that does not exceed the real number input as its argument.

Syntax: Intg({

Example: To determine the largest integer that does not exceed –1.5

})

– {MATH}

(Frac)

(Int)

1.5)

– {MATH}

(Intg)

1.5)

Using Engineering Notation

Using 10 3 Engineering Notation (ENG)

Engineering notation (ENG) expresses quantities as a product of a positive number between 1 and 10 and a power of 10 that is always a multiple of three. There are two functions that you can use to convert a number to engineering notation, ENG/ and ENG,.

Function Key Operation

ENG

(ENG)

(

ENG

)

E-53

ENG Conversion Examples

Example 1: To convert 1234 to engineering notation using ENG

1234

(ENG)

Example 2: To convert 123 to engineering notation using ENG

123

Using Engineering Symbols

Your calculator supports the use of ten engineering symbols (m, ƫ, n, p, f, k, M, G, T, P) that you can use for input of value or for calculation result display. You can use engineering symbols in calculations in all calculation modes, except for the BASE-N Mode.

Displaying Calculation Results with Engineering Symbols

Use the calculator’s setup screens to select “EngOn” for engineering symbols (page 13).

(

ENG

(

ENG

)

E-54

Inputting Values Using Engineering Symbols

Example: To input 500 k

500

Using ENG (10

– {MATH}

) Conversion while Engineering Symbols

ccc

(k)

Turned on (EngOn)

Performing ENG conversion while “EngOn” is selected for engineering symbols (page 13) will move the decimal point three places to the right, and change the engineering symbol accordingly (from M to k, for example). Conversely, performing ← ENG conversion will move the decimal point three places to the left, and change the engineering symbol accordingly (from k to M, for example).

Example: To calculate 999 k (kilo) + 25 k (kilo) = 1.024 M (Mega) = 1024 (kilo)

(ENG conversion)

999

z z

– {MATH} – {MATH}

ccc ccc

6 6

(k)

(ENG)

Complex Number Calculations (COMP)

To perform the example operations in this section, ﬁ rst select COMP ( calculation mode.

Inputting Complex Numbers

Inputting Imaginary Numbers ( i)

Use thei key to input imaginary number i.

E-55

) as the

Example: To input 2 + 3

Inputting Complex Number Values Using Polar Coordinate

2+3

Format

Complex numbers can also be input using polar coordinate format (

Example: To input 5 ∠ 30

Important!

When inputting argumentƧ, enter a value that indicates an angle in accordance with the calculator’s current default angle unit setting.

Complex Number Display Setting

See “Specifying the Complex Number Display Format” (page 13).

Complex Number Calculation Result Display Examples

Rectangular Coordinate Format ( a+bi)

(SETUP)

Example 1: 2 × (

(COMPLX)1(

3 +i) = 2 '3 + 2 i = 3.464101615 + 2

2*(!3e+i)

2*(!3)+i)

a+b

(

)

∠

)

r∠ Ƨ

Example 2: '2∠ 45 = 1 +

Polar Coordinate Format (

(SETUP)

(COMPLX)2(

When using linear display format, calculation results are displayed

in two lines showing the real part and imaginary part.

(

)

∠

)

r∠ Ƨ

∠

)

E-56

Example 1: 2 × ( '3 +i) = 2 '3 + 2 i = 4∠ 30

2*(!3e+i)

Example 2: 1 +i ='2∠ 45

2*(!3)+i)

When using linear display format, calculation results are displayed

in two lines showing the absolute value and argument.

Conjugate Complex Number (Conjg)

You can perform the operation below to obtain conjugate complex number z¯ =a – complex number

Example: Obtain the conjugate complex number of 2 + 3

Absolute Value and Argument (Abs, Arg)

You can use the procedure shown below to obtain the absolute value (| z|) and argument

)) on the Gaussian plane for a complex number in the format z =a +

(Arg(

Example: To obtain the absolute value and

argument of 2 + 2

z =a +b

– {COMPLX} 3(Conjg)

2+3i)

Imaginary axis

b = 2

for the

Absolute Value:

– {COMPLX} 1(Abs)

2+2i)

E-57

Real axis

a = 2

Real axis

Argument:

– {COMPLX} 2(Arg)

Extracting the Real Part (ReP) and Imaginary Part (ImP)

2+2i)

of a Complex Number

You can use the following operations to extract the real part ( a) or imaginary part ( b) of complex number

Example: Obtain the real part and imaginary part of 2 + 3

a +b

– {COMPLX} 4(ReP)

2+30)

– {COMPLX} 5(ImP)

Overriding the Default Complex Number Display Format

You can use the procedures described below to override the default complex number display format and specify a particular display format for the calculation you are currently inputting.

Specifying Rectangular Coordinate Format for a Calculation

Inputz – {COMPLX} 7(

Example: 2

Specifying Polar Coordinate Format for a Calculation

Inputz – {COMPLX} 6(

Example: 2 + 2

2∠ 45 = 2 + 2 i (Angle Unit: Deg)

= 2 '2∠ 45

2+2

a+b

2!2

∠

2+30)

) at the end of the calculation.

(

)

∠

e10

– {COMPLX} 7(

) at the end of the calculation.

– {COMPLX} 6(

a+b

∠

)

E-58

Matrix Calculations (COMP)

To perform the example operations in this section, ﬁ rst select COMP ( calculation mode.

Matrix Calculation Overview

Matrix calculations are performed by ﬁ rst storing the matrices in one of six matrix memory areas named Mat A through Mat F, and then using the matrix area variables to perform the

actual calculation. To perform a matrix calculation like

2 0

input

Matrix calculation results are displayed on a Mat Ans screen.

Any calculation result that is a matrix is stored in Matrix Answer memory named “Mat Ans”. You can use the Mat Ans screen to view the matrix that is currently stored in Mat Ans.

into Mat A and

0 2

About the Mat Ans Screen

• Each of cells on the Mat Ans screen shows up to six digits of the value currently stored in the cell.

• To check the value stored in a cell, use the cursor keys to move the highlighting to the cell. This will cause the full value contained to appear in the value display area at the bottom of the screen.

• If a cell contains a fraction or sexagesimal value, the applicable cell on the Mat Ans screen will show the decimal format equivalent. When you move the highlighting to the cell, the value will appear in the applicable fraction or sexagesimal format in the value display area.

• Though the Mat Ans screen looks very similar to the matrix editor screen, you cannot edit a matrix on the Mat Ans screen.

• Pressing E while the Mat Ans screen is on the display will switch to the calculation screen.

• You can press +,-, or another operator key while the Mat Ans screen is on the display to start a calculation that uses the current Mat Ans contents (like “Mat Ans+”). This is similar to Answer Memory operations (page 32). For more information, see “Performing Matrix Calculations” (page 62).

1 2

into Mat B, when perform the calculation Mat A + Mat B.

3 4

2 0 0 2

1 2

3 4

) as the

, for example, you would

Inputting and Editing Matrix Data

You can input data for up to six matrices, named Mat A through Mat F, and then use the matrix names as variables in calculations. There are two methods you can use to input data into a matrix: using the matrix editor screen and using the value assignment command ( /).

E-59

Using the Matrix Editor Screen to Input Matrix Data

1. Press z – {MATRIX} 1(EDIT) to display the matrix memory area menu.

• A memory area that already contains a matrix will show

the dimensions of its matrix (like 2 × 2), while an area that is empty will be indicated by “None”.

2. Use c andf to move the highlighting to the matrix you want to use for data input.

3. Press E.

• This displays a screen for specifying the dimensions of

the matrix. of columns.

Note

If you select a memory area that already contains a matrix in step 2, pressing

will display the matrix editor screen so you can edit the matrix. If you want to delete the existing matrix and make a new one with different dimensions, press e or

4. Specify the dimensions of the matrix you want to create, up to a maximum of 10 rows and 10 columns.

• To specify the number of rows, move the highlighting to

• Input a value for

• You can use c andf to move the highlighting between

5. After inputting the row and column values you want, press

• This will display the matrix editor screen.

6. On the matrix editor screen, input values into the cells of the matrix.

• Use the cursor keys to move the cursor to the cell you want and then input a value.

After inputting a value, press E to register it.

7. After inputting all the values you want, press J.

Using the Value Assignment Command ( /) to Input Matrix

is the number of rows, while n is the number

(Dim) in place ofE in step 3.

. This will cause the highlighting to move to

to specify the number of columns and then press E.

, input a value and then press

andn.

Cursor

Data

1. On the COMP Mode calculation screen, use the following syntax to input the matrix you want to input into matrix memory.

a11a

... a

a21a

am1a

• Inputting

... a

...

... a

[[a11, a12, ..., a1n][a21, a22, ..., a2n] ... [am1, am2, ..., amn]]

...

1 2

, for example, can be performed using the following key operation.

3 4

Si Si

([)

3,4

([)

1,2

(])

E-60

2. Input the value assignment command ( /).

– {PROG} –{/}

3. Specify the matrix memory (Mat A to Mat F or Mat Ans) where you want to store the matrix.

• To store it in Mat A, for example, perform the following key

operation: z – {MATRIX} 2(Mat)

Important!

If you specify a matrix memory that already contains matrix data, the existing data will be

overwritten with the data you input here.

4. To store the matrix, press E.

• This displays the stored matrix on the screen. The display

format is the same as that of the matrix editor screen, but you cannot edit the matrix on this screen.

• Pressing J will return to the COMP Mode calculation

screen.

(A).

Note

You can assign the contents of Matrix Answer memory to a matrix variable (such as Mat A) by executing the following: Mat Ans → Mat A.

Viewing the Contents of a Matrix

1. On the COMP Mode calculation screen, press z – {MATRIX} 1(EDIT) to display the matrix memory area menu.

2. Use c andf to move the highlighting to the matrix whose contents you want to view, and then pressE.

3. Now you can edit the cell contents of the matrix, if you want.

• Use the cursor keys to move the cursor to the cell whose value you want to change and

then input the new value. After inputting a value, press E to register it.

4. After you ﬁ nish making the changes you want, press J.

Deleting the Contents of a Particular Matrix Memory Area

1. On the COMP Mode calculation screen, press z – {MATRIX} 1(EDIT) to display the matrix memory area menu.

2. Use c andf to move the highlighting to the matrix memory whose contents you want to delete.

3. Press Y or

• This causes a conﬁ rmation message to appear.

4. To delete all programs currently stored in calculator memory, press E(Yes). To cancel the operation without deleting anything, press J(No).

(Del).

E-61

Performing Matrix Calculations

This section presents a number of actual examples of matrix calculations.

• Before performing matrix calculations, you need to perform the procedure under “Inputting and Editing Matrix Data” (page 59) to input data into the matrices you plan to use in the calculations.

• The table below shows the matrix name notation used in this section. When you see a matrix name in a procedure, you need to perform one of the key operations shown below.

When you see this matrix name: Perform this key operation:

– {MATRIX} 2(Mat)

Mat A

Mat B

Mat C

• All of the examples in this section are performed using natural display.

Adding and Subtracting Matrices

You can add or subtract matrices only if their dimensions are identical.

Example:

This example assumes that Mat A contains

Multiplying Matrices

You can multiply two matrices only if they both have the same number of rows.

Example:

This example assumes that Mat A contains

contains

1 2

2 0

3 4

0 2

2 0

1 2 3 4

0 2

– {MATRIX} 2(Mat)

2 0

and Mat B contains

0 2

Mat A

2 0 0 2

Mat B

, Mat B contains

1 2 3 4

1 2

3 4

, and Mat C

(A)

(B)

(C)

Mat A

E-62

Mat B

Mat C

Note

While a calculation screen is on the display, you can input the Mat Ans variable by pressing

– {MATRIX} 2(Mat)

Calculating the Scalar Multiplication of a Matrix

Your calculator supports the following types of scalar multiplication calculations.

• You can replace “Mat A” with any of the calculator’s matrices, from Mat A to Mat F, or Mat Ans.

, you can use a value, independent memory (M), variable, matrix name, constant (

• For

or scientiﬁ c constant), or scientiﬁ c function value (like sin(30)).

Example:

This example assumes that Mat A contains

Absolute Values of Matrix Elements

The following determines absolute values of the elements of a matrix and places them onto the Mat Ans screen.

Example: To determine the absolute values of the matrix

This example assumes that Mat C contains

2 0

0 2

(Ans).

× Mat A,n Mat A, Mat A ×n, Mat A ÷

1 2 3 4

3*(

– {MATH}

2 0

and Mat B contains

0 2

Mat A

1 –2

5 0

(Abs)

Mat B

1 –2 5 0

Mat C

)

1 2

3 4

E-63

Obtaining the Determinant of a Matrix

The det( function can be used to obtain the determinant of a square matrix.

det a11= a

det = a

Example: To obtain the determinant of the matrix

This example assumes that Mat C contains

a11a

– a

11a22

a21a

a11a12a a21a22a a31a32a

12a21

11a22a33

+ a

12a23a31

Transposing a Matrix

+ a

13a21a32

1 –2 5 0

– a

– {MATRIX} 3(det)

13a22a31

1 –2 5 0

Mat C

– a

12a21a33

)

– a

11a23a32

Tr ansposing a matrix basically means to change its rows in to columns and its columns into rows. Calculation is performed using the Trn( function as shown below.

1 2 3

Example: To transpose the matrix

This example assumes that Mat B contains

4 5 6

1 2 3 4 5 6

– {MATRIX} 4(Trn)

Mat B

)

Inverting a Matrix

You can use the procedure shown below to invert a square matrix.

–1

–a

a11a a21a

–1

a11a

–a

21a11

– a

12a21

E-64

a22a

– a

–a

a11a12a a21a22a a31a32a

–a

12a33

11a33

11a32

13a21a32

+ a

13a32a12a23

– a

13a31

+ a

12a31a11a22

– a

13a22a31

23a32

– a

+ a

21a33

a21a

+ a

– a

12a23a31

23a31

22a31

+ a

–1

a11a22a

–a

– a

11a23

– a

+ a

– a

12a21a33

13a22

13a21

12a21

– a

11a23a32

Important!

• Matrix inversion is supported for a non-zero square matrix only.

• Use the

Example: To invert the matrix

This example assumes that Mat C contains

Squaring a Matrix

–1

) key to input “ –1”.

(

)

1 –2 5 0

1 –2

5 0

Mat C

)

–1

(

)

You can use the procedure shown below to square a matrix.

Important!

Use thex key to specify the squaring operation.

Example: To square the matrix

This example assumes that Mat C contains

1 –2 5 0

1 –2

5 0

Mat C

Sequence Calculations (RECUR)

To perform the example operations in this section, ﬁ rst select RECUR ( calculation mode.

) as the

Sequence Calculation Overview

You can use either of the two following sequence types to create a sequence table.

Type Sequence

With this sequence type, you input the general term of the sequence (

with a sequence start value and end value.

Type Sequence

With this sequence type, you input the recursion formula for two-term recursion (

(

)), along with a sequence start value and end value.

=f ( n)), along

E-65

Selecting the Sequence Type

To select this sequence type: Perform this key operation:

Type

Sequence Editor Screen

– {TYPE} 1(

– {TYPE} 2(

)

Either of the sequence editor screens shown below appears immediately after you enter the RECUR Mode and select the sequence type. Use this screen to input the expression that deﬁ nes the expression (general term or recursion formula).

Type

Inputting a Formula on the Sequence Editor Screen

Example 1: To input

Example 2: To input

Note

To clear the screen during input, press o.

Table Range Screen

PressingE to register the formula you input on the sequence editor screen displays either of the table range screens shown below.

Use this screen to specify the start value (Start) and end value (End) of table creation.

+n + 1

)

(

+z1

=n + 5

Type Sequence

– {TYPE} 2(

(n)

– {TYPE} 1(

)

(

Type Sequence

)

for sequence

Specifying the Initial Term, Start Value, and End Value

1. On the table range screen, use c andf to move the highlighting to the setting you want to change.

2. Input the values or expressions you want.

• To clear the screen during input, press o.

• Pressing J during input will discard everything you have input up to that point, and

restores the values that were previously input on the screen.

E-66

3. After inputting everything you want, press E.

• This registers your input. If you input expressions, the calculation result of the

expression is registered.

• While any setting is highlighted, press E to display the sequence table screen (page

67).

Returning to the Sequence Editor Screen from the Table Range Screen

PressJ.

Sequence Table Screen

When you press E in step 3 under “Specifying the Initial Term, Start Value, and End Value”, the calculator will perform the sequence calculation in accordance with the formula (general term or recursion formula), initial term, start value, and end value that you have input, and display the result on the sequence table screen.

Type Sequence

• Each of cells on the sequence table screen shows up to six digits of the value currently stored in the cell.

• To see the full value in a cell, move the highlighting to it. The full value contained in the cell will appear in the value display area at the bottom of the screen.

• While a value is in the value display area, you can convert it using ENG conversion (page

53), sexagesimal-decimal conversion (page 27), or decimal-fraction format conversion (page 22).

• Note, however, that you cannot input into the value display area or edit the values displayed there.

Sequence Table Columns

This column: Contains this data:

Value from the start value to the end value speciﬁ ed for n on the table range screen.

Value of

Sum of

Value from the start value to the end value speciﬁ ed for table range screen.

Value of

Sum of

for the n-value in the same line.

from start value of n up to then-value in the same line

+1 on the

for the n+1 value in the same line.

from

ton+1 in the same line.

Returning to the Table Range Screen from the Sequence Table Screen

PressJ.

E-67

Creating a Sequence Table

Creating an

Example: To create a sequence table with the recursion formula

Enter the RECUR Mode:

Select the

Input the recursion formula:

Input

Create the sequence table:

range of 1

type:

= 2, Start = 1, End = 10:

Type Sequence Table

10 ( n = integer). Note, however, that

(RECUR)

– {TYPE} 2(

)

(

+z1

(This displays the table range screen.)

2E1E10

(This displays the sequence table screen.)

(n)

= 2.

)

+n + 1 using a

Creating an

Example: To create a sequence table with the general term

range of 2

Type Sequence Table

6 ( n = integer).

Enter the RECUR Mode:

Select the

Input the general term:

type:

1c2

2z1

(RECUR)

– {TYPE} 1(

(

)

(

-3

E-68

= (

)

+ 2 n – 3 using a

2E6

(M–))

(This displays the table range screen.)

Input Start = 2 and End = 6:

Create the sequence table:

(This displays the sequence table screen.)

Sequence Calculation Precautions

The following functions cannot be used during sequence calculations.

• CALC

• SOLVE

• Coordinate conversion (Pol(, Rec()

•

d/dx(,d

• Independent memory add and subtract ( l,

• Assignment of values to variables (

• Multi-statement input

(,∫ (,Σ (

(STO))

Sequence Table Generation Errors

• A sequence table can have up to 199 lines. A Range ERROR occurs if a table range setting causes this to be exceeded.

• A “Memory Full” error also occurs if the calculator runs out of calculation result memory while performing a sequence table calculation.

Math ERROR during Sequence Calculation

If a Math ERROR occurs during sequence table calculation, the sequence table screen appears on the display with “ERROR” in the cell that generated the error.

Equation Calculations (EQN)

Equation Calculation Overview

This section shows the general operational procedure for solving simultaneous linear equations with two unknowns. Natural display is used for this procedure.

X + 0.5Y = 3 2X + 3Y = 4

E-69

1. Press

• This displays an initial EQN type menu like the one shown below.

2. Press 1(aX+bY=c) to select simultaneous linear equations with two unknowns.

• This displays a coefﬁ cient editor screen like the one shown below. You can use this screen to input values for the equation’s coefﬁ cients.

3. Input values for the coefﬁ cients.

1E0.5E3E2E3E4

4. To display the solutions, press E.

• This displays the solution for X.

• Use c andf to switch the display between the solutions for X and Y.

(EQN).

X + 0.5Y = 3

2X + 3Y = 4

These values will produce the simultaneous equations shown above.

• To exit the solution screen and return to the coefﬁ cient editor screen, press J.

E-70

Selecting an Equation Type

The following shows the operations you can use to select an equation type.

To select this equation type:

Simultaneous Linear Equations with Two Unknowns

Simultaneous Linear Equations with Three Unknowns

Simultaneous Linear Equations with Four Unknowns

Simultaneous Linear Equations with Five Unknowns

Quadratic Equation

Cubic Equation

Perform this key operation:

(EQN)

EQN type menu item:

aX+bY=c

aX+bY+cZ=d

aX+bY+cZ+dT=e

aX+bY+cZ+dT+eU=f

+bX+c=0

+bX2+cX+d=0

Note

Changing the equation type after you are already using the EQN Mode to perform a calculation will cause all values currently input on the coefﬁ cient editor screen to be cleared.

Inputting Values for Coefﬁ cients

Use the coefﬁ cient editor for inputting values for the coefﬁ cients of an equation. The coefﬁ cient editor screen has cells that you can use to input values for each coefﬁ cient. The number of cells that appear on the coefﬁ cient editor screen depends on the equation type you selected.

Inputting and Editing Coefﬁ cient Values

• Use the cursor keys to move the cursor to the cell you want and then input a value. As you input a value or expression, it appears in the lower left corner of the display.

• To clear the contents of the cell where the cursor is currently located, press o.

• You must press E to ﬁ nalize input into the cell where the cursor is located. This will register your input and move the cursor to the next cell. Up to six digits of the input value will be displayed in the cell when you press E.

• You can input a value or calculation expression into each cell. If you input a calculation expression, pressing E will execute the calculation and display only the result in the applicable cell.

• To edit the contents of a cell, use the cursor keys to move the cursor to the cell and then input what you want.

E-71

Viewing Equation Solutions

PressingE while the coefﬁ cient editor is displayed will display the solutions of the equation.

Equation solution

• You can use c andf to scroll forward and back through the solutions.

• You can also press E while a solution is displayed to cycle through all of the other available solutions. Pressing E while the ﬁ nal solution is displayed will return to the coefﬁ cient editor screen.

• To exit the solution screen and return to the coefﬁ cient editor screen, press J.

• The display format of the solutions depends on the setup’s display format settings and complex number display format settings.

Statistical Calculations (SD/REG)

Perform statistical calculations in the SD Mode or REG Mode. The SD Mode is for singlevariable statistical calculations, while the REG Mode is for paired-variable regression calculations (linear, quadratic, logarithmic, e exponential, ab exponential, power, inverse).

Statistical Sample Data

Except for the number of variables, the procedure for inputting sample data is the same for both the SD Mode and the REG Mode. Use the STAT editor list screen to input sample data.

SD Mode STAT editor REG Mode STAT editor The applicable STAT editor screen appears ﬁ rst whenever you enter the SD Mode (

or REG Mode (

Sample Data Input Methods

You can input sample data either with statistical frequency tur ned on (FreqOn) or off (FreqOff). The calculator’s initial default setting is FreqOff. You can select the input method you want to use with the setup screen statistical frequency setting (page 13). The STAT editor screens include a FREQ column when statistical frequency is turned on (FreqOn). There is no FREQ column when statistical frequency is turned off (FreqOff).

)

E-72

Inputting Sample Data

The following example shows how to input the following sample data in the SD Mode.

Class Value (X) Frequency (FREQ)

24.5 4

25.5 6

26.5 2

Enter the SD Mode:

(SD)

Input the class values in the X column:

24.5E25.5E26.5

Move the cursor to the top cell of the FREQ column:

Input the frequency values in the FREQ column:

4E6E2

The only difference when inputting sample data in the REG Mode is that the STAT editor screen has three columns named X, Y, and FREQ.

The initial default for all frequencies is 1.

Note

• In the SD Mode, one set of sample data consists of an X value and FREQ value, while one set of REG Mode sample data consists of an X value, Y value, and FREQ value. Whenever you start input of a sample data set by inputting a value for any one of its columns on the STAT editor screen, the remaining column(s) in the same sample data set change(s) to their initial defaults (X = 0, Y = 0, FREQ = 1).

• Inputting a calculation expression into a cell and pressing E will register the result of the calculation.

• In both the SD Mode and REG Mode, you can input up to 199 STAT editor lines of sample data.

• Sample data you input is retained in memory until you delete it or reset the calculator. Changing to another calculation mode, changing the statistical frequency setting, or turning off the calculator does not affect sample data.

E-73

• Even though Y-data is not used and there is no indication of Y-data on the screen in the SD Mode, the calculator still maintains a Y-value (always zero) internally for each X-data. Because of this, if you perform a statistical calculation operation that involves Y-data (such

) after inputting single-variable data in the SD Mode, the calculator will produce a

result without displaying an error.

Editing Sample Data

You can use the procedures in this section to perform the following STAT editor screen editing operations: replace cell contents, insert a line, insert a cell, delete a cell, and delete all STAT editor screen data.

Replacing the Contents of a Cell

Use the cursor keys to move the cursor to the cell whose contents you want to replace and then input the value or calculation expression you want. After you are ﬁ nished, press E to register your input.

Inserting a Line

1. Move the cursor to the location where you want to insert the line.

2. Press

• This shifts the line where the cursor is located and everything below it downwards, and inserts a new line.

• All of the columns in the newly inserted lines are ﬁ lled in with the applicable initial default values (X = 0, Y = 0 if applicable, FREQ = 1).

(STAT) 1(Edit)1(Ins Row).

Deleting all STAT Editor Data

1. Press

• This causes the “Delete All Data?” conﬁ rmation message to appear.

2. To delete all STAT editor data, press E(Yes). To cancel the operation without deleting anything, press J(No).

(STAT) 1(Edit)2(Del All).

Inserting a Cell

1. Move the cursor to the location where you want to insert the cell.

2. Press

• This shifts the cell where the cursor is located and everything below it downwards, and

inserts a new cell. The cell at the bottom of the column where the new cell is inserted is deleted automatically.

(STAT) 1(Edit)3(Ins Cell).

(Ins Cell)

• The inserted cell is ﬁ lled in with the applicable initial default value (X = 0, Y = 0, or

FREQ = 1).

Deleting a Cell

1. Move the cursor to the cell you want to delete.

E-74

2. Press

• This deletes the cell where the cursor is located and shifts everything below it upwards.

A new cell is inserted at the bottom of the column where the cell is deleted.

• The new cell that is inserted at the bottom of the column is ﬁ lled in with the applicable

initial default value (X = 0, Y = 0, or FREQ = 1).

Performing Single-variable Statistical Calculations

• To perform the example operations in this section, ﬁ rst select SD ( calculation mode.

• The following operation assumes that the sample data under “Inputting Sample Data” on page 73 is already input.

Displaying the Statistical Calculation Result Screen

While the STAT editor screen (containing the sample data) is on the display, perform the following key operation.

(STAT) 1(Edit)4(Del Cell).

(Del Cell)

(RESULT)

(Usec andf to scroll.)

This is one example of possible calculation results.

) as the

Note

• Calculation results can be displayed up to 10 digits.

• To return to the STAT editor screen, press J.

• For the meanings of the values that appear on the statistical calculation result screen and the formulas used to produce them, see “SD Mode Statistical Command Reference” (page

76).

Performing a Speciﬁ c Statistical Calculation

1. While the STAT editor screen is on the display, press

• This displays the initial COMP Mode calculation screen.

2. Input the command for the statistical calculation you want to perform and then press E.

• To determine the mean value ( o) of the currently input sample data, for example, perform the operation shown below.

(/COMP).

E-75

(STAT) 2(VAR)

(o)

This is one example of possible calculation results.

For more information about statistical calculation commands, see the following section.

SD Mode Statistical Command Reference

(STAT) 2(VAR)

Obtains the number of samples.

= (number of

¯ x

Obtains the mean.

Obtains the population standard deviation.

–1

Obtains the sample standard deviation.

Obtains the sum of squares of the sample data.

Obtains the sum of the sample data.

minX

Determines the minimum value of the samples.

σn

σn–1

E-76

-data items)

Σx

Σ(x

– o)

Σ(x

– o)

Σ(x

– o)

Σ(x

– o)

n – 1

(STAT) 2(VAR)

P(t) =

X – o

(STAT) 3(DISTR)

−

∫

−∞

−

edx

t

−

edx

∞

−

edx

(STAT) 3(DISTR)

2π

maxX

Determines the maximum value of the samples.

For the argument

, determines the probability of standard normal distribution P( t).

P(t)

0 t

For the argument

, determines the probability of standard normal distribution Q( t).

Q(t)

Q(t) =

0 t

For the argument

Using the value (X) input immediately before the command as the argument, uses the following formula to determine standardized variate

, determines the probability of standard normal distribution R( t).

R(t)

R(t) =

0 t

X't =

Performing Paired-variable Statistical Calculations

• To perform the example operations in this section, ﬁ rst select REG ( calculation mode.

• The following operation assumes that the sample data under “Inputting Sample Data” on page 73 is already input.

) as the

E-77

Displaying the Statistical Calculation Result Screen

In the REG Mode, you can display a screen that lists the results of standard deviation and sum calculations. You can also display results for a speciﬁ c type of regression calculation.

Note

• Calculation results can be displayed up to 10 digits.

• To return to the STAT editor screen from the calculation result screen, press J.

• For the meanings of the values that appear on the result screen and the formulas used to produce them, see “REG Mode Statistical Command Reference” (page 80).

Displaying the Standard Deviation and Sum Calculation Result Screen

While the STAT editor screen (containing the sample data) is on the display, perform the following key operation.

(RESULT) 1(S-Var)

(Usec andf to scroll.)

This is one example of possible calculation results.

Displaying Regression Calculation Results

1. While the STAT editor screen (containing the sample data) is on the display, perform the following key operation.

• This displays the regression type menu.

(RESULT) 2(Reg)

E-78

2. Press the key that corresponds to the type of regression whose results you want to display.

To display the results of this type of regression calculation:

y =ax +b

y =ax

y =a +b

y =ax

y =a +b/x

)

+bx +c)

lnx)

)

Linear (

Quadratic (

Logarithmic (

Exponential ( y =

Power (

Inverse (

(Example screen when 1 is pressed)

Performing a Speciﬁ c Statistical Calculation

1. While the STAT editor screen is on the display, press

• This displays the initial COMP Mode calculation screen.

2. Input the command for the statistical calculation you want to perform and then press E.

• To determine the mean ( o andp) values of the current input sample data, for example,

perform the operation shown below.

Press this key:

(Line)

(Quad)

(Log)

(eExp)

(abExp)

(Power)

(Inv)

This is one example of possible calculation results.

(/COMP).

(STAT) 2(VAR)

(o)

(STAT) 2(VAR) 5(p)

This is one example of possible calculation results.

E-79

Performing a Speciﬁ c Regression Calculation

Example: To use the statistical data shown below to perform logarithmic regression to

obtain the correlation coefﬁ cient and the estimated value of

whenx = 100

x y

29 1.6 50 23.5

74 38.0 103 46.4 118 48.9

1. Display the logarithmic regression calculation result screen.

(RESULT) 2(Reg)3(Log)

2. Press J to return to the STAT editor screen.

3. Press

4. Determine correlation coefﬁ cient r and the estimated value of

• Correlation Coefﬁ cient

(/COMP) to display the COMP Mode calculation screen.

(STAT) 2(VAR)

ccc

(r)

whenx = 100.

• Estimated Value of

whenx = 100

100z7

(STAT) 2(VAR)

ccc

(n)

Note

• The r and n values produced by this example are for logarithmic regression because we ﬁ rst displayed the logarithmic regression calculation screen in step 1 before using the commands to calculate the values were wanted. If you do not display a particular regression calculation result screen ﬁ rst, the values produced by the commands are for linear regression by default.

• For details about statistical calculation commands, see “REG Mode Statistical Command Reference” (page 80).

REG Mode Statistical Command Reference

Mean and Standard Deviation Commands

(STAT) 2(VAR)

Obtains the number of samples.

= (number of

-data items)

E-80

¯ x

Obtains the mean of the sample

Obtains the population standard deviation of the sample x-data.

–1

Obtains the sample standard deviation of the sample x-data.

-data.

σn

σn–1

Σx

Σ(x

– o)

Σ(x

– o)

Σ(x

– o)

Σ(x

– o)

n – 1

¯ y

Obtains the mean of the sample

Obtains the population standard deviation of the sample

–1

Obtains the sample standard deviation of the sample y-data.

-data.

σn–1

σn

Σy

-data.

Σ(y

– y)

Σ(y

– y)

Σ(y

– y)

n – 1

Sum Commands

Obtains the sum of squares of the samplex-data.

Obtains the sum of the sample

-data.

(STAT) 2(VAR)

E-81

Obtains the sum of squares of the sample

Obtains the sum of the sampley-data.

Obtains the sum of products of the samplex-data andy-data.

Obtains the sum of cubes of the sample

Obtains the sum of squares of the sample

Obtains the sum of the fourth power of the sample

-data.

iyi

-data.

-data multiplied by the sample y-data.

-data.

Minimum and Maximum Value Commands

minX

Obtains the minimum value of the sample

maxX

Obtains the maximum value of the sample

minY

Obtains the minimum value of the sample

maxY

Obtains the maximum value of the sample

-data.

(STAT) 2(VAR)

E-82

Regression Coefﬁ cient and Estimated Value Commands

The values obtained by the following commands depend on the regression formula used for the calculation. The regression formula used is the one that is applicable for the regression calculation result screen (page 78) that was last displayed in the REG Mode.

(STAT) 2(VAR)

Obtains coefﬁ cient a of the regression formula.

Obtains coefﬁ cient b of the regression formula.

This command is supported for quadratic regression only. It obtains coefﬁ cient c of the regression formula.

Obtains correlation coefﬁ cient r. This command is not supported for quadratic regression.

ˆ x

Obtains the estimated value of immediately before this command.

ˆ x

This command is supported for quadratic regression only. It obtains the second estimated value of input immediately before this command. When used in a calculation that is not a quadratic regression calculation, this command produces the same results as the

for a value of y, which is assumed to be the value input

for a value of y, which is assumed to be the value

ˆ y

Obtains the estimated value of y for a value of x, which is assumed to be the value input immediately before this command.

Regression Coefﬁ cient and Estimated Value Calculations

The formulas used by the regression coefﬁ cient and estimated value commands depend on the regression calculation type. For details about regression calculation formulas, see <#02> and <#08> in the separate Supplement.

For more information about this type of regression calculation: Go here:

Linear Regression <#02>

Quadratic Regression <#03>

Logarithmic Regression <#04>

Exponential Regression

(STAT) 2(VAR)

command.

(STAT) 2(VAR)

<#05>

<#06>

ccc

E-83

For more information about this type of regression calculation: Go here:

Power Regression <#07>

Inverse Regression <#08>

Statistical Calculation Examples

This section provides some actual examples of statistical calculation examples as they are performed on your calculator.

Example 1: The nearby table shows the pulse rates of 50

Operation Procedure

Select the SD Mode: Select FreqOn for the statistical frequency setting:

Input the pulse rate data into the X-column:

Input the number of students data into the FREQ-column:

(1) Mean and Standard Deviation

Obtain the mean:

Obtain the sample standard deviation:

students who attend a high school for boys that has a total enrollment of 1,000 students.

Determine the mean and standard deviation of the sample

data.

Assuming that the population distribution is a normal

distribution, determine the distribution probability of students with pulse rates of 70 of greater.

(SD)

(SETUP)

55E57E59E61E63E65 67E69E71E73E75

1E2E2E5E8

9E8E6E4E3E2

(STAT) 2(VAR) 4(

(STAT) 1(FreqOn)

E E

(STAT) 2(VAR) 2(o)

(/COMP)

Pulse Rate Students

54 – 56 1 56 – 58 2 58 – 60 2 60 – 62 5 62 – 64 8 64 – 66 9 66 – 68 8 68 – 70 6 70 – 72 4 72 – 74 3 74 – 76 2

)

–1

(2) Distribution Probability

(STAT) 3(DISTR)3(R()

(STAT) 3(DISTR)4(

E-84

)

Example 2: The nearby data shows how the weight of a

Operation Procedure

Select the REG Mode: Select FreqOff for the statistical frequency setting:

Input the number of day data into the X-column:

Input the weight data into the Y-column:

(1) Linear Regression

Display the linear regression calculation result screen:

(2) Distribution Logarithmic Regression

Display the logarithmic regression calculation result screen:

(3) Weight Prediction

The absolute value of correlation coefﬁ cient r is close to 1, so logarithmic regression is used for its calculation. Obtainn when

newborn at various numbers of days after birth.

Obtain the regression formula and correlation coefﬁ cient

produced by linear regression of the data.

Obtain the regression formula and correlation coefﬁ cient

produced by logarithmic regression of the data.

Predict the weight 350 days after birth based on the

regression formula that best ﬁ ts the trend of the data in accordance with the regression results.

(REG)

(SETUP)

20E50E80E110E140E170 200E230E260E290E320

3150E4800E6420E7310

7940E8690E8800E9130 9270E9310E9390

= 350:

(STAT) 2(FreqOff)

(RESULT) 2(Reg)1(Line)

(RESULT) 2(Reg)3(Log)

(

COMP)

350z7

(VAR)

ccc

(STAT)

Number of Days

110 7310 140 7940 170 8690 200 8800 230 9130 260 9270 290 9310 320 9390

(n)

Weight

(g)

20 3150 50 4800 80 6420

E-85

Base-n Calculations (BASE-N)

To perform the example operations in this section, ﬁ rst select BASE-N ( calculation mode.

Performing Base- n Calculations

When you press display as shown below.

Number base indicator Negative value setting indicator

Number base indicator: Indicates the current number base (see table below). Negative value setting indicator: Indicates whether the use of negative values is allowed (see

Specifying the Number Base

Use the keys shown below to specify the number base.

to enter the BASE-N Mode, the current setup appears on the

“Changing the BASE-N Mode Negative Value Setting” on page 13).

DEC

HEX

[

BIN

i 6

OCT

]

) as the

To select this number base:

Decimal

Hexadecimal

Binary

Octal

Example Base- n Calculations

Example: To select binary as the number base and calculate 1 2 + 1

• Inputting an invalid value causes a Syntax ERROR.

• In the BASE-N Mode, input of fractional (decimal) values and exponential values is not supported. Anything to the right of the decimal point of the calculation results is cut off.

Press this key:

(DEC) Dec

(HEX) Hex

(BIN) Bin

(OCT) Oct

(BIN)

1+1

Which displays this screen indicator:

E-86

Hexadecimal Value Input and Calculation Example

Use the following keys to input the letters required for hexadecimal values (A, B, C, D, E, F).

∠

(

{A}

Example: To select hexadecimal as the number base and calculate 1F 16 + 1

{B}

sin–1{D} cos–1{E} tan–1{F}, {C}

$ sct

(HEX)

Effective Calculation Ranges

When the setup’s negative value setting is “Signed”

Number Base Effective Range

Positive: 00000000000000000000000000000000

Binary

Octal

Decimal –2147483648

Hexadecimal

When the setup’s negative value setting is “Unsigned”

Number Base Effective Range

Binary

Octal 00000000000

Decimal 0

Hexadecimal 00000000

• A Math ERROR occurs when a calculation result is outside of the applicable range for the current default number base.

Converting a Displayed Result to another Number Base

Pressingx(DEC),l(HEX),I(BIN), or6(OCT) while a calculation result is displayed will convert the result to the corresponding number base.

Negative: 10000000000000000000000000000000

Positive: 00000000000 Negative: 20000000000

Positive: 00000000 Negative: 80000000

00000000000000000000000000000000

<x<

11111111111111111111111111111111

4294967295

(F)

01111111111111111111111111111111

11111111111111111111111111111111

2147483647

37777777777

FFFFFFFF

7FFFFFFF

FFFFFFFF

17777777777

37777777777

E-87

Example: To convert the decimal value 30 10 to binary, octal, and hexadecimal format

(DEC)

(BASE-N)

(BIN)

(OCT)

(HEX)

Specifying a Number Base for a Particular Value

You can specify a number base that is different from the current default number base while inputting a value.

Specifying the Number Base during Input

Inputting a decimal value of 3, for example, can be performed using the following key operation.

E-88

(d)

Example Calculation Using Base- n Speciﬁ cation

Example: To perform the calculation 5 10 + 5 16, and display the result in binary

(BIN)

(BASE-N)1(d)

(BASE-N)2(h)

Performing Calculations Using Logical Operations and

5+ 5

Negative Binary Values

Your calculator can perform 32-digit (32-bit) binary logical operations and negative value calculations. All of the examples shown below are performed with binary ( i(BIN)) set as the default number base.

Note

Negative binary, octal, and hexadecimal values are produced by taking the binary two’s complement and then returning the result to the original number base. With the decimal number base, negative values are displayed with a minus sign.

Logical Product (and)

Returns the result of a bitwise product.

Example: 1010

Logical Sum (or)

Returns the result of a bitwise sum.

Example: 1011

Exclusive Logical Sum (xor)

Returns the result of a bitwise exclusive logical sum.

Example: 1010

and 1100 2 = 1000

or 11010 2 = 11011

xor 1100 2 = 110

1010z1

(and)

(or)

11010

(xor)

1100

1011z1

1010z1

(BASE-N)

Exclusive Logical Sum Negation (xnor)

Returns the result of the negation of a bitwise exclusive logical sum.

E-89

Example: 1111 2 xnor 101 2 = 11111111111111111111111111110101

1111z1

Complement/Inversion (Not)

Returns the result of a complement (bitwise inversion).

Example: Not(1010

Negation (Neg)

Returns the two’s complement of a value. Negation is supported only when the negative value setting is “Signed”.

Example: Neg(101101

) = 11111111111111111111111111110101

(BASE-N)

1010)

) = 11111111111111111111111111010011

(BASE-N)

101101)

(xnor)

(BASE-N)

101

(Not)

(Neg)

CALC

CALC makes it easy to solve an expression that contains variables. After you input the expression, simply enter values for the variables to calculate the result. You can change the values of the variables as many times as you like. CALC can be used only in the COMP Mode (

Using CALC

Inputting an expression that contains variables and pressing the s key displays a “value assignment screen”, which you can use to assign values to each variable. After inputting the values, press E to execute the calculation.

Performing Calculation with CALC

Important!

• In the CALC mode, a calculation that contains variables can use variables A through Z only. Extra variables (Z[1], Z[2], etc.) cannot be used as variables. If you try to use an extra variable in a calculation in the CALC mode, it will be treated as a constant using the current value assigned to it.

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Example: To assign the values A = 5, B = 3 and A = 5, B = 10 for the expression 3 × A + B

(A)

(B)

5E3

(This displays the value assignment screen.)

Assign A = 5 and B = 3:

Execute the calculation:

Display the value assignment screen again:

Leave A the way it is, and assign 10 to B:

Execute the calculation:

Note

• If natural display is selected for the calculator’s display format, the value assignment screen shows only one variable at a time.

• Use c andf to move the highlighting between variables and select the one you want to input.

Important!

The following functions cannot be used on the value assignment screen.

• Input and display of complex numbers

• SOLVE

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Displaying Comment Text on the Value Assignment Screen

You can use the following syntax to add comment text to an expression you input with CALC: "comment text" : {calculation expression}. The comment text will appear in the top line of the value assignment screen in place of the expression.

Example: To use CALC and input "AREA": S = A × B ÷ 2, assign the values A = 7, B = 8,

and then perform the calculation

(;-LOCK)!(")i(A)/(R)c(E)

(A)!(")

(A)

(:)

(S)

7E8

(B)

E E

(=)

SOLVE

SOLVE uses approximation based on Newton’s Law to solve equations. SOLVE can be used only in the COMP Mode (

Expressions Supported by SOLVE

SOLVE supports input of equations of the following formats

Examples: Y = X + 5, X = sin(M), X + 3 = B + C, XY + C (Treated as XY + C = 0)

Important!

• The following is not supported by SOLVE equations.

- Input of integration, differential, Σ (, Pol( and Rec( functions

- Multi-statement input

• SOLVE does not support input of complex number coefﬁ cients or display of complex number solutions.

Using SOLVE

Inputting an equation and pressing the. key displays a “value assignment screen”, which you can use to assign values to each variable. After assigning values to the variables, move the highlighting to the variable you want to solve for and then press E to solve.

Using SOLVE to Solve an Equation

Example: To solve the equation y =

+b for x, wheny = 0,a = 1,b = –2

(Y)

(X)

(=)

S S

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(A) (B)

(This displays the value assignment screen.)

Assign 0 to Y: Assign 1 to A: Input an initial value for X (Here, input 1): Assign –2 to B:

Specify the variable you want to solve for:

(Here we want to solve for X, so move the highlighting to X.)

Solve the equation:

• Press E to return to the value assignment screen. Then you can assign different values to the variables, change the initial value, and solve again.

• An error message (Can’t Solve) will appear if SOLVE is unable to solve the equation.

0 1 1 2

E E E E

Note

• If natural display is selected for the calculator’s display format, the value assignment screen shows only one variable at a time.

• Use c andf to move the highlighting between variables and select the one you want to input.

Scrolling the Equation on the Value Assignment Screen

If an equation is too long to ﬁ t on the variable assignment screen, you can scroll it left and right to bring other parts of it into view. To enable scrolling, press

Use thee andd keys to scroll the equation right and left.

To return the equation to its initial view after scrolling, press J.

SOLVE Precautions

• Depending on the initial value you input for the equation, SOLVE may not be able to produce a solution. If this happens, input a different initial value that you estimate is close to the actual value of the variable you are solving for, and try again.

• SOLVE may not be able to produce a solution for an equation, even though one actually exists.

(LOOK).

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• Due to the characteristics of Newton’s Law, the following scientiﬁ c functions tend to make it difﬁ cult to obtain solutions.

- Periodic functions (like y = sin( x))

- Functions that produce steep slopes when graphed (like

- Discontinuous functions (like

Solution Screen Contents

The SOLVE solution screen displays the information shown below.

(The equation you input.)

Var iab le solved for Solution

• Solutions are always displayed in decimal format.

• When natural display is selected as the calculator’s display format, the two lines “X=” and “L–R” are displayed in one line. If any of the data in a line does not ﬁ t on the screen, use

andd to scroll.

• “(Left Side) – (Right Side) result” shows the result when the right side of the equation is subtracted from the left side, after assigning the obtained value to the variable being solved for. The closer this result is to zero, the higher the accuracy of the solution.

Convergence in Progress Screen

The convergence in progress screen like the one shown below will appear on the display when SOLVE is unable to obtain a solution after a certain number of calculations. Pressing

while this screen is displayed will resume with the calculation.

To interrupt an on-going calculation operation, press o.

Equation

)

(Left Side) – (Right Side) result

y =e

,y =

)

Creating a Number Table from a Function (TABLE)

To perform the example operations in this section, ﬁ rst select TABLE ( calculation mode.

TABLE Mode Overview

The TABLE Mode lets you create an x andf(x) number table by specifying a range of values to be substituted for the function

f(x

) and for x.

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) as the

Expression Editor Screen

The expression editor screen appears ﬁ rst when you enter the TABLE Mode. You can use this screen to input the function of variable X, which will be used for generation of a number table.

Inputting on the Expression Editor Screen

Example: To input f(x) =

(X)

+'1c2

Note

• To clear the screen during input, press o.

• Any other variable other than X that is input on the expression editor screen is treated as a value (in accordance with the value currently assigned to it).

Table Range Screen

PressingE to register the expression you input on the expression editor screen displays the table range screen shown below.

Use this screen to specify the start value (Start), end values (End), and the step (Step) of

the

value, which will be used to generate the number table.

Specifying the Start Value, End Value, and Step

1. On the table range screen, use c andf to move the highlighting to the setting you want to change.

2. Input the values or expressions you want.

• To clear the screen during input, press o.

• Pressing J during input will discard everything you have input up to that point, and

restores the values that were previously input on the screen.

3. After inputting everything you want, press E.

• This registers your input. If you input expressions, the calculation result of the

expression is registered.

• While any setting is highlighted, press E to display the number table screen (page

96).

Returning to the Expression Editor Screen from the Table Range Screen

PressJ.

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Number Table Screen

When you press the calculator will perform the number table calculation in accordance with the function expression, start value, end value, and step that you have input, and display the result on the number table screen.

• Each of cells on the number table screen shows up to six digits of the value currently stored in the cell.

• To see the full value in a cell, move the highlighting to it. The full value contained in the cell will appear in the value display area at the bottom of the screen.

• While a value is in the value display area, you can convert it using ENG conversion (page

53), sexagesimal-decimal conversion (page 27), or decimal-fraction format conversion (page 22).

• Note, however, that you cannot input into the value display area or edit the values displayed there.

in step 3 under “Specifying the Start Value, End Value, and Step”,

Number Table Columns

This column: Contains this data:

F(X)

-values calculated in accordance with the start value, end value,

and step speciﬁ ed on the table range screen

for the f(x) value in the same line

Value of

Returning to the Table Range Screen from the Number Table Screen

PressJ.

Creating a Number Table

Example: To calculate the total principal and interest at the end of one year, three years,

Total principal and interest after

0.03) the step, and then create the number table.

Enter the TABLE Mode:

Input the function expression

and ﬁ ve years on an original principal amount of $100,000 with an annual interest rate of 3%, compounded annually

. Input the above function, specify a start value of 1 for x, 5 for the end value, and 2 for

100000(1+0.03)

years can be calculated using the formula 100000 × (1 +

(TABLE)

f(x

) = 100000 × (1 + 0.03) x:

(X)

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(This displays the table range screen.)

Input Start = 1, End = 5, and Step = 2:

1E5E2

Create the number table:

(This displays the number table screen.)

Number Table Creation Precautions

The precautions for number table creation are identical to the RECUR Mode precautions. For more information, see “Sequence Calculation Precautions” on page 69.

Built-in Formulas

Your calculator comes with 128 different mathematic and scientiﬁ c formulas. Built-in formulas can be used only in the COMP Mode (

Using Built-in Formulas

Searching for a Built-in Formula by Inputting a Character

1. Press G.

• This displays an alphabetic menu of built-in formulas.

2. Input the ﬁ rst letter of the name of the built-in formula you want.

• If you want to recall the Sector Area formula for example, press 1(S). This will jump to the section of the formula menu where the names start with the letter you speciﬁ ed (“S” in this example). The ﬁ rst formula with a name that starts with the letter will be highlighted, indicating that it is selected. Use c andf to scroll the highlighting to the formula you want (“Sector Area” in this example).

1(S)

• The formula names that appear on the display are abbreviated due to space limitations. For a full list of formulas, their abbreviated names, and their full names, see “Built-in Formula Names” (page 99).

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Searching for a Built-in Formula by Scrolling through the Menu

1. Press G.

2. Use c andf to scroll through the built-in formula names until the one you want to recall is selected.

Performing Calculation with a Built-in Formula

The following example shows how to use Heron’s formula to determine the area of a triangle when the lengths of its three sides (8, 5, 5) are known.

Operation Procedure

Search for Heron’s formula:

(H)c(HeronFormula)

)

Start the calculation:

(This displays a prompt for input of the first variable value.)

Input a = 8, b = 5, and c = 5:

8E5E5

(This displays the calculation result.)

• As shown above, the calculation result appears after you assign values to all of the required variables.

• In the case of a formula that produces multiple results (such as

symbol will turn on when the ﬁ rst calculation result is on the display. Press E to

display the other result(s) produced by the formula. The ﬁ nal result is on the display.

• Pressing E while the ﬁ nal calculation result is on the display ( will re-execute the formula from the beginning.

Displaying a Built-in Formula

While a prompt for input of a value for a formula variable is on the display, you can display the entire formula by pressing

(LOOK).

Y Conversion), the

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symbol will turn off when the

symbol turned off)

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Use thee andd keys to scroll the formula right and left.

PressJ or w to return to the screen that was displayed before you pressed

(LOOK).

Built-in Formula Names

For details about the calculation formula used by each built-in formula, see <#09> in the separate Supplement.

No. Displayed Name Formula Name

1 2-Line Int Angle of Intersect for Two Straight Lines 2 Acceleration Acceleration 3 Advance Dist Distance of Advance 4 Area&IntAngl Area and Interior Angle of a Triangle (3 Sides) 5ArithProgSum Sum of Arithmetic Progression 6AvgGasMolSpd Average Gaseous Molecular Speed 7 AxisMov&Rota Movement and Rotation of a Coordinate Axis 8 Bernoulli 1 Bernoulli’s Theorem (1)

9 Bernoulli 2 Bernoulli’s Theorem (2) 10 Bernoulli 3 Bernoulli’s Theorem (3) 11 Binomial PD Probability Function of Binomial Distribution 12 C-PointCoord Coordinate of a Center Point 13 CarnotCycEf1 Efﬁ ciency of Carnot’s Cycle (1) 14 CarnotCycEf2 Efﬁ ciency of Carnot’s Cycle (2) 15 CentriForce1 Centrifugal Force (1) 16 CentriForce2 Centrifugal Force (2) 17 ChordWarVel Velocity of Wave Transmitted by a Chord 18 CircCone Lat Lateral Area of a Circular Cone 19 CircCone Vol Volume of a Circular Cone 20 CircCylinLat Lateral Area of a Circular Cylinder 21 CircCylinVol Volume of a Circular Cylinder 22 CircMotCyc 1 Cycle of Circular Motion (1) 23 CircMotCyc 2 Cycle of Circular Motion (2) 24 CircMotCyc 3 Cycle of Circular Motion (3) 25 Circle Area Area of a Circle 26 ConductResis Resistance of a Conductor 27 Cont Equa 1 Equation of Continuity (1) 28 Cont Equa 2 Equation of Continuity (2) 29 Conv Y



Conversion

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Casio fx-5800P User Manual

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