• 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 ofany kind whatsoever by any other party arising out of the use of thisproduct and the items that come with it.
•Unless specifically stated, all sample operations in this manual assumethat the calculator is in its initial default setup. Use the procedure under“Initializing the Calculator” to return the calculator to its initial defaultsetup.
•The contents of this manual are subject to change without notice.
•The displays and illustrations (such as key markings) shown in thismanual are for illustrative purposes only, and may differ somewhat fromthe actual items they represent.
•Company and product names used in this manual may be registeredtrademarks or trademarks of their respective owners.
Initializing the Calculator
Perform the following procedure when you want to initialize the calculatorand return the calculation mode and setup (except for the Contrast setting)to their initial default settings. Note that this operation also clears all datacurrently in calculator memory.
(RESET)(Initialize All)(Yes)
Precautions
Be sure to read the following safety precautions before using the
calculator.
Safety Precautions
Battery
Keep batteries out of the reach of small children.
•
4
• Use only the type of battery specified for this calculator in this
manual.
Handling Precautions
• fx-83GT X: Even if the calculator is operating normally, replace the
battery at least once every two years (R03 (UM-4)).
fx-85GT X: Even if the calculator is operating normally, replace the
battery at least once every three years (LR44).
A dead battery can leak, causing damage to and malfunction of thecalculator. Never leave a dead battery in the calculator. Do not try usingthe calculator while the battery is completely dead (fx-85GT X).
•The battery that comes with the calculator discharges slightly duringshipment and storage. Because of this, it may require replacementsooner than the normal expected battery life.
•Avoid use and storage of the calculator in areas subjected totemperature extremes, and large amounts of humidity and dust.
•Do not subject the calculator to excessive impact, pressure, or bending.
•Never try to take the calculator apart.
•Use a soft, dry cloth to clean the exterior of the calculator.
•Whenever discarding the calculator or batteries, be sure to do so inaccordance with the laws and regulations in your particular area.
Getting Started
Removing the Hard Case
Before using the calculator, slide its hard case downwards to remove it,and then affix the hard case to the back of the calculator as shown in theillustration below.
Turning Power On and Off
Press to turn on the calculator.
•
• Press (OFF) to turn off the calculator.
5
Note
• The calculator also will turn off automatically after approximately 10 minutes of nonuse. Press the key to turn the calculator back on.
Adjusting Display Contrast
1. Press
(SETUP).
• This displays the setup menu.
2. Press .
3. Press (Contrast).
•This displays the contrast adjustment screen.
4. Use and to adjust display contrast.
5. After the setting is the way you want, press .
Important!
•If adjusting display contrast does not improve display readability, it probably meansthat battery power is low. Replace the battery.
Key Markings
Pressing the alternate function of the second key. The alternate function is indicated bythe text printed above the key.
or key followed by a second key performs the
(1) Keycap function (2) Alternate function
6
• The following shows what the different colors of the alternate function
key text mean.
•The following shows an example of how an alternate function operationis represented in this manual.
Example: (sin
-1*
)
* Indicates the function that is accessed by the key operation (
) before it. Note that this is not part of the actual key operation
you perform.
•The following shows an example of how a key operation to select an on-screen menu item is represented in this manual.
Example:
(Input/Output)
* Indicates the menu item that is selected by the number key
operation () before it. Note that this is not part of the actual keyoperation you perform.
•The cursor key is marked with four arrows, indicating direction, asshown in the illustration nearby. In this manual, cursor key operation isindicated as , , , and .
•Pressing the displays an options screen. The options screen showsfunctions that can be used in a calculation. The functions listed on theoptions screen depend on the calculation mode.
7
Reading the Display
(1) Input expression
(2) Calculation result
(3) Indicators
•If a or indicator appears on the right side of either the inputexpression line (1) or calculation result line (2), it means the displayedline continues to the right. Use and to scroll the line display.Note that if you want to scroll the input expression while both the and
indicators are displayed, you will need to press first and then use
and to scroll.
•The table below describes some of the typical indicators that appear atthe top of the screen (3).
This indicator:Means this:
The keypad has been shifted by pressing the key. The keypad will unshift and this indicator willdisappear when you press a key.
The alpha input mode has been entered bypressing the key. The alpha input mode willbe exited and this indicator will disappear whenyou press a key.
Indicates the current setting of Angle Unit (:
//
FIXA fixed number of decimal places is in effect.
SCIA fixed number of significant digits is in effect.
MThere is a value stored in independent memory.
Degree, : Radian, or : Gradian) on the setupmenu.
The calculator is standing by for input of a variable
name to assign a value to the variable. This
indicator appears after you press .
Indicates that MathI/MathO or MathI/DecimalO is
selected for Input/Output on the setup menu.
8
The display currently shows an intermediate result
of a multi-statement calculation.
This indicator is displayed while the calculator is
being powered directly by its solar cells, either
entirely or in some combination with the battery.
(fx-85GT X only)
Using Menus
Some of the operations of this calculator are performed using menus.Menus are displayed by pressing General menu operation operations are described below.
•You can select a menu item by pressing the number key thatcorresponds to the number to its left on the menu screen.
or and then (SETUP).
•A vertical scroll bar (1) indicates that the menu runs off the screen. Inthis case, you can use and to scroll the menu up and down. Aleft arrow (2) indicates that the currently displayed menu is a sub-menu.To return from a sub-menu to its parent menu, press .
•To close a menu without selecting anything, press .
9
Calculation Modes and
Calculator Setup
Calculation Mode
The calculation modes of this calculator are described below.
Icon:Description:
General calculations
(Calculate)
Statistical and regression calculations
(Statistics)
Generate a number table based on one or twofunctions
(Table)
Ratio calculations
(Ratio)
Specify the calculation mode that is suitable for the type of calculation youwant to perform.
1. Press to display the Main Menu.
2. Use the cursor keys to move the highlighting to the icon you want.
3. Press to display the initial screen of the mode whose icon you
selected.
10
Note
• You can also enter a mode without highlighting an icon in the Main Menu by inputting
the number or letter marked in the lower right corner of the icon.
• The initial default calculation mode is the Calculate Mode.
Configuring the Calculator Setup
Pressing
(SETUP) displays the setup menu, which you can use to
control how the calculations are executed and displayed.
To change the calculator setup
1. Press (SETUP) to display the setup menu.
2. Use and to scroll the setup menu, and then input the numberdisplayed to the left of the item whose setting you want to change.
Items and Available Setting Options
“◆” indicates the initial default setting.
Input/Output
Specifies the format to be used by the calculator for formula input andcalculation result output.
To specify this typeof input and output:
Perform this key operation:
Input: NaturalTextbookOutput: Format thatincludes a fraction
*1
Input: NaturalTextbookOutput: Converted todecimal value
Input: Linear
*2
Output: Decimal or
fraction
(SETUP)(Input/Output) (MathI/
MathO)◆
(SETUP)(Input/Output) (MathI/
DecimalO)
(SETUP)(Input/Output) (LineI/
LineO)
11
Input: Linear
*2
(SETUP)(Input/Output) (LineI/
Output: Converted to
DecimalO)
decimal value
*1 Decimal output is applied when this format cannot be output for some
reason.
*2 All calculations, including fractions and functions are input in a single
line. Same output format as that for models without Natural Textbook
Display (S-V.P.A.M. models, etc.)
Input/Output Format Display ExamplesMathI/MathO
MathI/DecimalO
LineI/LineO
LineI/DecimalO
Angle Unit
Specifies degree, radian or gradian as the angle unit for value input andcalculation result display.
To specify this as the
Perform this key operation:
default angle unit:
(SETUP)(Angle Unit) (Degree)
Degrees
◆
Radians(SETUP)(Angle Unit) (Radian)
12
Grads
(SETUP)(Angle Unit)
(Gradian)
90°= π/2 radians = 100 grads
Number Format
Specifies the number of digits for display of a calculation result.
To specify this:Perform this key operation:
Number of DecimalPlaces
Number of SignificantDigits
Exponential DisplayRange
(Fix) -
(Sci) -
(Norm) (Norm 1◆) or (Norm 2)
(SETUP)(Number Format)
(SETUP)(Number Format)
(SETUP)(Number Format)
Calculation Result Display Examples
•Fix: The value you specify (from 0 to 9) controls the number of decimalplaces for displayed calculation results. Calculation results are roundedoff to the specified digit before being displayed.
Example: 100
7(≈)* 14.286 (Fix 3)
14.29 (Fix 2)
•Sci: The value you specify (from 0 to 9) controls the number ofsignificant digits for displayed calculation results. Calculation results arerounded off to the specified digit before being displayed.
Example: 17(≈)* 1.4286×10-1(Sci 5)
1.429×10-1(Sci 4)
•Norm: Selecting one of the two available settings (Norm1, Norm2)determines the range in which results will be displayed in exponentialformat. Outside the specified range, results are displayed using non-exponential format.
0.005 (Norm 2)
* Pressing (≈) instead of after inputting a calculation will
display the calculation result in decimal form.
13
Fraction Result
Specifies either mixed fraction or improper fraction for display of fractions
in calculation results.
To specify this
fraction display
format:
Mixed
Improper
Statistics
Specifies whether or not to display a Freq (frequency) column in theStatistics Mode Statistics Editor.
To specify this:Perform this key operation:
Show frequency
Perform this key operation:
(SETUP)(Fraction Result)
(ab/c)
(SETUP)(Fraction Result)
(d/c)◆
(SETUP)(Statistics) (On)
Column
(SETUP)(Statistics) (Off)◆
Hide frequencyColumn
Table
Specifies whether to use function f(x) only or the two functions f(x) and g(x)
in the Table Mode.
To specify this:Perform this key operation:
f(x) only(SETUP)(Table) (f(x))
f(x) and g(x)(SETUP)(Table) (f(x),g(x))◆
14
Recurring Dec
Specifies whether or not to use recurring decimal form in calculation
results.
To specify this:Perform this key operation:
Use recurring decimal
form
Do not use recurringdecimal form
(On)◆
(Off)
(SETUP)(Recurring Dec)
(SETUP)(Recurring Dec)
Decimal Mark
Specifies whether to display a dot or a comma for the calculation resultdecimal mark. A dot is always displayed during input.
To specify thisdecimal point
Perform this key operation:
display format:
(SETUP)(Decimal Mark)
Dot (.)
(Dot)◆
(SETUP)(Decimal Mark)
Comma (,)
(Comma)
Note
•
When dot is selected as the decimal mark, the separator for multiple results is acomma (,). When comma is selected, the separator is a semicolon (;).
Digit Separator
Specifies whether or not to use separator symbols in calculation results.
To specify this:Perform this key operation:
Use three-digit
separator character
Do not use three-digit
separator character
(SETUP)(Digit Separator)
(On)
(SETUP)(Digit Separator)
(Off)◆
15
MultiLine Font
Specifies the display font size when LineI/LineO or LineI/DecimalO is
selected for Input/Output. Up to four lines can be displayed while Normal
Font is selected, and up to six lines can be displayed with Small Font.
To specify this:Perform this key operation:
Use normal font
Use small font
(SETUP)(MultiLine Font)
(Normal Font)◆
(SETUP)(MultiLine Font)
(Small Font)
Initializing the Calculation Mode and OtherSettings
Performing the following procedure initializes the calculation mode andother setup settings as shown below. (except the Contrast setting)
(RESET)(Setup Data)(Yes)
This setting:Is initialized to this:
Calculation ModeCalculate
Input/OutputMathI/MathO
Angle UnitDegree
Number FormatNorm 1
Fraction Resultd/c
StatisticsOff
Table
Recurring DecOn
Decimal MarkDot
Digit SeparatorOff
MultiLine FontNormal Font
• To cancel initialization without doing anything, press (Cancel) instead
of .
f(x),g(x)
16
Inputting Expressions and
Values
Inputting a Calculation Expression
Using Values
Inputting a Calculation Expression Using StandardFormat
Your calculator lets you input calculation expressions just as they arewritten. Then simply press the automatically judges the calculation priority sequence for addition,subtraction, multiplication, and division, functions, and parentheses.
Example:2(5 + 4) -2 × (-3) =
key to execute it. The calculator
25423
Note
•If you execute a calculation that includes both division and multiplication operations inwhich a multiplication sign has been omitted, parentheses will be insertedautomatically as shown in the examples below.
- When a multiplication sign is omitted immediately before an open parenthesis orafter a closed parenthesis.Example:6 ÷ 2(1 + 2) → 6 ÷ (2(1 + 2))
6212
- When a multiplication sign is omitted immediately before a variable, a constant,
etc.
Example: 4
π ÷ 2π → 4π ÷ (2π)
4
(π)2(π)
17
• Normally the input cursor appears as a straight vertical ( ) or horizontal () flashing
line on the display screen. When there are 10 or fewer bytes of input remaining in the
current expression, the cursor changes shape to to let you know. If the cursor
appears, terminate the expression at a convenient point and calculate the result.
Correcting an Expression
This section explains how to correct an expression as you are inputting it.The procedure you should use depends on the current Input/Outputsetting on the setup menu.
Changing the Character or Function You Just Input
Example:To correct the expression 369 × 13 so it becomes 369 × 12
36913
2
Deleting a Character or Function
Example:To correct the expression 369 × × 12 so it becomes 369 × 12
36912
18
Correcting a Calculation
Example: To correct cos(60) so it becomes sin(60)
60
Inserting Input into a Calculation
Use insert the character or function and then input it. Be sure always to use theinsert mode if LineI/LineO or LineI/DecimalO is selected.
and to move the cursor to the location where you want to
Clearing all of the calculation you are inputting
Press .
Overwrite Input Mode (LineI/LineO or LineI/DecimalO only)
In the overwrite mode, text you input replaces the text at the current cursorlocation. You can toggle between the insert and overwrite modes byperforming the operations: insert mode and as “” in the overwrite mode.(LineI/LineO or LineI/DecimalO)
(INS). The cursor appears as “” in the
(INS)
Deleting a Character or Function
Example: To correct the expression 369 × × 12 so it becomes 369 × 12
19
36912
Correcting a Calculation
Example:To correct cos(60) so it becomes sin(60)
60
Inputting an Expression UsingNatural Textbook Format (MathI/MathO or MathI/DecimalO Only)
Formulas and expressions that include fractions and/or special functionssuch as √appear when certain keys are pressed.
Note
• When you press and obtain a calculation result, part of the expression you input
may be cut off. If you need to view the entire input expression again, press and
then use and to scroll the input expression.
can be input in natural textbook format by using templates that
20
Natural Textbook Format Input Examples
• Pay close attention to the location and size of the cursor on the display
when you input using natural textbook format.
Example 1: To input 23 + 1
23
1
Example 2:To input 1 + √2 + 3
12
Example 3:To input 3
1
+ 5
2
3
32
()
312
() 532
Example 4: To input ( 1 +
1252
2
)2 × 2
5
21
Example 5: To input
Tip: While the input cursor is located within the input area of a template
(mixed fractions), pressing jumps to the position immediately
following (to the right) of the template, while pressing jumps tothe position immediate before (to the left of) it.
2 + √2
1 + √2
2212
Undo Operations
To undo the last key operation, press To redo a key operation you have just undone, press (UNDO)again.
(UNDO).
Incorporating a Value into a Function
When using natural textbook format, you can incorporate part of an inputexpression (a value, an expression within parentheses, etc.) into afunction.
Example:To incorporate the expression inside of the parentheses of 1 +
(2 + 3) + 4 into the √
function
1
234
(INS)
This changes the shape of the cursor as shown here.
This incorporates the expression in the parentheses into the function √ .
22
Displaying Calculation Results in a
Form that Includes √2, π, etc.
(Irrational Number Form)
While MathI/MathO is selected for Input/Output on the setup menu, you
can specify whether calculation results should be displayed in a form that
includes expressions like √2 and π (irrational number form).
•Pressing after inputting a calculation displays the result usingirrational number form.
•Pressing (≈) after inputting a calculation displays the result usingdecimal values.
Note
•When MathI/DecimalO or LineI/DecimalO is selected for Input/Output on the setupmenu, calculation results are always displayed using decimal values (no irrationalnumber form) regardless of whether you press or (≈).
•The following are the πforms that are supported.
n
π(n is an integer.)
d
b
πor a
c
π(depending on fraction display format setting)
c
Example 1:√
Example 2:sin(60) =
Example 3: sin-1(0.5) =
2 + √8 = 3√2 (MathI/MathO)
√32
28
28(≈)
(MathI/MathO) (Angle Unit: Degree)
60
1
(MathI/MathO) (Angle Unit: Radian)
π
6
23
(sin-1) 0.5
24
Basic Calculations
Recurring Decimal Calculations
Your calculator uses a recurring decimal when you input a value.
Calculation results also can be displayed using recurring decimal form
whenever applicable.
Inputting a Recurring Decimal
When inputting a recurrent decimal, press period (repetend) and then input the period up to the ending value. To
input the recurring decimal 0.909090.... (0.90), perform the following
operation: “0() 90”.
Important!
•
If the value starts with an integer part (like: 12.3123123...), do not include the integerpart when inputting the period(12.312).
•Recurring decimal input is possible only when MathI/MathO or MathI/DecimalO isselected for Input/Output on the setup menu.
Example 1:To input 0.33333… (0.
3)
0
() before inputting its
()
3
Example 2: To input 1.428571428571... (1.428571)
1()
25
428571
Example 3: To calculate 1.021 + 2.312
1() 021
2() 312
Calculation result displayed as recurring decimal value:
Displaying a Calculation Result as a RecurringDecimal Value
Calculation results that can be displayed as recurring decimal values willbe displayed as such when On is selected for the Recurring Dec setting onthe setup menu.Pressing the formats.
Example 1:
Display as recurring decimal:
key will cycle between the available calculation result
Conditions for Displaying a Calculation Result as aRecurring Decimal
If a calculation result satisfies the following conditions, pressing
display it as a recurring decimal value.
• The total number of digits used in the mixed fraction (including integer,
numerator, denominator, and separator symbol) must be no more than
10.
28
will
Recurring Decimal Examples
Example 1: 0.
Example 2: 1.6 + 2.8 = 4.5
Example 3:To confirm the following: 0.123=
0.12345 =
3 + 0.45 = 0.78
0() 3
0() 45
1() 6
2() 8
1234599999
123
, 0.1234 =
999
12349999
,
123999
12349999
1234599999
29
Toggling Calculation Results
While MathI/MathO or MathI/DecimalO is selected for Input/Output on the
setup menu, each press of
calculation result between its fraction form and decimal form, its √ form
and decimal form, or its π form and decimal form.
Example 1: Fraction → Decimal (MathI/MathO) (Recurring Dec: Off)
Each press of the key toggles between the two forms.
will toggle the currently displayed
56
The format of the fraction depends on the currently selected FractionResult setting (improper fraction or mixed fraction).
Example 2:
Example 3:(√2 + 2) × √3 = 5.913591358 = √6 + 2√3
(MathI/DecimalO)
π÷ 6 =
1
π= 0.5235987756 (MathI/MathO)
6
(π)6
223
30
While LineI/LineO or LineI/DecimalO is selected for Input/Output on the
setup menu, each press of will toggle the currently displayed
calculation result between its decimal form and fraction form.
Example 4: 1 ÷ 5 = 0.2 =
4
Example 5:1 -
1
=
5
= 0.2 (LineI/LineO)
5
1
(LineI/LineO)
5
145
15
Important!
•With certain calculation results, pressing the key will not convert the displayedvalue.
•You cannot switch from decimal form to mixed fraction form if the total number of digitsused in the mixed fraction (including integer, numerator, denominator, and separatorsymbol) is greater than 10.
To obtain a decimal value calculation result while MathI/MathO or LineI/LineO is selected
Press
(≈) instead of after inputting a calculation.
Arithmetic Calculations
Use the
Example: To divide the result of 7 × 8 - 4 × 5 = 36
, , , and keys to perform arithmetic calculations.
31
7845
• The calculator automatically judges the calculation priority sequence.
Number of Decimal Places and Number of
Significant Digits
You can specify a fixed number of decimal places and significant digits forthe calculation result.
Example:1 ÷ 6 =
Initial default setting (Norm 1)
16(≈)
3 decimal places (Fix 3)
16(≈)
3 significant digits (Sci 3)
16(≈)
Omitting a Final Closed Parenthesis
Example:(2 + 3) × (4 -1 = 15
2341
Fraction Calculations
Note that the input method for fractions depends on the current Input/
Output setting on the setup menu.
32
MathI/MathO
MathI/DecimalO
LineI/LineO
Improper FractionMixed Fraction
1
7
3
(() 213
2
3
(73 or 7
or () 21
3 or 73)
3)
LineI/DecimalO
Note
•Under initial default settings, fractions are displayed as improper fractions.
•Mixing fractions and decimal values in a calculation while something other than MathI/MathO is selected will cause the result to be displayed as a decimal value.
•Fractions in calculation results are displayed after being reduced to their lowest terms.
2
1
Example 1:
+
3
7
=
2
6
(73)
(213)
(MathI/MathO)
2312
(LineI/LineO)
Example 2:3
(MathI/MathO)
14
+ 1
2312
23
= 4
11
(Fraction Result: ab/c)
12
() 314
33
(LineI/LineO)
Example 3:4 -3
(MathI/MathO)
4() 312
(LineI/LineO)
() 123
314123
1
1
=
2
(Fraction Result: ab/c)
2
4312
Note
•If the total number of digits used for a mixed fraction (including integer, numerator,denominator, and separator symbols) is greater than 10, the value is automaticallydisplayed in decimal format.
•The result of a calculation that involves both fraction and decimal values is displayedin decimal format.
Switching between Improper Fraction and MixedFraction Format
Pressing the mixed fraction and improper fraction format.
() key toggles the display fraction between
Percent Calculations
Inputting a value and pressing (%) causes the input value to
become a percent.
Example 1: 2% = 0.02 (
2
100
)
34
2(%)(≈)
Example 2: 150 × 20% = 30 (150 ×
15020(%)
Example 3:Calculate what percentage of 880 is 660. (75%)
660880(%)
Example 4:Increase 2500 by 15%. (2875)
2500250015(%)
20
100
)
Example 5:Discount 3500 by 25%. (2625)
3500350025(%)
Example 6:Discount the sum of 168, 98, and 734 by 20%. (800)
16898734
20(%)
Example 7: 300 grams are added to a test sample originally weighing 500
grams, producing a final test sample of 800 grams. What percent of 500
grams is 800 grams? (160%)
35
500300500(%)
Example 8: What is the percentage change when a value is increased
from 40 to 46? How about to 48? (15%, 20%)
464040(%)
8
Degree, Minute, Second(Sexagesimal) Calculations
You can perform calculations using sexagesimal values, and convertvalues between sexagesimal and decimal.
Inputting Sexagesimal Values
The following is the syntax for inputting a sexagesimal value.{Degrees}
•Note that you must always input something for the degrees andminutes, even if they are zero.
Example:Input 2°0’30”
{Minutes}{Seconds}
2030
Sexagesimal Calculations
Performing the following types of sexagesimal calculations produces a
sexagesimal result.
- Addition or subtraction of two sexagesimal values
- Multiplication or division of a sexagesimal value and a decimal value
Example: 2°20’30” + 39’30” = 3°00’00”
36
2203003930
Converting Values between Sexagesimal and
Decimal
Pressing
between sexagesimal and decimal.
Example:Convert 2.255 to its sexagesimal equivalent.
while a calculation result is displayed toggles the value
2.255(≈)
Multi-Statements
You can use the colon character (:) to connect two or more expressionsand execute them in sequence from left to right when you press .
Example:To create a multi-statement that performs the following two
calculations: 3 + 3 and 3 × 3 (MathI/MathO)
33(:) 33
“” indicates this is an intermediate result of a multi-statement.
Note
• Inputting a colon (:) while LineI/LineO or LineI/DecimalO is selected for the Input/
Output setting on the setup menu causes a newline operation to be performed.
37
(LineI/LineO)
33(:) 33
“” indicates this is an intermediate result of a multi-statement.
Using Engineering Notation
A simple key operation transforms a displayed value to engineeringnotation. Engineering notation converts the exponent part of a displayedcalculation result value to a power of ten that is a multiple of 3, anddisplays the result.
Example 1:Transform the value 1234 to engineering notation, shifting the
decimal point to the right.
1234
Example 2:Transform the value 123 to engineering notation, shifting the
decimal point to the left.
38
123
(←)
(←)
Prime Factorization
In the Calculate Mode, a positive integer no more than 10 digits long can
be factored to prime factors.
Example:To perform prime factorization on 1014
1014
(FACT)
•To re-display the unfactored value, press (FACT) or .
Example:To perform prime factorization on 4104676 (= 22× 10132)
4104676
(FACT)
Any one of the following operations will exit prime factorization resultdisplay.
- Pressing
(FACT) or .
- Pressing any of the following keys: or .
Note
• The types of values described below cannot be factored, even if they have 10 or fewer
digits.
- One of the prime factors of the value is 1018081 or greater.
- Two or more of the prime factors of the value have more than three digits.
• The part that cannot be factored will be enclosed in parentheses on the display.
39
Calculation History and Replay
Calculation History
An
and/or at the top of the display indicates that there is more
calculation history content above and/or below. You can scroll through
calculation history contents using and .
Note that calculation history can be used in the Calculate Mode only.
Example:(MathI/MathO)
(1 + 1 = 2)
11
(2 + 2 = 4)
22
(3 + 3 = 6)
33
(Scrolls back.)
(Scrolls back again.)
Note
•Calculation history data is all cleared whenever you press , when you change to a
different calculation mode, when you change the Input/Output setting, or whenever
you perform a RESET operation (“Initialize All” or “Setup Data”).
• Calculation history memory is limited. When the calculation you are performing causes
calculation history memory to become full, the oldest calculation is deleted
automatically to make room for the new calculation.
40
Replay
While a calculation result is on the display, you can press
edit the expression you used for the previous calculation.
Example: 4 × 3 + 2 = 14
4 × 3 − 7 = 5
432
7
or to
Note
•If you want to edit a calculation when the indicator is on the right side of acalculation result display, press and then use or to scroll thecalculation.Example:Pol(2, √2) → Pol(2, 2)(MathI/MathO) (Angle Unit: Radian)
(Pol) 2(,)2
41
2
Using Memory Functions
Answer Memory (Ans)
The last calculation result obtained is stored in Ans (answer) memory.
Note
• Ans Memory contents are updated whenever you execute a calculation using any one
of the following keys: , (≈), , (M−), (RECALL),
.
•Ans Memory contents are not change if an error occurs during the current calculation.
Using Ans Memory to Perform a Series of Calculations
Example:To divide the result of 3 × 4 by 30
34
(Continuing) 30
Pressing
•With the above procedure, you need to perform the secondcalculation immediately after the first one. If you need to recall AnsMemory contents after pressing
automatically inputs “Ans” command.
, press the key.
Inputting Ans Memory Contents into an Expression
Example:To perform the calculations shown below:
123456
(Continuing) 789
42
Variables (A, B, C, D, E, F, M, x, y)
Your calculator has nine preset variables named A, B, C, D, E, F, M,
, and
x
y.
You can assign values to variables and use the variables in calculations.
• You can assign a specific value or a calculation result to a variable.
Example: To assign the result of 3 + 5 to variable A.
35(A)
Example:To assign the result of 4 × 6 to variable x.
46(x)
•Use the following procedure when you want to check the contents of avariable.
Example:To recall the contents of variable A
(Continuing) (RECALL)
*1
(A)
*1 Pressing (RECALL) displays a screen that shows the values
currently assigned to variables A, B, C, D, E, F, M, x, and y. On thisscreen, values are always displayed using the “Norm 1” NumberFormat. To close the screen without recalling a variable value, press
.
•The following shows how you can include variables inside of anexpression.
Example:To multiply the contents of variable A by the contents of
variable B
(Continuing) 12(B)
(A)(B)
43
*2
*2 Input a variable as shown here: press and then press the key that
corresponds to the desired variable name. To input x as the variable
name, you can press
(x).
Example:
9×6+3
5×8
= 1.425
963(B)
58(C)
(B)(C)(≈)
Clearing the Contents of a Specific Variable
Press 0contents you want to clear.
Example:To clear the contents of variable A
and then press the key for the name of the variable whose
0(A)
Independent Memory (M)
You can add calculation results to or subtract results from independentmemory. The “M” appears on the display when independent memorycontains a value.
•The following is a summary of the different operations you can performusing independent memory.
To do this:Perform this key operation:
Add the displayed
value or result of the
expression to
independent memory
44
Subtract the displayed
value or result of the
expression from
independent memory
Recall current
independent memory
contents
•Variable M is used for independent memory.
•You can also insert the M variable into a calculation, which tells thecalculator to use the current independent memory contents at thatlocation. The following is the key operation for inserting the M variable.
(M)
•The “M” indicator appears on the display when there is any value otherthan zero stored in independent memory.
(M−)
(RECALL)(M)
Calculation Examples Using Independent Memory
•If the “M” indicator is on the display, perform the procedure under“Clearing Independent Memory” before performing this example.
Example:23 + 9 = 32
53 - 6 = 47
-) 45 × 2 = 9099 ÷ 3 = 33
(Total)22
239
536
452(M−)
993
45
(RECALL)(M)
Clearing Independent Memory
Press 0
“M” indicator to disappear from the display.
(M). This clears independent memory and causes the
0(M)
Clearing the Contents of All Memories
Ans memory, independent memory, and variable contents are retainedeven if you press calculator.
Perform the procedure below when you want to clear the contents of allmemories.
(RESET)(Memory)(Yes)
•To cancel the clear operation without doing anything, press (Cancel)instead of .
, change the calculation mode, or turn off the
46
Function Calculations
Pi (
π), Natural Logarithm Base e
Pi (π)
You can input pi (
The following shows the required key operations and the values thiscalculator uses for pi (
π= 3.14159265358980 ((π))πis displayed as 3.141592654, but π= 3.14159265358980 is used for
internal calculations.
Natural Logarithm Base
You can input natural logarithm base einto a calculation.The following shows the required key operations and the values thiscalculator uses for
e= 2.71828182845904 ((e))eis displayed as 2.718281828, but e= 2.71828182845904 is used for
•The angle unit required by trigonometric functions is one specified asthe calculator’s default angle unit. Before performing a calculation, besure to specify the default angle unit you want to use.
Example:sin 30 =
Inverse Trigonometric Functions
The angle unit required by inverse trigonometric functions is one
•
specified as the calculator’s default angle unit. Before performing a
calculation, be sure to specify the default angle unit you want to use.
•Input a function from the menu that appears when you press (Hyperbolic Func)*.* Depending on the calculation mode, you should press .
Example 1:sinh 1 = 1.175201194
(Hyperbolic Func)
(sinh) 1
Example 2:cosh 0 = 1
(Hyperbolic Func)
(cosh) 0
Inverse Hyperbolic Functions
Input a function from the menu that appears when you press
•
(Hyperbolic Func)*.
* Depending on the calculation mode, you should press .
Example : cosh-1 1 = 0
(Hyperbolic Func)
48
(cosh-1) 1
Converting an Input Value to the
Calculator’s Default Angle Unit
After inputting a value, press specification menu shown below. Press the number key that correspondsto the angle unit of the input value. The calculator will automaticallyconvert it to the calculator’s default angle unit.
* Depending on the calculation mode, you should press
° : Degrees, r: Radians, g: Gradians
Example 1:To convert the following values to degrees:
50 grads = 45°The following procedure assumes that the calculator’s default angle unitis degrees.
• For the logarithmic function “log(”, you can specify base m using the
syntax “log (
If you input only a single value, a base of 10 is used for the calculation.
• “ln(” is a natural logarithm function with base e.
• You can also use the key when inputting an expression with the
form of “logmn” while using MathI/MathO or MathI/DecimalO format. For
details, see Example 1. Note that you must input the base (base
when using the
Example 1:log216 = 4
(MathI/MathO)
(LineI/LineO)
m, n)”.
m)
key for input.
216
(or ) 2(,) 16
Example 2:log16 = 1.204119983
16
A base of 10 (common logarithm) is used if no base is specified.
Example 3:ln 90 (= loge90) = 4.49980967, ln e= 1
90
(e)
51
Power Functions and Power Root
Functions
Example 1: (1 + 1)
Example 2:(52)3= 15625
Example 3:(√2 + 1)(√2-1) = 1
(MathI/MathO)
2121
2+2
= 16
1122
5
(LineI/LineO)
2121
Example 4:5√32 = 2
(MathI/MathO)
(LineI/LineO)
() 532
5() 32
Example 5: (-2)
(MathI/MathO)
2
3
= 1.587401052
52
223
(LineI/LineO)
223
Example 6:3√5 + 3√-27 = -1.290024053
(MathI/MathO)
() 5
()27
(LineI/LineO)
() 5
()27
Example 7:= 12
(MathI/MathO)
34
Rectangular-Polar CoordinateConversion
Coordinate conversion can be performed in the Calculate and Statistics
•
calculation modes.
53
• Pol converts rectangular coordinates to polar coordinates, while Rec
converts polar coordinates to rectangular coordinates.
• Specify the angle unit before performing calculations.
Converting to Polar Coordinates (Pol)
Pol(X, Y)X: Specifies the rectangular coordinate X value
Y: Specifies the rectangular coordinate Y value
• Calculation result θ is displayed in the range of -180° < θ < 180°.
• Calculation result θ is displayed using the calculator’s angle unit.
•Calculation result ris assigned to variable X, while θis assigned to Y.
Converting to Rectangular Coordinates (Rec)
r, θ)r: Specifies the polar coordinate rvalue
Rec(
θ: Specifies the polar coordinate θvalue
•Input value θis treated as an angle value, in accordance with thecalculator’s angle unit setting.
•Calculation result xis assigned to variable X, while yis assigned to Y.
•If you perform coordinate conversion inside of an expression instead ofa stand-alone operation, the calculation is performed using only the firstvalue (either the r-value or the X-value) produced by the conversion.Example: Pol (√
This function obtains the factorials of a value that is zero or a positiveinteger.
Example: (5 + 3)! = 40320
53(x!)
55
Absolute Value Calculation (Abs)
Generate three 3-digit random numbers.The random 3 digit decimal values are converted to 3-digitinteger values by multiplying by 1000.Note that the values shown here are examples only. Valuesactually generated by your calculator will be different.
When you are performing a real number calculation, this function simply
obtains the absolute value.
Example: Abs(2 - 7) = |2 - 7| = 5
(MathI/MathO)
27
(LineI/LineO)
27
Random Number (Ran#), RandomInteger (RanInt#)
Random Number (Ran#)
Function that generates a pseudo random number in the range of 0.000 to
0.999.The result is displayed as a fraction when MathI/MathO is selected forInput/Output on the setup menu.
Example:
1000(Ran#)
56
Random Integer (RanInt#)
To generate random integers in the range of 1 to 6.
Note that the values shown here are examples only.
Values actually generated by your calculator will be different.
For input of the function of the form RanInt#(
random integer within the range of
Example:
(RanInt) 1(,) 6
a to b.
a, b), which generates a
Permutation (nPr) and Combination
nCr)
(
These functions make it possible to perform permutation and combinationcalculations.nand rmust be integers in the range of 0 ≦r≦n< 1 × 1010.
Example:To determine the number of permutations and combinations
possible when selecting four people from a group of 10.Permutations:
10(nPr) 4
Combinations:
10(nCr) 4
57
Rounding Function (Rnd)
Using the Rnd function causes decimal fraction values of the argument to
be rounded in accordance with the current Number Format setting.
Number Format: Norm 1 or Norm 2
The argument is rounded off to 10 digits.
Number Format: Fix or Sci
The argument is rounded off to the specified digit.When Fix 3 is the Number Format setting, for example, the result of 10 ÷ 3is displayed as 3.333, while the calculator maintains a value of
3.33333333333333 (15 digits) internally for calculation. In the case ofRnd(10÷3) = 3.333 (with Fix 3), both the displayed value and thecalculator’s internal value become 3.333. Because of this a series ofcalculations will produce different results depending on whether Rnd isused (Rnd(10÷3) × 3 = 9.999) or not used (10 ÷ 3 × 3 = 10.000).
Example:To perform the following calculation when Fix 3 is selected for
the number of display digits: 200 ÷ 7 × 14 = 400 (MathI/DecimalO)
200714
(Calculation is performed internally using 15 digits.)
2007
14
The following performs the same calculation with rounding.
2007
(Round the value to the specified number of digits.)
(Rnd)
58
(Check rounded result.)
14
59
Using Calculation Modes
Statistical Calculations
Perform the steps below to start a statistical calculation.
1. Press
2. On the Select Type screen that appears, press one of the keys below toselect a statistical calculation type.
, select the Statistics Mode icon, and then press .
Performing any of the above key operations displays the Statistics
•Editor.
Single-variable (x)
Paired-variable (x, y), linear regression
Paired-variable (x, y), quadratic regression
Paired-variable (x, y), logarithmic regression
Paired-variable (x, y), abexponentialregression
Paired-variable (x, y), power regression
Paired-variable (x, y), inverse regression
Note
•When you want to change the calculation type after entering the Statistics Mode,
perform the key operation (Select Type) to display the calculation type
selection screen.
60
Inputting Data with Statistics Editor
Statistics Editor
There are two Statistics Editor formats, depending on the type of
statistical calculation you selected.
Single-variable
Paired-variable
•The first line of the Statistics Editor shows the value for the firstsample or the values for their first pair of samples.
Freq (Frequency) Column
If you turn on the Statistics setting on the setup menu, a column labeled“Freq” will also be included on the Statistics Editor.You can use the Freq column to specify the frequency (the number oftimes the same sample appears in the group of data) of each samplevalue.
Single-variable
Paired-variable
61
Rules for Inputting Sample Data on the Statistics Editor
• Data you input is inserted into the cell where the cursor is located.
Use the cursor keys to move the cursor between cells.
•After inputting a value, press . This registers the value anddisplays up to six of its digits in the currently selected cell.
Example 1:To input the value 1234 in cell X1
(Move the cursor to cell X1.)
1234
The value you input appears in the formula area.
Registering a value causes the cursor to move down one cell.
Example 2:To select logarithmic regression and input the following
data: (170, 66), (173, 68), (179, 75)
(Select Type)(y=a+b・ln(x))
170173179
666875
Statistics Editor Input Precautions
The number of lines in Statistics Editor (the number of sample data
•
values you can input) depends on the type of statistical calculation
you selected, and on the Statistics setting on the setup menu.
62
Statistics
setting
Off
(No Freq column)
On
(Freq column)
calculation type
Single-variable160 lines80 lines
Paired-variable80 lines53 lines
•Pressing the key while the Statistics Editor is on the screen willdisplay a statistical calculation screen for performing calculationsbased on the input data. What you need to do to return to theStatistics Editor from the statistical calculation screen depends on thecalculation type you selected. Press (Data) if you selectedsingle-variable or (Data) if you selected paired-variable.
Precautions Concerning Sample Data Storage
•All data currently input in the Statistics Editor is deleted whenever youexit the Statistics Mode, switch between the single-variable and apaired-variable statistical calculation type, or change the Statisticssetting on the setup menu.
Editing Sample Data
To replacing the data in a cell
1. On the Statistics Editor, move the cursor to the cell you want to edit.
2. Input the new data value or expression, and then press .
Important!
•Note that you must totally replace the existing data of the cell with new input. You
cannot edit parts of the existing data.
To delete a line
1. On the Statistics Editor, move the cursor to the line you want to
delete.
2. Press
.
To insert a line
1. On the Statistics Editor, move the cursor to the line that will be
under the line you will insert.
2. Press
(Editor).
3. Press (Insert Row).
63
Important!
• Note that the insert operation will not work if the maximum number of lines allowed
for the Statistics Editor are already used.
To delete all Statistics Editor contents
1. On the Statistics Editor, press
2. Press (Delete All).
(Editor).
Statistical Calculation Screen
The statistical calculation screen is for performing statistical calculationswith the data you input with the Statistics Editor. Pressing the keywhile the Statistics Editor is displayed switches to the statistical calculationscreen.
Using the Statistical Menu
While the Statistics Editor or statistical calculation screen is on the display,press The content to the statistical menu depends on whether the currentlyselected statistical operation type uses a single variable or pairedvariables.
Statistics Editor: Single-variable
Select this menuitem:
(Select Type)
to display the statistical menu.
When you want to do this:
Display the statistical calculation type
selection screen
(Editor)
(1-Variable Calc)Display statistical values based on input data
Display the Editor sub-menu for editing
Statistics Editor contents
64
(Statistics Calc)Display the statistical calculation screen
Statistics Editor: Paired-variable
Select this menuitem:
(Select Type)
(Editor)
(2-Variable Calc)Display statistical values based on input data
(Regression Calc)
(Statistics Calc)Display the statistical calculation screen
Statistical calculation screen: Single-variable
When you want to do this:
Display the statistical calculation typeselection screen
Display the Editor sub-menu for editingStatistics Editor contents
Display regression calculation results basedon input data
65
Select this menu
item:
When you want to do this:
(Select Type)
(1-Variable Calc)Display statistical values based on input data
(Data)Display the Statistics Editor
(Summation)
(Variable)
(Min/Max)
Display the statistical calculation typeselection screen
Display the Summation sub-menu ofcommands for calculating sums
Display the Variable sub-menu of commandsfor calculating the mean, standard deviation,etc.
Display the Min/Max sub-menu of commandsfor obtaining maximum and minimum values
Statistical calculation screen: Paired-variable
66
Select this menu
item:
When you want to do this:
(Select Type)
(2-Variable Calc)Display statistical values based on input data
(Regression Calc)
(Data)Display the Statistics Editor
(Summation)
(Variable)
(Min/Max)
Display the statistical calculation type
selection screen
Display regression calculation results based
on input data
Display the Summation sub-menu ofcommands for calculating sums
Display the Variable sub-menu of commandsfor calculating the mean, standard deviation,etc.
Display the Min/Max sub-menu of commandsfor obtaining maximum and minimum values
(Regression)
Display the Regression sub-menu ofcommands for regression calculations
Displaying Statistical Values Based On Input Data
From the Statistics Editor:
(1-Variable Calc or 2-Variable Calc)
From the statistical calculation screen:
(1-Variable Calc or 2-Variable Calc)
Displaying Regression Calculation Results BasedOn Input Data (Paired-Variable Data Only)
From the Statistics Editor:
(Regression Calc)
From the statistical calculation screen:
(Regression Calc)
67
Single-variable Statistical Calculation Commands
The following are the commands that appear on the sub-menus that
appear when you select Summation, Variable, or Min/Max on the statistical
menu while a single-variable statistical calculation type is selected.
The following is the calculation formula used for each command.
Summation Sub-menu ((Summation))
Select this menu
When you want to obtain this:
item:
(Σx)
(Σx2)
Sum of the sample data
Sum of squares of the sample data
Variable Sub-menu ((Variable))
Select this menu
When you want to obtain this:
item:
(x)Mean of the sample data
2
(σ
)
x
(σx)
2
(s
)Sample variance
x
Population variance
Population standard deviation
(sx)Sample standard deviation
68
(n)
Min/Max Sub-menu ((Min/Max))
Number of items
Select this menuitem:
(min(x))
(Q1)First quartile
(Med)Median
(Q3)Third quartile
(max(x))
When you want to obtain this:
Minimum value
Maximum value
Single-variable Statistical Calculation Examples
Select single-variable and input the following data: {1, 2, 3, 4, 5, 6, 7, 8, 9,10} (Statistics: On)
(Select Type)(1-Variable)
12345678910
Edit the data to the following, using insert and delete: {0, 1, 2, 3, 4, 5, 6, 7,
9, 10}
(Data)
69
(Editor)
(Insert Row)
Edit the Freq data to the following: {1, 2, 1, 2, 2, 2, 3, 4, 2, 1}
(Data)
2222342
Display statistical values based on input data.
(1-Variable Calc)
70
Calculate sum of squares of the sample data and sum of the sample data.
(Summation)
(Σx2)
(Summation)
(Σx)
Calculate number of samples, mean, and population standard deviation.
(Variable)
(n)
(Variable)
(x)
(Variable)
(σx)
Calculate minimum value and maximum value.
(Min/Max)
(min(x))
(Min/Max)
(max(x))
71
Linear Regression Calculation (y=a+bx)
Commands
With linear regression, regression is performed in accordance with the
following model equation.
y = a + bx
The following is the calculation formula used for each command.
Summation Sub-menu ((Summation))
Select this menuitem:
(Σx)
(Σx2)
(Σy)
(Σy2)
When you want to obtain this:
Sum of the x-data
Sum of squares of the x-data
Sum of the y-data
Sum of squares of the y-data
72
(Σxy)
Sum of products of the x-data and y-data
(Σx3)
(Σx2y)
(Σx4)
Sum of cubes of the x-data
Sum of (x-data squares × y-data)
Sum of biquadrate of the x-data
Variable Sub-menu ((Variable))
Select this menu
When you want to obtain this:
item:
(x)Mean of the x-data
2
(σ
)
x
Population variance of the x-data
(σx)
2
(s
)Sample variance of the x-data
x
Population standard deviation of the x-data
(sx)Sample standard deviation of the x-data
(n)
Number of items
(y)Mean of the y-data
2
(σ
)
y
(σy)
2
(s
)Sample variance of the y-data
y
Population variance of the y-data
Population standard deviation of the y-data
(sy)Sample standard deviation of the y-data
Min/Max Sub-menu ((Min/Max))
73
Select this menu
item:
When you want to obtain this:
(min(x))
(max(x))
(min(y))
(max(y))
Regression Sub-menu ((Regression))
Select this menuitem:
(a)
Minimum value of the x-data
Maximum value of the x-data
Minimum value of the y-data
Maximum value of the y-data
When you want to obtain this:
Regression coefficient constant term a
(b)
(r)
(xˆ)
(yˆ)
Regression coefficient b
Correlation coefficient r
Estimated value of x
Estimated value of y
Linear Regression Calculation Examples
Select linear regression and input the following data (Statistics: Off)
xyxy
1.01.02.11.5
1.21.1 2.41.6
1.51.2 2.51.7
1.61.3 2.71.8
1.91.4 3.02.0
74
(Select Type)(y=a+bx)
11.21.51.61.9
2.12.42.52.73
11.11.21.31.4
1.51.61.71.82
Display statistical values based on input data.
(2-Variable Calc)
Display regression calculation results based on input data.
(Regression Calc)
Calculate sum of products of the x-data and y-data, Population standard
deviation of the x-data, and maximum value of the y-data.
(Summation)
75
(Σxy)
(Variable)
(σx)
(Min/Max)
(max(y))
Calculate regression coefficient constant term a, regression coefficient b,and correlation coefficient r.
eexponential regression, regression is performed in accordance with
With the following model equation.
y = ae
The following is the calculation formula used for each command.
•Summation Sub-menu, Variable Sub-menu, Min/Max Sub-menu, andRegression Sub-menu operations are the same those for linear
regression calculations.
bx
e Exponential Regression Calculation Examples
exponential regression and input the following data (Statistics:
Select
Off)
e
82
xy
6.921.4
12.915.7
19.812.1
26.78.5
35.15.2
(Select Type)(y=a・e^(bx))
6.912.919.826.735.1
21.415.712.18.55.2
Display statistical values based on input data.
(2-Variable Calc)
Display regression calculation results based on input data.
83
(Regression Calc)
Calculate regression coefficient constant term a, regression coefficient b,
and correlation coefficient r.
(Regression)
(a)
(Regression)
(b)
(Regression)
(r)
Calculate estimated values.(y=20 → xˆ=?)
20(Regression)
(xˆ)
(x=16 → yˆ=?)
16(Regression)
(yˆ)
ab Exponential Regression Calculation (y=a・b^x)
Commands
exponential regression, regression is performed in accordance
ab
With
with the following model equation.
y = ab
The following is the calculation formula used for each command.
x
84
•Summation Sub-menu, Variable Sub-menu, Min/Max Sub-menu, andRegression Sub-menu operations are the same those for linearregression calculations.
abExponential Regression Calculation Examples
Select Off)
abexponential regression and input the following data (Statistics:
xy
-10.24
34
516.2
10513
(Select Type)(y=a・b^x)
13510
0.24416.2513
Display statistical values based on input data.
85
(2-Variable Calc)
Display regression calculation results based on input data.
(Regression Calc)
Calculate regression coefficient constant term a, regression coefficient b,and correlation coefficient r.
(Regression)
(a)
(Regression)
(b)
(Regression)
(r)
Calculate estimated values.
(y=1.02 → xˆ=?)
1.02(Regression)
86
(xˆ)
(x=15 → yˆ=?)
15(Regression)
(yˆ)
Power Regression Calculation (y=a・x^b)Commands
With power regression, regression is performed in accordance with thefollowing model equation.
y = ax
The following is the calculation formula used for each command.
b
•Summation Sub-menu, Variable Sub-menu, Min/MaxSub-menu, andRegression Sub-menu operations are the same those for linearregression calculations.
Power Regression Calculation Examples
Select power regression and input the following data (Statistics: Off)
xy
282410
303033
333895
354491
385717
87
(Select Type)(y=a・x^b)
2830333538
24103033389544915717
Display statistical values based on input data.
(2-Variable Calc)
Display regression calculation results based on input data.
(Regression Calc)
Calculate regression coefficient constant term a, regression coefficient b,
and correlation coefficient r.
(Regression)
88
Calculate estimated values.(y=1000 → xˆ=?)
1000(Regression)
(a)
(Regression)
(b)
(Regression)
(r)
(xˆ)
(x=40 → yˆ=?)
40(Regression)
(yˆ)
Inverse Regression Calculation (y=a+b/x)Commands
With inverse regression, regression is performed in accordance with thefollowing model equation.
y = a +
The following is the calculation formula used for each command.
bx
89
• Summation Sub-menu, Variable Sub-menu, Min/Max Sub-menu, and
Regression Sub-menu operations are the same those for linear
regression calculations.
Inverse Regression Calculation Examples
Select inverse regression and input the following data (Statistics: Off)
xy
1.118.3
2.19.7
2.96.8
4.04.9
4.94.1
(Select Type)(y=a+b/x)
1.12.12.944.9
18.3
Display statistical values based on input data.
9.76.84.94.1
(2-Variable Calc)
90
Display regression calculation results based on input data.
(Regression Calc)
Calculate regression coefficient constant term a, regression coefficient b,and correlation coefficient r.
(Regression)
(a)
(Regression)
(b)
Calculate estimated values.(y=15 → xˆ=?)
15(Regression)
(Regression)
(r)
(xˆ)
91
(x=3.5 → yˆ=?)
3.5(Regression)
(yˆ)
Creating a Number Table
The Table Mode generates a number table based on one or two functions.
You can use the function
Configuring a Number Table Generation Function
Perform the following steps to generate a number table.
1. Press
•This displays the function input screen.
, select the Table Mode icon, and then press .
f(x) or the two functions f(x) and g(x).
2. Use the xvariable to input two functions, one in the format f(x) and theother in the format
•Be sure to input the xvariable ((x)) when generating a numbertable. Any variable other than
•If you are using a single function, input a function in the format f(x)only.
3. On the Table Range dialog box that appears, input values for Start, End,and Step.
For this:Input this:
Start
End
g(x).
xis handled as a constant.
Input the lower limit of x(Default = 1).
Input the upper limit of x(Default = 5).
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Input the increment step (Default = 1).
Note: The Step specifies by how
much the Start value should be
sequentially incremented as the
Step
•Pressing generates and displays the number table in accordancewith the Table Range dialog box.
•Pressing while the number table screen is displayed will return tothe function input screen in step 2.
Example:To generate a number table for the functions
g(x) = x2-
1
for the range -1 ≦x≦1, incremented in steps of 0.5
2
number table is generated. If you
specify Start = 1 and Step = 1, x
sequentially will be assigned the
values 1, 2, 3, 4, and so on to
generate the number table until theEnd value is reached.
f(x) = x2+
12
and
(x)12
(x)12
110.5
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Tip:
• In the number table, you can change the value in the currently
highlighted x cell. Changing the x value causes the f(x) and g(x) values
in the same line to be updated accordingly.
• If there is value in the x cell above the currently highlighted x cell,
pressing
or automatically inputs into the highlighted cell the
value equal to the value of the cell above it plus the step value. So
also, pressing automatically inputs the value equal to the value of
the cell above less the step value. The f(x) and g(x) values in the
same line are also updated accordingly.
Note
•The maximum number of rows in the generated number table depends on the setupmenu table setting. Up to 45 rows are supported for the “f(x)” setting, while 30 rowsare supported for the “
•The number table generation operation causes the contents of variable xto bechanged.
f(x),g(x)” setting.
Important!
•Functions input in this mode are deleted whenever the Input/Output settings arechanged in the Table Mode.
Ratio Calculations
The Ratio Mode lets you determine the value of X in the ratio expressionA : B = X : D (or A : B = C : X) when the values of A, B, C and D areknown. The following shows the general procedure for using Ratio.
1. Press
2. On the menu that appears, select (A:B=X:D) or (A:B=C:X).
3. On the Coefficient Editor screen that appears, input up to 10 digits for
each of the required values (A, B, C, D).
• To solve 3 : 8 = X : 12 for X, for example, press in step 1, and
then input the following for the coefficients (A = 3, B = 8, D = 12): 3
812.
, select the Ratio Mode icon, and then press .
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• Pressing will reset all of the coefficients to one.
4. After all the values are the way you want, press .
• This displays the solution (value of X).
• Pressing again will return to the Coefficient Editor.
Important!
•A Math ERROR will occur if you perform a calculation while 0 is input for a coefficient.
Changing the Ratio Expression Type
Press want from the menu that appears. Changing the ratio expression typecauses the values of all Coefficient Editor coefficients to change to one.
(Select Type) and then select the ratio expression type you
Ratio Mode Calculation Example
Example 1:To calculate X in the ratio 1 : 2 = X : 10
(Select Type)(A:B=X:D)
1210
Example 2:To calculate X in the ratio 1 : 2 = 10 : X
(Select Type)(A:B=C:X)
1210
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Technical Information
Errors
The calculator will display an error message whenever an error occurs for
any reason during a calculation.
Displaying the Location of an Error
While an error message is displayed, press calculation screen. The cursor will be positioned at the location where theerror occurred, ready for input. Make the necessary corrections to thecalculation and execute it again.
Example:When you input 14 ÷ 0 × 2 = by mistake instead of 14 ÷ 10 × 2
=.
1402
(or )
or return to the
1
Clearing the Error Message
While an error message is displayed, press screen. Note that this also clears the calculation that contained the error.
to return to the calculation
Error Messages
Math ERROR
Cause:
The intermediate or final result of the calculation you are performing
•
exceeds the allowable calculation range.
Your input exceeds the allowable input range (particularly when using
•
functions).
• The calculation you are performing contains an illegal mathematical
operation (such as division by zero).
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Action:
• Check the input values, reduce the number of digits, and try again.
• When using independent memory or a variable as the argument of a
function, make sure that the memory or variable value is within the
allowable range for the function.
Stack ERROR
Cause:
•The calculation you are performing has caused the capacity of thenumeric stack or the command stack to be exceeded.
Action:
•Simplify the calculation expression so it does not exceed the capacityof the stack.
•Try splitting the calculation into two or more parts.
Syntax ERROR
Cause:
•There is a problem with the format of the calculation you areperforming.
Action:
•Make necessary corrections.
Argument ERROR
Cause:
There is a problem with the argument of the calculation you are
•performing.
Action:
•Make necessary corrections.
Range ERROR
Cause:
An attempt to generate a number table in the Table Mode whose
•conditions cause it to exceed the maximum number of allowable rows.
The maximum number of rows is 45 when “f(x)” is selected for the
setup menu table setting and 30 when “
Action:
Narrow the table calculation range by changing the Start, End, and
•
Step values, and try again.
f(x),g(x
)” is selected.
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Before Assuming Malfunction of the
Calculator...
Perform the following steps whenever an error occurs during a calculation
or when calculation results are not what you expected. If one step does
not correct the problem, move on to the next step.
Note that you should make separate copies of important data before
performing these steps.
1. Check the calculation expression to make sure that it does not containany errors.
2. Make sure that you are using the correct mode for the type ofcalculation you are trying to perform.
3. If the above steps do not correct your problem, press the
•This will cause the calculator to perform a routine that checks whethercalculation functions are operating correctly. If the calculator discoversany abnormality, it automatically initializes the calculation mode andclears memory contents.
4. Return the calculation mode and setup (except for the Contrast setting)to their initial default settings by performing the following operation:
(RESET)(Setup Data)(Yes).
key.
Replacing the Battery
A low battery is indicated by a dim display, even if contrast is adjusted, orby failure of figures to appear on the display immediately after you turn onthe calculator. If this happens, replace the battery with a new one.
Important!
•Removing the battery will cause all of the calculator’s memory contents to be deleted.
1. Press
To ensure that you do not accidentally turn on power while replacing
•the battery, slide the hard case onto the front of the calculator.
2. On the back of the calculator, remove the screws and the cover.
(OFF) to turn off the calculator.
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3. Remove the battery, and then load a new battery with its plus (+) andminus (−) ends facing correctly.
4. Replace the cover.
5. Initialize the calculator: (RESET)(Initialize All)(Yes).
•Do not skip the above step!
Calculation Priority Sequence
The calculator performs calculations according to a calculation prioritysequence.
•Basically, calculations are performed from left to right.
•Expressions within parentheses have the highest priority.
•The following shows the priority sequence for each individual command.
1Parenthetical expressions
Functions that have parentheses (sin(, log(, etc., functions
2
3
4Fractions
5Negative sign ((-))
6
7Multiplication where the multiplication sign is omitted
8
9Multiplication (×), division (÷)
that take an argument to the right, functions that require aclosing parenthesis after the argument)
Functions that come after the input value (x2, x3, x-1, x!, °’ ”, °,