Casio fx-991ES PLUS C User Manual

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fx-115ES PLUS

fx-991ESPLUS C

User's Guide

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CASIO Worldwide Education Website

http://edu.casio.com

CASIO EDUCATIONAL FORUM

http://edu.casio.com/forum/

RJA525440-001 V01

CASIO~

.J?p~tel!,t!

Important Information 2 Sample Operations 2

Initializingthe Calculator 2 Safety Precautions 2 Handling Precautions 2

Removing the Hard Case 3

Turning Power On and Off 3

Adjusting Display Contrast 3 Key Markings 3

Reading the Display 4 Using Menus 5 Specifying the Calculation Mode 5 Configuring the Calculator Setup 5 Inputting Expressions and Values 7

Recurring Decimal Calculations 10

Togging Calculation Results 14

Basic ~~ 14 ~1deI ~ 18 Prime F ~. 19 Func::IiDr~ 20

Comp6ex~ CaK'oIbtinqs(CMPlX) 25 Using CAi..C 26 Using SOLVI" 27 Statistical Calculations (STAT} 29

Base-n Calculations (BASE-N) 33 Equation Calculations (EQN) 35

MatrixCalculations (MATRiX) 37 Creating a NumberTablefrom 1WoFunctions (TABLE) 39

Vector Calculations (VECTOR) 41 Inequality Calculations (lNEQ) 43

Using VERIFY(VERIF) 45 Distribution Calculations (DIST) 47 Scientific Constants 50

MetricConversion 51 Calculation Ranges, Number of Digits, and Precision 52

Errors 54 Before Assuming Malfunction of the Calculator_ 56 Replacing the Battery 56

Specifications 57 Frequently Asked Questions 57

.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 ofthe use of this product

and the items that come with it.

.Be sure to keep all user documentation handy for future reference.

t.§anipleop...Ii,jiojs- ~~ I

Sample operations in this manual are indicated by a / icon. Unless

specifically stated, all sample operations assume that the calculator is in its initial default setup. Use the procedure under "Initializingthe Calculator" to

return the calculator to its initial default setup. For infonnation about the 1miD, 1IImI, 1m, and _ marks that am shown

in the sample operations, see "Configuring the Calculator Setup".

""1i'faii~ins.{l:I~a1Cmat~ j.c : ...2,[ ]

Perfonn the followingprocedure when you want to in~ialjze the calculator and return the calculation mode and setup to their initialdefault settings. Note that this operation also clears all data currently in calculator memory.

I!!!I ([) (CLR)III (All)e)(Yes)

Lt.Battery

.Keep batteries out of the reach of smalt children.

.Use only the type of battery specified for this calculator in this manual.

ITHandUD..It""clitrons -:- -.,

~.,.."..,:",..:,~~.\.j[t.:~ ~

.Even Ifthe calculator Is operating normally, replace the battery at least

once every three years (LR44(GPA76». A dead battery can leak, causing damage to and malfunctionof the calculator.Neverleave a dead batteryin the calculator.Donot tryusing

the calculatorwhilethe batteryiscompletelydead.

.The battery that comes withthe calculator discharges slightly during

shipment and storage. Because of this, It may require replacement sooner than the normal expected battery life.

.Do not use an oxyrlde battery' or any other type of nickel-based

primary battery with this product. Incompatibility between such batteries and product specifications can result in shorter battery tlfe and product malfunction.

.Avoid use and storage of the calculator In areas subjected to

temperature extremes, and large amounts of humidityand dust.

.Do not subject the calculator to excessive Impact, pressure, or

bending. E-Z

.Never try to take the calculator apn.

.Use a soft, dry cloth to clean the exIericI" ",::.e calculator.

.Whenever discarding the calculator or bar;aeries,be sure to do so In

accordance with the laws and regulations in .,.,.. particular area.

. Company and product names used in this manual may be registered

Irl'demarks or trademarks of their respectiveowners.

~.. .-~~'the a..d£'is!.

~e...~ slide its hard

~(I

LJ!l"_. thecalculator, ndthenaffix 'I..J

Before

O~~:~rds to remo

~~t~eacalculatoras

~ ,.

case tothe bac .

thehard ca

se illustration nearby_

shown In t e

-=-=:d

Turningpovver Oh"and Off

"'" .""" -.-

Press I2!Jto turn on the calculator. Press f!!jj@(OFF) to turn off the calculator.

_ p ,.Off

-'cucaD wi:ttJmoftautomaticalyifyoudonotpertormanyoperation

io< abou. . 0 '"'tir1tJIes. ~ _ happens,press the I2!J key to turn the calculator

trod<or

Adjusting DispIaY.Contra'Si:

~ "'" ~ saee<' !It-perlonning the following key operation:

~~ISEl1.R,@OO''''CONT~J. Next, use @ and <E>to adjust cxrcrasL A.~.erIhe setOOgis Ihe way you want, press @.

Important: If adjusmg display

contrastdoes not Improvedisplayreadability,

it probably meansthat balfery power is low. Replacethe battery.

[~Ma"kliig,-_ . _ _:_

Pressing the I!!iIor ~ key followed by a second

key pertorms the alternate function of the second key. The alternate function is indicated by the text printed above the key. . The following shows what the different colors of the alternate function key text mean.

Alternate function

sin-1rD,

Keycap function

E-3

~di_f;'.QI~'.liDRJJJf2;[.'I'~. TI ;11,~.22~1

Thedisplay oUhe calculatorshowsexpressionsyouinput,calculation results,

and various indicators. Inputexpression ~ Indicators

q'f§H:g;.ID...: ~~:~.:..:::.::.:.P.9Tn;.4H?I?~~?f.j

f.f ::::::::::::::::r.~~;:~~4[::::::::r.~2;6~ii;:7.8.5.3.~8i!:}

Calculation result

.If a ~ indicator appears on the right side of the calculation result,it means

the displayed calculation result continues to the right. Use <E>and @ to scroll the calculation result display.

.If a I> indicatorappears on the right sideof the inputexpression, it means

thedisplayedcalculationcontinuestothe right.Use <E>and @ to scrollthe inputexpressiondisplay. Notethat ifyou wantto scrolltheinput expression whileboth the ~ and I> indicatorsare displayed, you will needtopress @) first and then use <E>and @ to scroll.

Display Indicators

E-4

If key marking

text

It means this:

Is this color:

Press@!jJ andthen the key to accessthe

Yellow

applicable function. Press andthen the key to i1puI the

Red

applicable variable, constant, 0<symbol.

Purple (or enclosed

Enter the CMPLX

Mode10access!he function.

in purple brackets) Green (or enclosed in

IEnterthe BASE '!oOe .. ac:essthefunction.

green brackets)

This

Means this:

indicator:

The keypadhas been shifted by pressing the

I!!iI key. The

keypad will unshift and this indicator will disappearwhen you press a key.

The alphainput mode has been entered by pressing the

I!!i!i!Ikey. The alpha input mode will be exited and this

indicator will disappear when you press a key.

M There is a value stored in independent memory.

The calculator is standing by for input of a variable name to

STO

assign a value to the variable. This indicator appearsafter

youpress@!iJmm(STO).

The calculator isstanding by for input of a variable name to

RCL recall the variable's value. This indicator appears after you

press mm.

STAT

The calculator isin the STAT Mode.

CMPLX

The calculator is in the CMPLX Mode.

MAT

The calculator is in the MATRIX Mode.

VCT

The calculator is inthe VECTOR Mode.

The default angle unit is degrees.

rn The default angle unit is radians.

r!!

The defaullangle unitis grads.

FIX

A fixed number of decimalplaces is in effect.

SCI

A fixed number of significantdigits isin effect.

Math

Natural Display is selected as the display format. Calculation history memory data is available and can be

...'"

replayed,or there is moredata abovelbelow the current

screen.

ThedisplaycooenItt_ an~te resultofa

multi-statement calculation.

Important: Forsome type ofcalculationthattakes a long timeto execute,

the display may show only the above indicators (without any value) while it performs the calculation intemally.

Dlsp

~'" = ::-J

Some of the calculator's operations are performed using menus. Pressing I!!IDor 11iiiJ,for example, will display a menu of applicable functions.

The foltowing are the operations you should use to navigate between menus.

.You can select a menu item by pressing the number key that corresponds

to the number to its left on the menu screen.

.The ~ indicator in the upper right corner of a menu means there is another

menu below thecurrent one.The '" indicator means another menu above. Use and @ to swilch between menus.

.Toclose a menu without selecting anything, press @.

Note:

The initialdefault calculation mode is the COMP Mode.

riOl!ISJiriagi!~Ca.1c.UlAtj)rS"t!t!l2. --=:J

First perform the following key operation to display the setup menu:

~I!!!!J(SETUP). Next,use and @ and the numberkeys to configure

the seUingsyou want. Underlined (_) settings areinitial defaults.

E-5

IDMthlO

mLinelO Specifies the display format.

Natural Display (MthIO) causes fractions, r::;- irrational numbers,and other expressions to be

I~+~

displayed as they are written on paper.

m NItti.

22 15

MthIO:SelectsM!!!!JQorLineO. MathOdisplaysinputandcalculationresults

usingthe same formatasthey arewritten on paper. LineOdisplays inputthe same way as MathO, but calculation results are displayed in linear format.

Unear Display (UnetO) causes fractions and I m

other expressions to be displayed in a single

4J5+2J3

line.

Note: .The calculator switches to Linear Display automatically whenever you

enter the

STAT, BASE-N, MATRIX,or VECTOR Mode. 'In this manual, the

CtmIsymbol next to a sample operation indicates Natural Display (MathO),

while the I!IZ!J symbol indicates Linear Display.

(!) Deg (!) Rad IIDGra Specifies

degrees,radians orgrads asthe angle

unit for value input and calculation resultdisplay,

Note: Inthis manual, the _symbol next to a sampleoperation indicates

degrees, while the

1msymbol indicates radians.

lID Fix CZJSel lID Norm Specifies the number of digits for display of a

calculation resulr.--

Fix: The value you specify (from 0 to 9) controls the number of decimal

places for displayed calculation results. Calculation results are rounded off to the specified digit before being displayed.

Example: I!IZ!J 100 + 7 =14.286 (Fix 3)

14.29 (Fix 2)

Sel: The value you specify (from 1to 10) controls the number of significant

digits for displayed calculation results. Calculation results are roundedoff to

the specified digit betorebeing displayed.

Example: I!IZ!J 1 + 7 =1.4286 x 10-' (Sci 5)

1.429 x 10-' (Sci 4)

Norm: Selecting one of the two available settings (Norm 1, Norm 2)

determines the range in which resultswill be displayed in non-exponential format. Outsidethe specified range,resultsare displayed using exponential format. Norm

1: 10-' > lxi,Ixli:;10'. Norm2: 10-<'> lxi,Ixlii: 10"

Example: I!IZ!J 1 + 200 =5 x 10-> (Norm 1)

0.005 (Norm 2)

IDab/c m die Specilies either mixed fraction (ab/c) or improper

fraction(dlc)~ of fractions in calculation results,

(!) CMPLX ID a+bi ;

mrLe Specifies eitherrectangular coordinates

(a+b.) or polarcOoidinaies (rLe) for EON Mode solutions.

(!)STAT IDON; mOFF Specifieswhether or notto display a FREO

(frequency) column iniiieS'fiiT Mode Stat Editor.

IIDTABLE IDf(x); mf(x),Q(x) Specifieswhether to use functionj(x)

only or the two functionsj(x) and

g(x)in the TABLE Mode.

E-6

When you want to performthis type of

Perform

this key

operaIion: operation: GenefaI",

I!ii!)ID(COMP)

....ooer caIcUations

I!ii!)m(CMPLX)

SIaIisticaI and regression calcutations

I!ii!)(!)(STAT)

Calculations invoImg specific number systems (binal)', octal, decimal,

e (!) (BASE-N)

hexadecimal) Equation solution

e lID(EON)

Matrix calculations

I!ii!)lID(MATRIX)

Generate a number table based on one or

@2i!)CZJ(TABLE)

two functions Vector calculations

e lID(VECTOR) Inequality solution. Ii!i!IID(INEO) Verify a calculation

li!i!Im(VERIF) Distribution Calculations

I!!!!J@)(DIST)

~ [!) Rdec [D ON ; m OFF SpeciIies whether or not to display

calculation resUiiSUSlng recurmg deanaliorm.

~ m Disp [D Dot; m Comma Specifies whether to display a dot or a comma for the calculation result decimal point. A dot is always displayed during input.

Note: When dot is selected as the decimal point, the separator for multiple results is a comma (,). When comma is selected, the separator is a semicolon (;).

~ !II CONT~ Adjusts display contrast. See "Adjusting Display Contrast" for details.

Initializing Calculator Settings

Perform the foltowing procedure to initialize the calculator, which returns the calculation mode to COMP and returns alt other settings, including setup menu setlings, to their initialdefaults.

(!!iJ [[)(CLR) [D (Setup)§) (Yes)

Inputtinq E~~t8SSiohS' ~nd VallAt$ 1

Basic Input Rules

Calculations can be input in the same form as they are written, When you press §) the pIioIity sequence of the input calculation will be evaluated

~ and the result will appear on the display.

/ 4.sD30xl30~10x3)=I20

4 !ID~30m !IDIIJ30ffi 10(2g3 m §)

I J. I I

*2 *3

m MlIII...

4xsin(30)x(30+1~

120

., Input of the closing parenthesis is required tor sin, sinh, and other functions

that includeparentheses. .

.,These multiplication symbols (x) can be omitted. A multiplication symbol

can be omittedwhenitoccursimmediatelybeforeanopeningparenthesis,

immediatelybefore sin or other function that includes parentheses, immediatelybeforethe Ran# (randomnumber)function,or immediately

beforea variable(A,S,C, 0, E, F,M,X,Y),scientificconstants,1tore.

., The closingparenthesis immediatelybefore the §) operationcan be

omitted.

Input example omitting (2g" and CD" operations in the above

example.

. m MaUl"

4@30 CDIIJ30ffi 101ID3§) ,4S1n(30)(30+10X3

120

Note: .It the calculation becomes longer than the screen width during

input, the screen willscroll automatically to the right and the indicator will appear on the display. When this happens, you can semi back to the left by

using @ and <e) to move the cursor.

.When LiIear Display is selected,

pressing @ willcause the cursor to jump tothe ~ of the calculation,

while ~ will jump to the end. .When NaIuIaI Display is selected, pressing

E-7

<e) while the cursor is at the end of the input calculation willcause ~to jump

to the beginning, while pressing @ while the cursor is at the beginning will

cause it to jump to the end. .You can input up to 99 bytes for a calculation.

Each numeral, symbol, or function normally uses one byte. Some functions

require three to 13 bytes. .The cursor will change shape to . when there are

10 bytes or less of allowed input remaining. It this happens, end calculation

input and then press §).

Calculation Priority Sequence

The prioritysequence of input calculations is evaluated in accordance w~h the rules below. When the priorityof two expressions is the same, the calculation

is performed trom left to right.

Inputting with Natural Display

Selecting Natural Display makes it possible to input and display fractions and certain functions (log, XZ,XZ,x', r., >r., 'ro, x-', 10', e',l, dJdx,I, II,

Abs) just as they are writteninyourtextbook.

2+-12

1+-12

E-8

Isl

Parenthetical expressions

2nd

Functions that require an argument to the right and a closing parenthesis "j" following the argument.

3rd

Functionsthatcome after the input value (r, x3,x-1,x!, 01.,°," g,

%, I), powers (xl), roots ('ro)

4th Fractions

Negative sign H, base-n symbols (d, h, b, 0) Note: When squaring a negative value (such as 2), the value being squared must be enclosed in parentheses (IIJ IBJ2 m

5th

§). Since XZhas a higher priority than the negative sign,

inputting IBJ2 §) would result in the squaring of 2 and then appending a negative sign to the result. Always keep the priority sequence in mind, and enclose negative values in parentheses when required.

6th

Metric conversion commands (cmin, etc.),

STAT Mode estimated values (x, 9, XI, X2)

7th

Multiplication where the multiplication sign is omitted

8th

Permutation (nPr), combination (nCr), complex number polar coordinate symbol (L)

9th

Dot product (.)

10th

Multiplication (x), division (+), remainder calculations (+R)

11th

Addion, subtraction (+,-)

12th

Logical AND (and)

13th

Logical OR, XOR, XNOR (or, xor, xnor)

Important: .Certain types of ~~'" can cause the height of a

calculation formulato be greater than one dislJlayline. The maximum allowableheightofa calculationformulaistwo<ispIayscreens (31dotsx2).

Furtherinputwillbecomeimpossibleifthe heightofthe calculationyou are

inputting exceeds the allowable limit. .Nesting of functions and parentheses

is allowed. Further input willbecome impossible ifyou nest too many functions andlor parentheses. Ifthis happens, divide the calculation into multiple parts and calculate each part separately.

Note: When you press lEI and obtain a calculation result using Natural Display, 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 <E>to

scroll the input expression.

Using Values and Expressions as Arguments

(Natural Display only) Avalue oran expressionthat you have already inputcan be used as the

argument of a function. After you have input t, for example, you can make

itthe argument of

r, resulting in fl.

/ To input 1 + t and then change it to 1 + fl ED

1~7fSJ6 [1+~

@@@@I!!!J@(INS) ~

~[!;i

....

As shown above, the value or expression to the right of the cursor after

I!!!J@)(INS) are pressed becomes the argument of the function that is specified next. The range encompassed as the argument is everything up to the first open parenthesis to the right, ifthere is one, or everything up to the first function to the right (sin(30), log2(4), etc.) This capability can be used with the following functions: ~, ~, liB.

1!!!J1iS(Ir'), !m~(~-), @@~(!H. 1!!!J~('ro), !m(§](IO').

1!!!J(ji;J(e'), @, ~.!m@(3r.;), I!i!!lI!iI(Abs). Overwrite Input Mode (Linear Display only)

You can select either insert or overwrite as the input mode, but only while Linear Display is selected. In the overwrite mode. text you input replaces the text at the current cursor location. You can toggle between the insert and overwrite modes by performing the operations: I!!!J@ID(INS).The cursor appears as "I" in the insert mode and as "_" in the overwrite mode.

Note: Natural Display always uses the insert mode, so changing display format from Linear Display to Natural Display will automatically switch to

the insert mode.

Correcting and Clearing an Expression

To delete a single character or function: Move the CUlSOIso itis directly to the right of the character or function you want 10delete. and then press

@ID.

In the overwrite mode, move the cursor so i is <iredIy under the character or function you want to delete, and then press §.

E-9

To Insert a character or function fnto a calculation: Use @ and <E>to move the cursor to the location where you want to insert the character or function and then input it. Be sure always to use the insert mode if Linear

Display is selected.

To clear all of the calculation you are Inputting: Press @.

~e~ul'rinscDi.CT~a1Cula'lOiiii

Yourcalculatoruses a recurringdecimalwhenyouinputa value.Calculation

results also can be displayed using recurring decimal form whenever applicable.

Inputting a Recurring Decimal

When inputting a recurrent decimal, press @@~(.) before inputting its 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: "08@@liiH.)90". Important: .If the value starts with an integer part (like: 12.3123123...), do

not include the integer part when inputting the period (12.312).

.Recurring

decimal input is possible only when Natural Display is selected.

/ To input 0.33333... (0.3) m

08 [0.1

@@@(.) [0.0

3 [o.a

m Mo.

m--1iattl

~th

To input 1.428571428571... (1.428571) ED

18@@@(.) [0

m Mo.

428571

1.4285711

/ To calculate 1.021 + 2.312 ED

18@@@(.)021(E)~

28 @@@(ii)3121E1

rn Malll.

1. 021 +2. 312 10

Calculation result displayed as recurring decimal value:

_ rn Ma\fl.

@ 11.021 +2. 312

3.3

E-10

~ ....

Note: . You can specify up to 14 decimal places for the recurring decimal

period. Ifyou input more than 14 decimal places, the value willbe treated as

a terminating decimal and not a recurring decimal. .Recurring decimal value

input can be performed regardless of the Rdec selling on the setup menu.

Displaying a Calculation Result as a Recurring Decimal Value

Calculation results that can be displayed as recurring decimal values willbe displayed as such when ON is selected for the Rdec selling on the setup

menu.Pressingthe §!iiI keywillcyclebetweenthe availablecalculationresult

formats as shown below.

~I Recurring Decimal

Decimal Value According to Display (Norm, Fix, Sci) Sellings

Or .

Decimal Value According to Display (Norm, Fix, Sci) Sellings

RecUrringDecimall~

§!iiIll+7

Return to initialdisplay format (Norm 1):

0.1428571429

..!...=0.142857 =0.1428571429 (Norm 1) I!IDI

11BJ7@ ! 1~7

§!iiI11i7

Display as recurring decimal:

0.142857

Decimalvalue accordingtoNorm1selling: ~ 11~7

0.1428571429

Returnto initialdisplayformat(fraction): §!iiI\1 ~7 m 1:71

/ +=0.142857=0.t428571429(NOrm1) rmm

11BJ7@ E ]

/ 1+7 =0.1428571429 (Norm1)= 0.142857=+ I!IDI

1 B:)7@ ,1+7

SitDisplay as recurring decimal:

0.142857

Display as fraction:

Decimal value according to Norm 1 selling:

8 I7"

0.1428571429

Display as recurring decimal:

0.142857

Return to initialdisplay format (fraction):

~ ,1+7

Return to initialdisplay format (Norm 1):

0.1428571429

1 + 7 =..!...= 0.142857 = 0.1428571429 (Norm 1)

m _.

Conditions for Displaying a Calculation Result as a Recurring Decimal

If a calculation result satisfies the following conditions, pressing S will 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.

Display as fraction:

Display as recurring decimal:

O. 142857

E-12

E-11

.The data size of value to be displayed as the recurring decimal must beno

larger than 99 bytes. Each value and the decimalpointrequireone byte,

and each digij ofthe

periodrequires one byte. The following,for example,

would require

oltotalof Bbytes (4 bytesforthevalues, 1byteforthe decimal

point, 3 bytes for the period): 0.123

Note: Forinfonnationabout switching the display fonnat of a calculation

resutt when OFF is selected for the Rdec setting on the setup

menu, see

"Toggling Calculation Resutts..

Recurring Decimal Examples

/ 0.3+0.45=0.78 IZID

o81!!!1 ~.! ii)3 @>IE 10.3+0. 458

08~~(.)45§)1i3i

....

O.78

/ 1.6+2.8=4.5

1.6+2. 8"

IZID

18~~(ii)6@1E

28~~(ii)B§)1Ei

....

4.5

To confinn the following: 0.123 =~, 0.1234 =~,

_ 12345 999 9999

0.12345=99999

IZID

m ....

1231A1999§) I~~~

333

Ii3iI~~~

G ....

E-13

-- --- ----.

Toggling Calculation ,!!!uJ!!.._ _ J

While Natural Displayis selected, each press of Ii!!iIwill toggle the currently displayed calculation result between its fraction fonn and decimal fonn, ijs

r fonn and decimal fonn, or its n fonn and decimal fonn.

/ n + 6 = -tn =0.5235987756 IZID _

I!!!I~ (n)ffi6§) -tn §i 0.5235987756

/ (,12 + 2) x -13 =,16 + 2-13 = 5.913591358 IZID

m~2@>1E2m!XI~3§) ,16+2-13

~ 5.913591358

While

Unear Displayis selected, each press of Ii!!iIwill toggle the currently

displayed calculation result between its decimal fonn and fraction fonn.

Important: .Dependingonthetypeofcalculation resuttthat isonthe display

when you press the Ii3i key, the conversion process may take some time

to perform. .With certain calculation results, pressing the ~ key will not

convert the displayed value. .When ON isselected for Rdecon the setup

menu, pressing Ii3iwill switch the calculation resutt to recurring decimal fonn.

For details, see "Recurring Decimal Calculations'. .You cannot swijch from

decimal fonn to mixedfraction fonn if the total number of digits used inthe mixed fraction (including integer, numerator, denominator, and separator symbols) is greaterthan 10.

Note: Wijh Natural Display (MathO), pressing I!!!I§) instead of §) after inputting a calculation will display the calculation result in decimal fonn. Pressing

Ii3iafter that will swijch the calculation resutt to recurring decimal

fonn, fraction fonn or n fonn. The

r fonn of the result will not appear in

this case.

~ -- - - - - - -.

I Basic Calculations

___ __ ___I

Fraction Calculations

Notethat the input methodforfractions is different, dependingupon whether

you are using Natural Display or Linear Display.

7~6

E.14

0.123

1234

12341aJ9999§) 19999

1234

9999

iiJJiiiiA

1234

Ii3i19999

0.1234

12345

12345(E 99999§)

199999'

4115

33333

I '?A!=i:

1i3i.

0.12345

/ 1+5=0.2=t

ImII

1ffi5§)

0.2 15

/ 1-t=t=0.2

ImII

1E)4(E5§)

15 0.2

/4-3t=trmm 48f!BtaJl-§-13@1~2§) t

_ 4831!!111BJ2§)1~2

Note: .Mixing fractions and decimal values 81a calculation while Linear

Display is selected willcause the resun to be displayed as a decimal value.

.Fractions in calculation results are displayed after being reduced to their

lowest terms.

To switch a calculation result between improper fraction and mixed

fraction form: Perform the following key operation: I!!!I ~(a%.%)

To switch a calculation result between fraction and decimal form:

Press 1i!ID.

Percent Calculations

Inputtinga valueandpressing @!j)CD(%)causes the inputvalueto become

a percent.

Degree, Minute, Second (Sexagesimal) Calculations

Performinganadditionorsubtractionoperationbetweensexagesimalvalues,

ora multiplicationor divisionoperationbetweena sexagesimalvalueand a decimalvaluewillcause the resulttobe displayedas a sexagesimalvalue. You also can convert between sexagesimal and decimal.The following is the inputformatfor a sexagesimal value:(degrees) 8 (minutes) 8 (seconds) 8.

Note: You must always input something for the degrees and minutes, even ifthey are zero.

/ 2°20'30"+ 39'30"= 3°00'00"

2820830 8 ~ 08 39830 E3§)

/ Convert2°15'18"to itsdecimalequivalent.

28158188§)

(Convertssexagesimaltodecimal.)

(Convertsdecimal10sexagesimal.) 8

2°15'18-

2.255

2°15'18"

E-15

Multi-Statements

You can use the colon character (:) to connect two or more expressions and execute them in sequence from left to right when you press §).

/ 3+3:3x3

3~3(!iE!}~(:)31&J3§)

§)

6 9

Using Engineering Notation

A simple key operation transforms a displayed value to engineering notation.

/ Transform the value 1234 to engineering notation, shifting the

decimal point to the right.

1234 §)

@ @ID

1234

1.234x103 1234x10.

Transform the value 123 to engineering notation, shifting the decimal point to the left.

123§) 123 @!!It~](<-) 0.123x103 1!!iI~(<-) 0.000123x10'

Calculation History

In the COMP, CMPLX, or BASE-N Mode, the calculator remembers up to approximately 200 bytes of data for the newest calculation. You can scrolt through calculation history contents using @ and ~.

1~1§) 2

2~2§) 4

3~3§) 6

(Scrolls back.) @ 4

(Scrolls back again.) @ 2

Note: Calculation history data is all cleared whenever you press ~, when you change to a different calculation mode, when you change the display

format, or whenever you perform any reset operation.

1 + 1 =2

2+2=4 3+3=6

Replay

While a calculation result is on the display, you can press <3:>or ~ to edit the expression you used for the previous calculation.

/ 4 x3+2.5= 14.5 _ 41&J3~2.5§)

4x3-7.1 =4.9 (Continuing)<3:>t!IDt!ID1!ID@)87.1

§)

14.5

4.9

Note: If you want to edit a calculation when the ~ indicator is on the right

side of a calculation result display (see "Reading the Display"), press §J and then use <3:>and ~ to scroll the calculation.

E-16

/ 150x20%=30 150 I&J20 I!!!ICD(%)§)

/ Calculate what percentage of 880 is 660. (75%)

660

ffi 880 @!j)CD(%)§)

/ Increase 2500 by 15%. (2875)

2500 2500 I&J151!!!1CD(%)§)

2875

/ Discount 3500 by 25%. (2625)

3500133500 I&J251!!!1 CD(%)§)

2625

Answer Memory (Ans)/Previous Answer Memory (PreAns)

The last calculation result obtained is stored "' Ans ':answer) memory, The calculation result obtained prior to the last one is sto<ed "' PreAns (previous answer) memory. Displaying the result ofa new calculation willmove current

Ans memory contents to PreAns memory and store the new calculation

results in Ans memory. PreAns memory can be used only in the COMP Mode. PreAns memory contents are cleared whenever the calculator enters

another mode from the COMP Mode.

For T,-, = T,.\ + T, (Fibonacci sequence), determine the sequence from T, to T,. Note however, that T, = 1 and T, = 1. Em

I m .0.'I

T,=1 1§) 1 1

(An.:f,: 1)

I m 1

T,=1 1§) 1 1

(Ans "" T:= 1, PreAns = TI = 1)

13=12+T1=1+1 I iii MaUl.

. 1!!!!!1E1!ffi!!I1!!!!!(PreAns)§) Ans+PreAns

T. = T3+ T, = 2 + 1

(Ans "" T3 "" 2. PreAns ""T;:"1)

(!] Math.

§),AnS+PreAnS

T, = T. + T, = 3 + 2

(Ans;z T~ "" 3. PreAns "" 13 = 2)

iii Me"'.

§) ,Ans+PreAns

Result: The sequence is {1, 1,2,3, 5}.

E-17

Variables (A,B,C,D,E,F,X,Y)

Yourcalculator has eight preset variables named A, B, C. D, E, F, X,and Y. You can assign values to variables and also use the variables in calculations.

/ / /

To assign the result of 3 + 5 to variable A

31E 51!!i]1ffiI(STO)IE)(A)

To multiply the contents of variable A by 10

(Continuing) I!ffi!!lIE)(A)1ID10 §)

To recall the contents of variable A (Continuing) I!!IDIE) (A)

oTo clear the contents of variable A

OI!!i]I!!ID(STO)IE)(A)

Independent Memory (M)

You can add calculation results to or subtract results from independent

memory.The"M"appears on the displaywhenthereisanyvalueotherthan

zero stored in independent memory.

/ Toclear the contentsofM OI!!!lIffil(STO)!!i!I(M) 0 / Toadd the resultof10x 5 toM (Continuing) 10lID5!!i!1 50 / Tosubtractthe resultof 10+ 5fromM

(Continuing) 10IE 5@!j)[iE(M-) 15

/ Torecallthecontents of M (Continuing) I§) ~(M) 35

Note: VariableMis

used for independent memory.

Clearing the Contents of All Memories

Ansmemory, independentmemory,and variablecontentsare retainedeven

if you press gg, change the calculationmode, or turn off the calculator. PreAns memory contents are retained even if you press

gg and turn off the

calculatorwithout exiting the COMP Mode. Perform the following procedure when you want to clear the contents of altmemories.

I!!!IIID (ClR) o (Memory) §) (Yes)

~-~dft~Cal~uiaiiMi~"~'~: - ~:J

Youcan use the +Rfunctionin order to obtain the quotient and remainder

in a division calculation.

To calculate the quotient and remainder of5 +2

51!!!iiiJ1II(+R)2§) .5+R2

2,R=1

QuotientRemainder

51!!!iiiJ'jiH+R)2§)15+R2 d

R= 1

QuotientRemainder

E-18

Todividetheresultof3 x4 by 30 ImIJ

121

31ID4§) I

(ZJ30 §) I Ans+30

041

(Continuing)

/ 123+456=579 Em

1231E456§) I

5791

789 -579 =210 !789-Ans

MalliA

(Continuing) 789 Ell!!!!!§)

210

Note: .Only the quotient value of a +R caIcUaIion is stored in Ans memory.

.Assigning the result of a remainder division calculation to a variable

will assign the quotient value only. Performing the operation 5 ~

lJiH+R)2@I@(STO)m(X) (which assigns the result of 5+R2 to X)

will assign a value of 2 to X.

.If a +R calculation is part of a multi-step

calculation, only the quotient is passed on to the next operation. (Example; 10

IE 17 ~1iiI(+R)6 §) 10+ 2) .Operation olthe ~ and 8 keysis

disabled while a remainder division result is on the display.

Cases when Remainder Division becomes Non-remainder Division

If either of the following cond~ions exists when you pertorm a remainder division operation, the calculation willbe treated as normal (non-remainder)

division.

.When e~her the dividend or the divisor is a very large value

Example:20000000000 I!ffii!)1.)(+R)17§)

Calculated as: 20000000000 + 17

.When the quotient is not a pos~ive integer, or if the remainder is not a

positive integer or positive fractional value Example;

lEI5 ~ I)IJ(+R) 2 §) ->Calculatedas; -5 + 2

~Prime Factorization .~.~.~mv.~.~ :1

-- ~: ",~"""".' ~ .....-

In the COMP Mode, you can factor a positive integer up to 10 digits into prime factors up to three digits.

To pertorm prime factorization on 1014

1014

IE![

IS!!Jf3(FACT)[

10141

2x3X13z1

When you pertorm prime factorization on a value that includes a factor that is prime number with more than three dig~s, the part that cannot be factored willbe enclosed in parentheses on the display.

To pertorm prime factorization on 4104676 (= z2 x 10132)

@f3(FACT) I 2zx(1026169) I

Anyone of the following operations will exit prime factorization result display.

.Pressing 1!!!If3(FACT) or §).

.Pressing any of the following keys; ~ or f3.

.Using the setup menu to change the angle unit setting (Deg, Rad, Gra) or

the display digits setting (Fix, SCi, Norm).

Note: .You willnot be able to execute prime factorization while a decimal

value, fraction, or negative value calculation result is displayed. Trying to do so will cause a math error (Math ERROR).

.You will not be able to

execute prime factorization while the result of a calculation that uses Pol, Rec, +R is displayed.

E-19

For actual operations using each function,see the "Examples' section

following the list below.

1t: 1t is displayed as3.141592654, buf 1t=3.14159265358980isused for

intemal calculations.

e: e is displayed as 2.718281828, bute =2.71828182845904 is used for

intemal calculations. sin, cos, lan, sln-', coso" tan-': Trigonometric functions. Specify the

angle un~ before pertorming calculations. See LJ.. sinh, cosh, tanh, slnh-'. cosh-', tanh-': Hyperbolic functions. Input a

function from the menu that appears when you press ffiJ. The angle unit setting does not affect calculations. See Itl..

',',9: These functions specify the angle unit. .specifies degrees, 'radians,

and 9 grads. Input a function from the menu that appears when you pertorm the following key operation; IS!!JfiW(DRG~). See h.

10., e.: Exponential functions. Note that the input method is different depending upon whether you are using Natural Display or Unear Display. Seeh.

log: logarithmic function. Use the

~ key to input log.b as log (a, b). Base

10 is the default setting if you do not input anything for a. The ~ key also

can be used for input, but only while Natural Display is selected. In this case, you must input a value for the base. See h.

In: Natural logarithm to base e. See h,. x", x", xl, r., 'r., o.rc;,.r': Powers, power roots, and reciprocals. Note

that the input methods for x", r., 'r., and o.rc;are different depending upon whether you are using Natural Display or linear Display. See LJ...

Note: .The following functions cannot be input in consecutive sequence;

r, x', x", x-'. Ifyou input 2@1@1, for example, the final @I willbe ignored.

To input 222, input 2@1, press the @ key, and then press @I(ED).

.r, x', x-' can be used in complex number calculations.

/J.: Function for pertorming numerical integration using the Gauss-Kronrod method. Natural Display input syntax is

J:f(x),while linear Display input

syntax isJ(f(x),a,b,tol). to/ specifies tolerance, which becomes 1 x

1~ when nothing is input for tot. Also see "Integration and Differential Calculation Precautions" and ''Tips for Successful Integration Calculations" for more information. See 6.

i;.: Function for approximation of the derivative based on the central

differencemethod. Natural Displayinput syntax is fx (f(x))Ixo.'while

linear Displayinputsyntaxis fx (f(x),a, tol).to/ specifies tolerance,

which becomes 1 x 10-'0when nothing is input for tot. Also see "Integration

and Differential Calculation Precautions' for more information. See h.

~-: Function that, for a specified

range ofj(x),determines sum L (f(x))

....

=j(a) + j(a+l) + j(a+2) + ...+j(b). Natural Display input syntax is L (f(x)), while linear Display input syntax is I(j(x),a, b).a and b are inte9~rs that

E-20

can be specified within the range 01-1 x 10'"< a ;;; b < 1 x 10.°. See ~.

Note: The following cannot be used ilJtx): Pol, Rae, +R. The followingcannot be used inJ!x), a, or b: I, dldx, L, n.

~-: Determ~nes the product of J!x) over a given range. The calculation

formula is: II(j(x)) =J!a) xJ!a+l) xJ!a+2) x... xJ!b). The Natural Display

~ b .

inputsyntax is II(j(x)), whilethe LinearDisplayinputsyntax is n(/!x), a,

b). a and b arei';;tegers inthe range of a < 1 x 10'°,b< 1 x 10'°,a;;; b.

See&.

Note: The following cannot be use\! inJ!x): Pol, Rec, +R. The following cannot

be used inJ!x), a, or b: I, dldx, L, n.

Pol, Rec: Pol converts rectangular coordinates to polar coordinates, while Rec converts polar coordinates to rectangular coordinates. See .lll.

Pol(x, y) = (r, 8) Rec(r, 8) = (x, y) Specify the angle unit before

performing calculations.

p(;r.y) p(r,8) .

The calculatoon result for rand 8

i -2!!l and forx and yare each assigned

i respectively to variables Xand Y.

° . . x Calculation result 8 is displayed

Rectangular Polar in the range of _180. < 8 :5

Coordinates(Rae) Coordinates(Pol) 1800.

XI: Factorialfunction.See ~. Abs: Absolute value function. Note that the input method is different

dependinguponwhetheryou are using NaturalDisplayor LinearDisplay.

See~. Ran#: Generates a 3-digitpseudo random number that is less than 1.

The result is displayed as a fractionwhen Natural Displayis selected.

Ranlnt#: For input offhe function of the form Ranlnt#(a. b), which generates a random integer wifhin the range of a to b. See ~.

nPr, nCr: Permutation (nPr) and combination (nCr) functions. See LIz. Rnd :The argument ofthis function is made a decimal value and then rounded

in accordance with the current number of display digits setting (Norm, Fix, or Sci). With Norm 1 or Norm 2, the argument is rounded off to 10 digits. With

Fix and Sci, the argument is rounded off to the specified digit. When Fix 3 is the display digits setting, for example, the result 0110 + 3 is displayed

as 3.333, while the calculator maintains a value of 3.33333333333333 (15

digits)intemallyfor calculation.Inthe case of Rnd(10+3)=3.333 (with Fix

3), both the displayed value and the calculator's intemal value become

3.333. Because of this a series of calculations will produce different results depending on whether Rnd is used (Rnd(10+3) x 3

=9.999) or not used (10

.. 3 x 3

=10.000). See As.

GCD, LCM: GCD determines the greatest common divisor of two values. while LCMdetermines the least common multiple. See ~. Int: Extracts the integer part of a value. See ~.

E.21

Intg: Deferminesthe largest integerthat does not exceed a value. See ~.

Note: Usingfunctionscan slowdowna calculation,whichmaydelaydisplay ofthe result.Donotperformany subsequentoperationwhilewaitingforthe calculationresultto appear. To interruptan ongoingcalculationbefore its

resultappears, press @.

Integration and Differential Calculation Precautions

.Integration and differential calculations can be performed in the COMP

Mode(~[IJ) only.

.The following cannot be used inJ!x): Pol, Rec, +R. The following cannot

be used inJ!x), a, b, or /01: I, dldx, L, n.

. When using a trigonometric function in J!x), specify Rad as the angle

unit.

.A smaller /01 value increases precision, but it also increases calculation

time. When specifying /01, use value that is 1 x 10-" or greater.

Precautions for Integration Calculation Only

.Integration normally requires considerable time to perform.

.For J!x) < 0 where a ;;; x ;;;b (as in the case of J~ 3r -2 =-1), calculation

willproduce a negative result.

.Depending on the content of J!x) and the region of integration, calculation

error that exceeds the tolerance may be generated, causing the calculator

to display an error message.

Precautions for Differential Calculation Only

.If convergence to a solution cannot be found when /01 input is omitted, the

/0/ value will be adjusted automatically to determine the solution.

.Non-consecutive points, abrupt fluctuation, extremely large or small points,

inflection points, and the inclusion of points that cannot be differentiated, or a differential point or differential calculation result that approaches zero

cancausepoorprecisionorerror.

Tipsfor Successful Integration Calculations

When a periodic function or integration interval results in positive and

negative fix) function values

Perform separate integrations for each cycle, or forthe positive part and the

negative part, and then combine the results.

ft~

a f(x)dx

=J(x)dx +(- .f(x)dx)

PositivePart NegativePart

(5 Positive) (5 Negative)

When integration values fluctuate widely due to minute shifts in the

integration Interval

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

of wide fluctuation into small parts), perform integration on each part, and

then combine the results.

f~)

tJ\~

af(x)dx= 0f(x)dx + x,f(x)dx+.

+I>X)dx

E.22

...

Examples

Li sin 30°= 0.5 ImllIEI

sin-'O.5=30° ImllIEI

h sinh1= 1.175201194

cosh-'1=0

1!i!!130[IJlEI

i!!jJ I!i!!I(sin-') 0.5 [IJ lEI

ffiW!D(sinh)1 [IJIEI 1.175201194

ffiWlID(cosh-') 1 [IJ lEI 0

6. 1t/2radians= 90°, 50 grads = 45° lEI

1ffiI@ijj(1t)1E2[IJ i!!jJ f!!!J(DRG~)[IJ(')1EI

50 i!!jJ f!!!J(DRG~) (II (9) lEI

~ Tocalculate e' x2 to three significantdigits (Sci 3)

IffiII!2i!J(SETUP) ILl(Sci) (II

rmm

ImII

2.97x102

2.97x1 Q2 3

4 4

1m@(e")5 <E>(jg 2 lEI i!!jJ !W (el) 5 [IJ (jg 2 lEI

h log,.1000 =log 1000= 3

log216=4

§) 1000 [IJ lEI

§) 2 i!!jJ [IJ (,) 16 [IJ lEI ~2<E>161E1

h TocalculateIn90 (= log, 90) to three significant digits (Sci 3)

i!!jJI!@(SETUP)ILI(Sci)(II !W90[IJlEI 4.50x10.

L:z. 1.2

x 10'= 1200rmm 1.2(jg10@)31E1

(1+1)'" = 16 rmm mIlE 1[IJ @)21E 2lEI

(5')'=15625 m 51£1[IJi!!jJ1£I(x3)lEI

~=2 rmm 1m@)('Yo)5<E>321E1

ImII 51!!j)@)('Yo)32 [IJ lEI

Tocalculate 12 x3(= 312 = 4.242640687...) to three decimal

places (Fix 3)

i!!jJ1!2i!J(SETUP)!II(Fix)@ rmm

1200

15625

2 2

Gi) 2 <E>(jg 3 lEI

I!!j)IEI

Gi) 2 [IJ (&) 3 lEI

3-12

4.243

h J:ln(x) =1

rmm 11iB!W~ [IJ(X)[IJ <E>1<E>~ @ijj(e)1EI ImII 11iB!W

I!!WII)(X)[IJ IffiI[I)(,)

1 1m [IJ (,)I!!W@ijj(e)[IJ lEI

h To obtain the derivative at point x = rrJ2for the functiony =sin(x)

rmm 1ffi111iB(£-.) I!i!!I~ [IJ (X)[IJ

<E>III1m(@(It)<E>2lEI 0

ImII i!!jJas(£-.)@I!!W[I) (X)[IJ

i!!jJ[IJ (,)i!!jJ(@(It)1II2 [IJlEI 0

E-23

0.5 30

& L(X+I)=20

,.,

rmm 1ffiI~(:;:-)~II)(X)IEI<E>I<E>51E1 20 I!IZII I!!j)~(:;:-)~[I)(X)IE 11!!j)[I)(,)1

i!!jJ[I) (,)5 [I) lEI 20

Lh IT(X + 1) =720

rmm ~~(!H~II)(X)IEI<E>I<E>51E1 720 ImII ~~(~-)~[I)(X)IE 11!!j)[I)(,)1

1m[IJ(.)5[I) lEI 720

h To convert rectangular coordinates (12, 12) to polarcoordinates

lEI

rmm ImIE(Pol)~2<E>i!!jJ[I)(,)~2<E>[IJ1EI r=2,11=45 I!IZII i!!jJIE (Pol)Gi)2 m IffiIm(,)Gi) 2[I) m lEI r= 2

11=45

Toconvertpolarcoordinates(12, 45°)torectangularcoordinates

lEI rmm ImEJ(Rec)~2<E>i!!jJm(,)45mlEl X=1,V=1

& (5 + 3) ! =40320 m 51E3II)i!!jJ~(x!) lEI 40320 ~ 12-7Ix2=10

rmm I!IZII

IffiIffiW(Abs) 2 EJ 7 <E> (&) 2 lEI

i!!jJ ffiW(Abs)2EJ7[IJ (jg 2 lEI

10 10

~ To obtain threerandom three-digit integers

1000

I!!j)8 (Ranll)lEI 459

lEI 48 lEI 117

(Results shown here are for illustrative purposes only. Actual results will differ.)

h To generate random integers in the range of 1to 6

I!!W8(Ranlnt) 11m [IJ(,)6 [I) lEI

lEI lEI

2 6 1

(Results shown here afe for illustrative purposes only. Actual results will differ.)

~ To determine the number 01penmutationsand combinations

possible when selecting four people from a group 0110

Penmutations: 10 I!!j)(jg(nPr)41E1

Combinations: 10 I!!j)IE (nCr)4 lEI

5040

210

& Toperlonmthe following calculations when Fix 3 is selected for fhe

number01displaydigits:10.;.3 x 3andRnd(10.;.3)x 3 ImII

1mI!2i!J(SETUP)!II(Fix)(II 10IE3(&)3lEI 10.000

IffiI@)(Rnd)10IE3[IJ(&)3lEI 9.999

E-24

~ Todetenninethe greatest common divisor of 28 and 35

~ IKI(GCD)281!!i1 en(,)35m §

To detennine the least common multiple of 9 and 15

~ IE(LCM)91!!i1 m(,) 15 m §

& To extract the integer part of -3.5

~ ~ (Int)ffjJ 3.5m §

~ To detennine the largest integer that does not exceed -3.5

~EI(lntg)1B3.5en§ -4

,Complex Number Calculatie»ns TC-MPLXLJ

To perform complex number calculations, first press I!!ID m (CMPLX)to enter the CMPLX Mode. You can use either rectangularcoordinates (a+b,) or polar coordinates (rL8) to input complex numbers. Complex number

calculation results are displayed in accordance with the complex number

fonnat selling on the setup menu.

/ (2 + 6') + (2') =3 -i (Complex number fonnat: a + b,)

m2~6(@(,)enlEm2ffijg)(,)en§ 3-i

/ 2 L 45= .f2 +.f2i ED_ (Complexnumberfonnat:a+ b,)

21!!i1ffjJ(L)45§ v'2+v'2i

/ .f2 +.f2i =2 L 45ED_ (Complexnumber'onnat:rL8)

~2@~GSJ2@~(')§ 2L45

Note:

.Ifyou are planning to perfonn input and display of the calculation

resultinpolarcoordinatefonnat,specifytheangleunitbeforestartingthe

calculation. .The () value of the calculation result is displayed in the range

of -180. < () :; 180.. . Displayofthe calculation resultwhile Linear Display is selected will show a and bi (or rand () on separate lines.

CMPLX Mode Calculation Examples

/ (1 - ,)-' =t+ti ED (Complexnumberfonnat:a+bi)

m1EI(@(,)en~§

/ (1H)'+(1-')'=0 ED

m 11E(@(')IIJ~~m1 EI(@(,)en~§

To obtain the conjugate complex numberof 2 +3i (Complex number fonnat: a + b,)

I!!iIm (CMPLX)m (Conjg)2~ 3(!!g(')en§ 2-3i

/ To obtain the absolute value and argument of 1+ i ED_

AbsoluteValue: I!!ilI!iI(Abs) 1~ (@(,)§ v'2 Argument:I!!iI m(CMPLX)II) (arg)1~~(,)en § 45

E-25

Using a Command to Specify the Calculation Result Format

Eitheroftwospecialcommands(~rL() or ~a+b,) can be input at the end

of acalculation to specify the display fonnat of the calculation results. The command overrides the calculato(s complex number fonnat selling.

/ .f2+.f2i=2L45, 2L45=.f2+.f2i ED_

2 @ ~ GSJ2@~(')1!!iI m(CMPLX)(!](~rL()§

21!!i11B1(L)451!!i1m(CMPLX)(!J(~a+b,)§

-3

2L45

v'2+v'2i

Using~L!L-__ _ _ _ ..

CALC letsyou savecalculationexpressionsthat containvariables,whichyou

can Ihen recall and execute in the COMP Mode (I!!ID II) andtheCMPLX

Mode(@IDm).

The following describesthe types of expressions you can

savewith CALC.

.Expressions: 2X + 3Y, 2AX + 3BY + C, A + Bi

. Multi-statements: X + Y : X (X + Y)

.Equalities with a single variable on the left and an expression including

variables on the right: A = B + C, Y = X' + X + 3

(Use

~ @!£I(=)to inputthe equals sign of the equality.)

/ To store 3A+ B andthen substitute the following valuesto perfonn

the calculation: (A, B) = (5,10), (7, 20)

3~ffjJ(A)~~E3(B)13A+EI m... \

~ ·- 01

Prompts for input of a value for A Currant value of A

5§10§\3A+B 9 -:5\

I m 1

@!£I(or §) A? 5

7§20§ 13A+B

II -:1\

To exit CALC: €£I

E-26

To store A + Bi and then determine .f3 + i, 1 + .f3 i using polar

coordinates (rL9) 1m

f!2ID1IJ(CMPLX)

+ _.. m

~!BJ(A)(E~E3(B)~(/) A B. rl..fJ

I!!!IIIJ(CMPLX)III(~rL9) .

@!ID@3[D@1 @[

@!ID(or @)1 @11iJ3[D@[

To exij CALC: tgj

Note: Duringthetimefromwhenyoupress@!IDuntilyouexitCALCby

pressing tgj, you should use LinearDisplay inputprocedures for input.

...

21..301

21..601

~~~

SOLVE uses Newton's Law to approximatethe solution of equations. Note that SOLVE can be used in the COMP Mode (@!!1)III)only. The following describes the types of equations whose solutions can be obtained using SOLVE.

.Equations that Include variable X: X' +2X - 2, V = X + 5, X = sln(M), X

+3=B+C

SOLVE solves forX. An expression like X' + 2X - 2 is treated as X' + 2X

-2 =0.

. Equations Input using the following syntax: (equation), (solution

variable) SOLVE solvesfor V, for example, when an equation is inputas: V = X + 5,

Important:

.If an equation contains input functions that include an open

parenthesis (such as sin and log), do not omit the closing parenthesis.

.The following functions are not allowed inside of an equation: I, dJdx, :E,

n, Pol, Rec, +R.

/ To solvey = a.x'+b forx when y = 0, a = 1, and b =-2

1!mi!I(§!g(Y)~@!ID(=)~!BJ(A)IY=AXZ+Bm ... I

~[D(X)@)(E~E3(B)

"'~""'~ . -11

Prompts for input of a value for Y Current value of Y

m M~th

0@1@!BJ2@,Solve for X

Current value of X

E-27

Input an initial value for X (Here,input 1):

m ~

1@1~~AXZi~414213562

L-R= 0

To exitSOLVE: tgj

Note: During the time from when youpress I!!!I@!ID(SOLVE)until you exit SOLVE by pressing tgj, you should use Linear Display input procedures for input.

Important:

.Depending on what youinputfor the initialvalue for X (solution

variable), SOLVE may not be ableto obtain solutions. If this happens, try changingthe inijial value sothey arecloserto thesolution.

.SOLVEmaynot

be able to determine the correct solution, even when one exists.

.SOLVE

usesNewton's law, so even ifthere are mulliple solutions,only one of them wiil be returned.

.Dueto limitations in Newton's law, solutions tend to be

difficult to obtain for equations like the following: y = sin(x), y = c, y = rx.

Solution Screen Contents

Solutionsare alwaysdisplayed indecimal form.

Equation (The equation you input.)

Variable solved for

Solution

(Left Side) - (Right Side) result

"(Left Side) -(Right Side) resull" 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 resultis to zero, the higher

the accuracy of the solution.

Continue Screen

SOLVE performs convergence a preset number of times. If it cannot find a

solution, it displays a confirmation screenthat shows "Continue: [=)".asking

if you want to continue.

Press @ to continue or tgj to cancel the SOLVE operation.

/ Tosolvey=x'-x+ 1forxwheny=3, 7, and 13

~ (§!g(Y)~ @!ID(=)IY=XZ-X+11

IimiiI(D(X)@)ElIimiiI [D(X)(E 1

3@ ,Solve formX

E-28

Inputan initialvalueforX(Here,input1): 1§

I*~X2-X+1

L-R=

Moth

No.

L~atisti~a!.pa.culations~I$TA!)

To start a statistical calculation, perform the key operation ~ [I) (STAT) to enter the STAT Mode and then use the screen that appears to select the type of calculation you want to perform.

Pressing any of the above keys (II) to !II) displays the Stat Editor. Note: When you want to change the calculation type after entering the STAT

Mode, perform the key operation @!!I1I)(STAT/DIST)II)(Type) to display

the calculation type selection screen.

Inputting Data

Use the Stat Editor to input data. Perform the following key operation to display the Stat Editor: @!iI1I)(STATIDIST)[IJ(Data). The Stat Editor provides 40 rows for data input when there is an X column only or when there are Xand Ycolumns, 20 rows when there are Xand FREO columns, or 26 rows when there are X, Y, and FREO columns.

Note: Use the FREO (frequency) column to input the quantity (frequency) of identical data items. Display ofthe FREO column can be tumed on (displayed) or off (not displayed) using the Stat Format setting on the setup menu.

L:t To select linear regression and input the following data:

(170,66), (173, 68), (179, 75)

STAT m

~[I)(STAT)[IJ(A+BX) I !I I v I

170§ 173§ 179§<E>

66§68§75§

Important: .Alldata currently input in the Stat Editor is deleted whenever

you exit the STAT Mode, switch behveen the single-variable and a paired- variable statistical calculation type, or change the Stat Format setting on

the setup menu. .The following operations are not supported by the Stat

Editor:1MtJ,@!jJIMtJ(M-),@@I(STO), Pol, Rec, +R, and multi-statements

also cannot be input with the Stat Editor.

To change the data In a cell: In the Stat Editor, move the cursor to the cell that contains the data you want to change, input the new data, and then

press §.

To delete a line: In the Stat Editor, move the cursor to the line that you want

to delete and then press @).

To Insert a line: In the Stat Editor, move the cursor to the location where

you want to insert the line and then perform the following key operation:

@ II) (STAT/DIST)[I)(Edit)II)(Ins).

To delete all Stat Editor contents: Inthe Stat Editor, perform the following key operation: @!!III) (STAT/DIST)[I) (Edit)[IJ (Del-A).

Obtaining Statistical Values from Input Data

To obtain statistical values, press @9 while in the Stat Editor and then recall the statistical variable (ax, rx', etc.) you want. Supported statistical variables and the keys you should press to

recallthem are shown below.

For single-variable statistical calculations, the variables marked with an asterisk (') are available.

Sum: rx", rx', ty', ty,!:.!:y, tx", rx'y, rx'

@!j)II) (STAT/DIST) [I) (Sum) II) to !II

Number of Items: n', Mean:x', y, Population Standard Deviation: ax',

Oy,Sample

Standard Deviation:$x', Sy

@!!I1I)(STAT/DlST) (!J(Var) II) to m

Regression Coefficients: A, B, Correlation Coefficient: r, Estimated Values: X,y

@!!III) (STAT/DIST) [ID(Reg) II) to [ID

Regression Coefficients for Quadratic Regression: A, B, C, Estimated

Values: XI, Xz,Y

@!!III)(STAT/DIST) [ID(Reg) II) to lID

.See the table at the beginning of this section olthe manual for the regression

formulas.

To select this type of statistical calculation:

Press this key:

(Regression formula shown in parentheses)

Single-variable (X)

II) (1-VAR)

Paired-variable(X,V),linearregression (y =A + Bx)

[IJ (A+BX)

Paired-variable (X, V), quadratic regression

[I)L+CX')

(y=A +Bx + Cx")

Paired-variable (X, V), logarithmic regression

(!J (InX)

=A + Blnx)

Paired-variable (X, Y), e exponential regression

[ID(eAX)

(y=Ae"-')

Paired-variable (X, Y), ab exponential regression

lID (A'SAX)

(y=AB-')

Paired-variable (X, V), power regression

=Ax")

ILl (A'XAB)

Paired-variable (X, Y), inverse regression

lID(1/X)

(y =A + B/x)

..£,.£" .£,and yare not variables. They are commands of the type that take

an argument immediately before them. See "Calculating Estimated Values.

for more information.

Minimum Value: minX., minY, Maximum Value: maxX., maxY

@!!)II) (STAT/DIST) lID(MinMax) II) to rn

(When the single-variable statistical calculation is selected.)

@!!)II) (STAT/DIST) lID(MinMax) II) to (!)

(When a paired-variable statistical calculation is selected.) First Quartile: Qt, Median: med, Third Quartile: Q3

I!!iIII)(STAT/DIST) lID(MinMax) lID to (ID (When the single-variable statistical calculation is selected.) Note: While single-variable statistical calculation is selected, you can input

the functions and commands for performing normal distribution calculation from the menu that appears when you perform the following key operation:

@!!)II) (STAT/DIST) (ID(Distr). See "Performing Normal Distribution

Calculations. for details.

h To input the single-variable data x = (t, 2, 2, 3, 3, 3, 4, 4, 5), using

the FREQ column to specify the number of repeats for each items

(Ix.; freq.) ={1;1, 2;2, 3;3, 4;2, 5;1)), and calculate the mean and

population standard deviation.

@!!)1i!ID(SETUP)(!)(STAT)II)(ON)

@J1ID(STAT)II)(1-VAR)

1§)2§)3§)4§)5§)<E>

113213313213 _

1!9@!!) II)(STAT/DIST)(!){Var)rn{x)§) [

1!9@!!) II) {STAT/DIST)(!){Var)lID (crx)13 [

STAt iii

~I' ~I~I

L 1547005381

Results: Mean: 3 Population Standard Deviation: 1.154700538

~ To calculate the linear regression and logarithmic regression

correlation coefficients for the following paired-variable data and determine the regression formula for the strongest correlation: (x, y) = {20, 3150), (110, 7310), (200, 8800), (290, 9310). Specify Fix 3 (three decimalplaces) for resulls.

@!!)~(SETUP) (!){STAT) rn (OFF) @!jJ1i!ID(SETUP)IID(Fix)1ID

@)1ID(STAT)rn(A+BX)

20 13 110 13 200 13 290 13 <E\

315013 7310 138800 13 931013

@@!jJII)(STATIDIST)(ID(Reg)lID(r)§) [

1!91!!i11I)(STAT/DIST)II)(Type)(!)(ln X)

1!91!!i11I)(STAT/DIST)(ID(Reg)lID(r)§)

[

@1!!iI1I)(STAT/DIST)IID(Reg)II)(A)§) [

E-31

SfAT IiJ FIX

Keaa

~BDa

~ ... .iiII

0.9231

0.9981

-3857.9841

@Iffi II)(STATIDIST)(ID(Reg)rn (B)13 1 2357.5321

Results: Linear Regression Correlation Coefficient: 0.923

logarithmic Regression Correlation Coefficient: 0.998 logarithmic Regression Formula: y =-3857.984 + 2357.5321nx

Calculating Estimated Values

Based on the regression formula obtained by paired-variable statistical calculation, the estimated value of y can be calculated for a given x-value. The corresponding x-value {two values, x. and x" in the case of quadratic regression) also can be calculated for a value of y in the regression

formula.

~ To determine the estimate value for y when x = 160 in the

regression formula produced by logarithmic regression of the data in

h. Specify Fix 3 for the result. (Perform the following operation

after completing the operations in

h.)

@ 1601mII){STATIDIST)(ID(Reg)(IDlY)13 1 8106.8981

Result: 8106.898 Important: Regression coefficient, correlation coefficient, and estimated

value calculations can take considerable time when there are a large number of data items.

Performing Normal Distribution Calculations

While single-variable statistical calculation is selected, you can perform normal distribution calculation using the functions shown below from the menu that appears when you perform the following key operation:

@!!)

II) (STAT/DIST)(ID{Distr).

P, Q, R: These functions take the argument t and determine a probability of standard normal distribution as illustrated below.

AJeAX

o tOt 0 t

~t: This functionis preceded by the argument X, and determines the

normalized variate X.t _X~i .

h Forthe singlevariabledata {x. ;fraq.}=(0;1,1;2,2;1,3;2,4;2,5;2,

6;3,7;4,9;2, 10;1), to determine the normalized variate (~r) when x = 3, and P(t) at that point up to three decimal places (Fix 3).

@!!)@)(SETUP)(!)(STAT)II){ON)

@!!)@ii!)(SETUP)IID(Fix)IID@JlID(STAT)1I)(1-VAR)

013 113213313413513613713913 s;." F~~UfIX

10§)$<E\1 132131 13213213213313 Iyl lal~1

413213113

E-32

STAt

@ 31m m(STAT/DIST)CID(Distr)(!)(~t)@ ,3.t

m AK

-0.762

STAt

I!i!iI m (STA T/DIST) CID (Distr) m(POI!i!I (II @ I P(Ans)

iii fiX

0.223

Results:Normalized variate(~t): -0.762

P(t): 0.223

!"'"88!e;p~culaiibn~(84~Ejit

Press @ID@(BASE-N) to enter the BASE-N Mode when you want to

perform calculations using decimal, hexadecimal, binary, and/or octal values. The initialdefault number mode when you enter the BASE-NMode

is decimal, which means input and calculation results use the decimal number format. Press one of the following keys to switch number modes:

~(DEC) for decimal, @(HEX) for hexadecimal, (§](BIN) for binary, or I]!!)(OCT) for octal.

/ To enter the BASE-N Mode, switchto the binary mode, and

calculate112+ 12 I

I§!)@(BASE-N)

(§](BIN)

Bin

0000000000000000

Bin

111%)1@ 10000000000000100

Continuing from above, switch to the hexadecimal mode and

calculate IF..+ I..

I I

@@(HEX) 1 I§) (F)I%)1@ 00000~~6

Continuing fr9m above, switch to the octal mode and calculate

78+ 18

@1]!!)(OCT)71%)1 @

[

Oct

00000000010

Note: .Use the following keys to input the letters A through F for hexadecimal

values: 8(A), 8(B), ffiii)(C),@(D), §J(E), G!i!)(F). .In the BASE-N

Mode, inputoffractional (decimal) valuesand exponents is not supported. If a calculation result has a fractional part, it is cut off.

.The inputand oulput

ranges is 16bitsfor binary values,and 32 bitsfor other types of values.The following shows details about input and output ranges.

Base-n Mode

Input/OutputRanges

Positive: 0000000000000000 ~ x ~ 0111111111111111 Negative: 1000000000000000 :a x ~ 1111111111111111

Binary

E-33

Octal

Positive: 00000000000 ~ x ~ 17777777777 Negative: 20000000000 :; x ::; 37777777777

-2147483648:ii x::; 2147483647

Positive: 00000000 ~ x ~ 7FFFFFFF

Negative: 80000000

:; x :5FFFFFFFF

Decimal Hexadecimal

Specifying the Number Mode of a Particular Input Value

You can input a special command immediately following a valueto specify the number modeof that value. The special commands are: d (decimal), h (hexadecimal), b (binary),and 0(octal).

/ To calculate 10..+ 10,6+10H 10. and display the resultas a decimal

value

@I£J(DEC) ImIID(BASE)~m(d)10 I%)

m IID(BASE)~ rn(h) 10I%) @!!)IID(BASE)~ lID(b)10I%)

@!!)IID(BASE)~ @(o)10 @

Converting a Calculation Result to another Type of

Value

You can use anyone of the followingkey operations toconvert the currently displayed calculation result to another type of value: ~(DEC) (decimal),

@(HEX) (hexadecimal), (§](BIN) (binary), I]!!)(OCT)(octal).

/ To calculate 1510x 37,0in the decimal mode, and then convert

theresulttohexadecimal,binary,andoctal

@1£J(DEC)15~37@ 555

@(HEX) 00000228

(§](BIN)0000001000101011

I]!!)(OCT) 00000001053

Logical and Negation Operations

Your calculator providesyou with logical operators (and, or, xor, xnor) and functions (Not, Neg) for logical and negation operations on binary values.

. Use the menu that appears when you press m lID(BASE)toinputthese

logical operators and functions. All of the following examples are perfonned inthe binary mode (~(BIN)).

/ To detennine the logicalAND of 1010, and 1100, (1010, and 1100,)

@ 1010@!jJlID(BASE)m(and) 1100@ 0000000000001000

/ Todeterminethe logical OR of 10112 and 110102(101hor 11010,)

@10111!i!!11ID(BASE)rn(or)11010@ 0000000000011011

E-34

/ To determinethe logicalXOR 0110102and 1100, (1010, xor 1100,)

@ 1010 lID @](BASE)@](xor)1100 lEI 0000000000000110

/ To determine the logical XNOR 01111" and 10" (111"xnor 10")

@ 11111!!!1@](BASE)@)(xnor)1011E1 1111111111110101

/ To determine the bitwise complement011010, (Not(101O,))

@1!!!I@](BASE)II)(Not)1010rn lEI

1111111111110101

/ To negate (takethe two's complement) of 10110" (Neg(10110"))

@1ID@](BASE)!II(Neg)101101 CDlEI 1111111111010011

Note: In the case of a negative binary, octal or hexadecimal value, the calculator converts the value to binary, takes the two's complement, and then converts back to the original number base, For decimal (base-I 0) values, the calculator merely adds a minus sign,

ll::i!!a,~'~~c!lJatio]s 1I(Qil,<..=--

You can usethe followingprocedure inthe EONModeto solve simultaneous linearequations with two or three unknowns,quadratic equations,and cubic

equations.

1.Press Ii@ II) (EON) to enter the EON Mode.

2. On the menu that appears, select an equation type. To select this calculation type: Press this key:

Simultaneous linear equations with two lIJ(a,X + b,y = c,) unknowns

Simultaneous linear equations with

three unknowns

Ouadratic equation Cubic equation

rn(a,X + b,y + c..z= d,) @](aX'+bX+c=O)

@)(aX'+bX'+cX+d=O)

3.Use the Coefficient Editorthat appears to input coefficient values. "To solve 2x"+x-3 =0, lor example, press @] in step2, and then input

the following for the coefficients (a = 2, b = I, C = -3): 21E111E11B 3lEI

"To change acO,efficientvalue you alreadyhave input, move the cursor

to the appropriate cell, input the newvalue, and then press lEI.

" Pressing @ will clear all of the coefficients to zero.

Important: The following operations arenot supportedbythe Coefficient

Editor. 1MB,@!iI1MB(M-),IID@!!I(STO). Pol,Rec,+R,andmulti-statements also cannot be input with the Coefficient Editor.

4.After all the values are the way you want, press lEI.

"This will display a solution. Each press 01 lEI will display another

solution. Pressing lEI while the linal solutionis displayedwill retum to the Coefficient Editor.

"You can scrollbetween the solutions usingthe

~ and@ keys.

" To retumto the CoefficientEditor while any solutionis displayed, press

Note: "Even il Natural Display is selected, the solutions of simultaneous

linear equations are not displayed using any form that includes r.

"Values cannotbe converted to engineeringnotationonthe solutionscreen.

E-35

" A message appears to let you know when there is no solution or when there are infinite solutions.Pressing @ or lEI will retum to the Coefficient

Editor.

Changing the Current Equation Type Setting

Press 1i@!II(EON) and then select an equation type from the menu that appears. Changing the equation type causes the values of all Coefficient Editor coefficientsto change to zero.

EaN ModeCalculation Examples

2x"-3x-6=0 rmm

I!!ffiII)(EON)@](aX' + bX +c = 0) 2 IEIIB 31E11B 6 lEI lEI

(X,=) 3+{ff (X,=) 3-{ff

~ (V-ValueMinimum=)- _ 5:

.Thelocal minimumvalueisdisplayedwhena > O.The local maximumvalue

is displayed when a < O.

(X-Value Minimum=)"

/ x'-2v'2x+2=0 rmm

I!Q!!)!II(EON)@](aX'+bX + c = 0)

11E11B2~2rn1El21E11E1

(X=) V2

E-36

x+ 2y=3, 2x+ 3y=4

1i@!II(EON)IIJ(a.X + b,y = c,)

Mo.

1lEI 2lEI 3 lEI

[ .

2 lEI 3 lEI 4 lEI

lEI

(X=) -1 (V=)

x- y+ Z=2, x +y-z = O,-x+ y+z =4

1!Q!!)!II(EON)rn(a,X + boY+ c..z = d,)

1IEIIB 1lEI 1lEI 2lEI

...

1 lEI 1 IEIIB 1 IEIOlEI

'I -, , 21

2 ,

-1-'

IBI lEI1lEI1lEI4lEI

. ,

lEI

(X=) 1 (V=) 2 (Z=) 3

/ x"-2r-x+2=0

(!i!!J (ID(EON)I!J (aX' + bX" + eX + d =0)

1EJIE)2EJIE)1EJ2EJEJ

~ ~

(X,=) -1 (X>=) 2 (X,:) 1

r MatrixCaICulationsjH~TRI~L ..: :1

Use the MATRIXMode to perform calculations involving matrices of up to 3 rows by 3 columns. To perform a matrix calculation, you first assign data to special matrix variables (MalA, MatB, Mate), and then use the variables in

the calculation as shown in the example below.

h Toassign[~ :]toMalAand[_; -~]toMatB,andthenperform

the following calculations:

[

2 1

]

[

2 -1

]

(MalAxMatB),

1 1 -1 2

[

2 1

]+[

2 -1

]

(MalA+MatB)

1 1 -1 2

1. Press ~ [!) (MATRIX) to enter the MATRIX Mode.

2. Press [D (MalA) rn (2x2).

.This will display the Matrix Ednor for input

of the elements of the 2 x 2 matrix you specified for MatA.

3. Input the elements of MalA: 2 EJ 1 EJ 1 EJ 1 EJ.

4. Perform the following key operation: I!!!II!J (MATRIX) (II (Data) (II (MatB)rn(2x2).

.This willdisplay the Matrix Editor for input of the elements of the 2 x 2

matrix you specified for MatB.

5. Input the elements of MatB: 2 EJ 1BJ1 EJ 1BJ1 EJ 2 EJ.

6. Press @ to advance to the calculation screen, and perform the first

calculation (MatAxMatB): I!iiiII!J (MATRIX)!IJ (MalA) I2D I!!!II!J(MA TRIX)

I!J (MatB) EJ.

.This will display1he MalAns screen with the calculation results.

'..Ii;;;;;;;;;;;:MAlmD i"Ans" S~ndS tor

~ 1-; I] "MalAns.

01 3

MAIm

MatAxMatll

Note: "MalAns" stands for "Matrix Answer Memory". See "Matrix Answer Memory" for more information.

7. Perform the next calculation (MatA+MatB): @ I!!!I !II (MATRIX)

!IJ (MalA) IE I!!!II!J (MATRIX) !II (MatB) EJ.

MATm

MatA+MatEl

MATm

..1-,

~I 1-0

E-37

MatrixAnswer Memory

Whenever the result of a calculation executed in the MATRIX Mode is a matrix, the MalAns screen will appear with the result. The resull also willbe

assigned to a variable named "MalAns". The MatAns variable can be used in calculations as described below.

.To insert the MalAns variable into a calculation, perform the following

key operation: I!!!II!J(MATRIX)[!)(MalAns).

.Pressing anyone of the following keys while the MatAns screen is

displayed willswitch automatically to the calculation screen: IE, EJ, IXJ,

~,~,I£I, 1!!!I~(x"). The calculation screen willshow the MalAns

variable followed by the operator or function for the key you preSSed.

Assigning and Editing Matrix Variable Data

Important: The following operations are not supported by the Matrix Editor.

1M3,I!!!J1M3(M-), I!!!I§(STO). Pol, Rec, +R, and multi-statements also

cannot be input with the Matrix Editor.

To assign new data to a matrix variable:

1. Press I!!!I!II (MATRIX)CD(Din), and then, on the menu that appears, select the matrix variable to which you want to assign data.

2. On tha next menu that appears, select dimension (mxn).

3. Use the Matrix Editor that appears to input the elements of the matrix.

To assign

[

1 0 -1

]

to MaIC

0-1 1

l!!jJ I!J(MATRIX)

CD(Dim)!IJ(MatC) 1!J(2x3) [

1 EJOEJIEI1 EJO§)IE) 1 EJ1 EJ

-Y 1IIIi\]

MATm

To edit the elements of a matrix variable:

1.Press I!!!II!J(MATRIX)(II(Data), and then, on the menu that appears, select the matrix variable you want to edit.

2. Use the Matrix Editor that appears to edit the elements of the matrix.

.Move the cursor tothe cell that contains the element you want to change,

input the new value, and then press EJ.

To copy matrix variable (or MalAns) contenta:

1. Use the Matrix Editor to display the matrix you want to copy.

.If you want to copy MatA, for example, perform the following key

operation: I!!!II!J(MATRIX)(II(Data)[D(MalA).

.Ifyou want to copy MalAns contents, perform the following to display the

MalAns screen: @ I!!!II!J (MATRfX)[!) (MalAns) EJ.

2. Press I!!!I ~(STO), and then perform one olthe following key operations to specify the copy destination: IE)(MalA), G(MatB), or I!i)(MatC).

. This will display the Matrix Editor with the contents of the copy

destination.

Matrix Calculation Examples

[2,]

[

2 -1

]

The following examples use MalA = 1 1 and MatB = -1 2 from £..1,

and MatC = [6 _~ -:] from~. You can input a matrix variable into a key

operation by pressing I!!!II!J (MATRIX)and then pressing one of the

followingnumberkeys: !IJ(MalA),I!J(MatB),(ID(MaIC). 1

E~ I

h. 3x MatA (Matrix scalar multiplication).

..1-,

@3!IDMatA(5)l-3

---..-

h Obtainthe determinant of MatA (det(MatA)).

@ ~ (!)(MATRIX) ILl (det) MatA I]) (5)

L3. Obtain the transposition of MatC (Tm(MatC)).

@~(!)(MATRIX)IID(Tm) MatCI]) (5)

..~

I -Y

6 Obtain the inverse matrix of MatA (MatA").

Note: You cannot use ~ for this input. Use the Ia;)keyto input "-'''.

..~

@MatAIa;)I5)l~i

L:z. Obtain the absolute value of each element of MatB (Abs(MatB)).

..1-

@l!§)ffiiiI(Abs)MatBI])(5) l-j

h Determine the square and cube of MatA (MatA'. MatA').

Note: You cannot use

~ for this input. Use ~ to specify squaring.and

@!j)~ (x3)tospecifycubing.

@MatA~ (5)

@MatA@!j)~(x3) (5)

h Determine the MatA=

[

~ ~ ~

]

row echelon form.

789

f-i

@@!j)(!)(MATRIX)~CD(Ret)MatAml5) 01.1~2'l.m~

o 0 0

[

1 2 3

]

& Determine the MatA= 4 5 6 reduced rowechelon form.

. 7 8 9

..f-1

@@!j)(!)(MATRIX)~m(Rref)MatAml5) I a

fCreating*7N nberTabiifrorn "Two'

:F'ijnct.ion..!JTAB~ ____

TABLE generates a number table based on one or two functions. You can

use the function.f(x) orthe two functions.f(x)and g(x). See "Configuring the Calculator Setup" for more information. Performthe foilowing steps to generate a number table.

1.Press I!@ILI(TABLE) to enter the TABLE Mode.

2.Use the X variable to input two functions. one in the format .f(x) and the other in the format g(x).

E-39

.Be sure to input the X variable (!!!HIDI]) (X)) when generating a number

table. Any variable other than X is handled as a constant.

.If you are using a single function. input a function in fhe format.f(x)

only.

.The foilowing cannot be used in the function: Pol, Rec.l. d/dx. ~. II

-jJ

For this prompt:

Input this:

Start?

Inputthe lower limit of X (Default =1).

End?

Inputthe upperlimit of X (Default = 5).

Note: Makesure that the End value is always greater than

the Startvalue.

Step?

Input the increment step (Default =1).

Note:The Stepspecifies by how much the Start

value should be sequentiaily incremented as the number table is generated. If you specify Start = 1 and Step = 1, X sequentiaily willbeassigned the values 1.2. 3. 4. andso on to generate the number

table until the End value is reached.

.Inputting the Stepvalue and pressing (5) generates and displays the

number table in accordance with the parametersyou specified.

.Pressing @ while the number table screen is displayed wiil return to

the function input screen in step 2.

"To generate a number table forthe functions f(x) = xl + + and

g(x) = x3 - +for the range -1 :;; x;;; 1, incremented in steps of 0.5

mmI

ILI(TABLE)I f(X)=!

M..

@!j)@!i!)(SETUP) lID(TABLE)m(f(x),g(x))

M..

!!!HID1])(X)(i)

t 2

f(X)=X2+

(5) 19(X)=!

e M..

.Pressing (5) without inputting anything for g(x) wiil generate a number

table based on.f(x)only.

M..

!!!HID1])(X)13 t 2

9(X)=X2_

''-1 F(W)I G7 I

(5)lEI1(5) 1(5)0.515)

1 1.5 0.5

2 -D.' 0.'5 -0.25

a a D.5 -0.5

-1

setting,while 20 rows are supported for the "f(x).g(x)" setting. "You can

use the numbertable screen for viewing values only. Table contents cannot be ed~ed. "The number table generation operation causesthe contents of variable X to be changed.

Important: The function you input for number table generation isdeleted wheneveryoudisplaythesetupmenuintheTABLEModeandsw~chbetween

Natural Display and Linear Display.

~t!i'-q1ilii~ik)iiil¥J'"iT!!RL_~i"-]

Use the VECTOR Modeto perform2-dimensional and3-dimensional vector calculations.To perform a vector calculation. you first assigndata to special vector variables (VctA. VctB. VctC). and then use the variables in the calculation as shown in the example below.

h To assign (1. 2) to VctA and (3. 4) to VctB. and then perform the

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

1.Press @!!)III (VECTOR) to enter the VECTOR Mode.

2.Press (I)(VctA)!I)(2).

"This willdisplay the Vector Editor for input

of the 2-dimensioflal vector for VctA.

vere

R_ DI

-A"stands for "VetA".

3.Input the elements of VctA: 11512151.

4.Perform the following key operation: @ III (VECTOR) m (Data) m(VctB)m(2). " Thiswill display the Vector Editor for input of the 2-dimensional vector

for VetB.

5.Input the elements of VctB: 31514151.

6.Press @ toadvancetothe calculation screen. andperformthecalculation (VctA + VctB): @ III (VECTOR) [ID (VctA) IE I!!iIIII (VECTOR) (!J (VctB)151.

"This will display the VctAns screen with the calculation results.

vere I V~e I

VctA+VctEl

..~

-AnS- stands for

-7 - 6 "VetAns".

o 4

Note: "VetAns"stands for "Vector Answer Memory". See"Vector Answer Memory"for more information.

Vector Answer Memory . Whenever the result of a calculation executed in the VECTOR Mode is a

vector. the VctAns screen will appear w~hthe result.The result also will be assigned to a variable named "VctAns".

The VctAns variable can be used in calculations as described below.

" To insert the VctAns variable into a calculation. perform the following key

operation: I!!iIIII(VECTOR)III (VctAns).

" Pressinganyone of the followingkeyswhilethe VctAnsscreen isdisplayed

will switchautomatically to the calculation screen: IE. 13. IX). 1:). The calculation screen will show the VctAns variable followed by the operator

for the key you pressed.

E-41

Assigning and Editing Vector Variable Data

Important: The followingoperations are not supported by the Vector Editor:

1iID.I!!ilIiID(M-). I!!iI ~(STO). Pol. Rec. +R. and multi-statementsalso

cannot be input with the Vector Editor.

To assign new data to a vector variable:

1.Press I!!iIIII (VECTOR)(I) (Dim). and then. on the menu thatappears, select the vector variable to which you want toassign data.

2.On the next menu that appears. select dimension (m).

3.Use the Vector Editor that appears to input the elementsof the vector.

1!!1. To assign (2. -1,2) to VctC

I!!iIIII(VECTOR)(I)(Dim)[ID(VctC)(I)(3)

Ie[

21518 11512151

To edit the elements of a vector variable:

1.Press I!!iIIII (VECTOR)m (Data), and then. on the menu that appears. select the vector variable you wantto edit.

2.Use the Vector Ed~orthat appears to ed~the elements of the vector.

"Movethe cursorto the cellthat contains theelementyou wanttochange.

input the new value.and then press 151.

To copy vector variable (or VctAns) contents:

1.Usethe Vector Ed~orto display the vector you want to copy. " Ifyouwantto copyVetA,forexample,performthefollowingkeyoperation:

I!!iIIII(VECTOR) m (Data)(I) (VctA).

" Ifyouwant to copyVctAns contents.perform the following todisplay the

VctAns screen: @1!!iI1II(VECTOR)III(VctAns)l5I.

2.Press I!!ilIi!!!I(STO). andthen performone ofthe following keyoperations to specify the copy destination: 8(VctA). B(VctB). or ffij(VctC).

"This will display the Vector Editor with the contents of the copy

destination.

Vector Calculation Examples

ThefollowingexamplesuseVetA=(1.2)andVctB=(3.4) from6. andVctC= (2.-1. 2) from h. You can inputa vector variable intoa keyoperation by

pressing I!!iIIII(VECTOR) and then pressing one of the following number keys: [ID(VetA). (!J(VctB), III(VctC).

h 3 x VetA (Vector scalar multiplication). 3x VetA -VetB (Calculation

exampleusingVctAns)

@3lX)VctAl5I[..~

EIVctBIi)

[...,

vere

E-42

~ VctA. VctB (Vector dot product)

VCTm

@VctAt!!!I ([J(VECTOR)IL)(Dot)VctB@ I VetA'VetB

h VctA x VctB (Vector cross product)

@VctAOOVctB@I.......

Obtain the absolute values of VctC.

VCTm

@t!!!I ffiii)(Abs)VctCQ) @ I Abs(VetC)

Determine the angle formed by VctAand VctB to three decimal places (Fix 3). lEI

(A.B) .

. (A.B)

(cos 6 =IAIIBI ,which becomes 6 =cos- IAIIBI)

1!!1!I@2ffi(SETUP)[ID(Fix)!I) @mVctA@ij)([J(VECTOR)IL)(Dot)VctBIJ)IE

VCTm fIX

m t!!!I ffiii)(Abs)VctAIJ) @iiJffiii)(Abs)

(VetA'VctB)..(Ab~

VctBIJ)Q)@ 0.984

YCTm nx

@iiJ l§j(cos")1!;) IJ) @ I cos-I(Ans)

10.305

~gu~liiyC!lc..u!at1O"n$(i)lI!Qf ..... 2~

You can use the following procedure to solve a quadratic inequality or cubic inequality.

,. Press @2ffi<i)CD(INEQ)to enter the INEQ Mode.

2.Onthe menu thatappears, select an inequalitytype. To select this Inequalitytype: Press this key:

Quadraticinequality

m (aX'+bX+c)

Cubicinequality m (aX' + bX' +cX+ d )

3.Onthemenuthatappears,usekeys CDthroughI1Jtoselecttheinequality

symboltypeand orientation.

4.Usethe CoefficientEdrtorthat appears to inputcoefficientvalues.

.To solve x' + 2x - 3 < 0, for example, input the coefficients a = I, b = 2,

c =-3 bypressing1@2 @!El3@.

E-43

.To change a coefficient value you already have input, move the cursor

to the appropriate cell, input the new value, and then press @.

.Pressing @ willclear all of the coefficients to zero.

Note: The followingoperations are not supported bythe Coefficient Editor: !iE), t!!!IlMB(M-),I!!1!II§)(STO). Pol, Rec, +R, and multi.statements also

cannot be input with the Coefficient Editor.

5. After allthe values are the way you want, press @.

.This will display the solutions.

.To return to the Coefficient Editor while the solutions are displayed, press

Note: Valuescannot be convertedto engineeringnotationon the solution

screen.

Changing the Inequality Type

Press @2ffi<i)CD(INEQ) and Ihen select an inequality type from the menu

thatappears.Changingtheinequalitytypecausesthe values of allCoefficient

Editor coefficientsto change to zero.

INEQ Mode Calculation Examples

/ x'+2x-3<0 rmm

1: aX2 +bX+C >°

@!ID<i)CD(INEQ)CD(aX'+ bX + c) 2:aX2+bX+c<O

3:aX2+bX+c;'O 4: aX2+bX+C=0

m(aX' + bX+c <0)

m NItti

~ b. cUI

aX2+bX+c<O

m ...

I · I b .~)

aX2+bX+c<O

-3

@ .A<X<B

-3<X<

Note: Solutions are displayed as shown here when Linear Display is selected.

-3

/ x'+2x-3;;; 0 rmm

@2ffi<i)CD(INEQ)CD(aX'+bX+c)

!I) (aX' + bX + c ;: 0)

1 @2@!El3@

m ...

I' I b ~)

aX2+&X+C~O

-3

m Math

X~-3.HX

'E-44

/ 2.<'-3x2 e; 0 rmm

@!i!)~(])(INEQ)CIJ(aX'+ bX'+cX+d)

!I) (aX'+bX' +cX+d e;0)

21EJ831EJ

m ...

I · 2 b -3 IIIIiIr.

aX3+t.X2+cX+d~0

X=A.B~X

IEJI X=O,~~X

/ 3x>+3x2-x>0 Em

@!i!)~(])(INEQ)CIJ(aX'+ bX'+cX+d)

(])(aX'+ bX'+cX+ d > 0)

31EJ31EJ811EJ

Note: Solutions are displayed as shown here when Linear Display is selected.

ID Math

I b 3 c _I '-"1

aX3+bX2+cX+d>0

A<X<B,C<X A= -1.263762616

B= 0

C= 0.2637626156

Special Solution Display

."All Real Numbers" appears on the solution screen when the solution of an

inequality is all numbers.

x2 i: 0 rmm

@!i!)~ (]) (INEQ) (]) (aX' + bX + c)

!I) (aX' + bX + c e; 0)

1 IEJ 0 IEJ 0 IEJIEJ

Ii)

Malll

All Real Numbers

."No-Solution" appears on the solution screen when no solution exists for

an inequality (such as X' <0).

rU~VERfFY iVEfill:'l~c_~."--

VERIFY is a function you can use to verify whether an input equality or

inequality is true (indicated by TRUE) or false (indicated by FALSE). The following shows the general procedure for using VERIFY.

/ To verify whether 4V9 =12 is true rmm

1. Press @!!I~ CIJ(VERIF)to enter the VERIFY Mode.

E-45

ID Malll

TRUE/FALSE

2. Input 4V9 =12.

4GSJ9 <E>l!i!!IlII (VERIFY) (]) (=)12 . You can select the equality symbol or

inequality symbol from the menu that appears when you press l!i!!IlII(VERIFY).

3. To verify, press IEJ.

IiJ M.th.

4./9=12

TRUE

You can input the following expressions for verification in the VERIFY Mode.

.Equalities or inequalities that include one relational operator 4 = m,

4 '" 3, " >3, 1 + 2 :;; 5, (3 x 6) < (2 + 6) x 2, etc.

.Equalities or inequalities that include multiple relational operators 1 ;; 1 <

1 + 1, 3 < " < 4, 2' =2 + 2 =4, 2 + 2 =4 < 6, 2 + 3 = 5 '" 2 + 5 = 8, etc.

Note: . The verification result willcause 1 to be assigned to Ans memory

when TRUE and 0 when FALSE.

.The input expression can be a total of

99 bytes, including the lelt side, right side, and relational operators. .Any

variable (A, B, C, D, E, F, X, Y, M) input into an expression is treated as a

value, using the value currently assigned to the variable. .+R, Pol and Rec

functions cannot be used in an expression. In the VERIFY Mode, the calculator performs a mathematical operation

on the input expression and then displays TRUE or FALSE based on the

result. Because of this, calculation error can occur or a mathematically correct result may not be able to be displayed when the input calculation expression includes calculation that approaches the singular point or

inflection point of a function, or when the input expression contains multiple calculation operations.

Expression Input Precautions

The followingtypes of expressions cause a SyntaxERROR and cannot be verified.

.An expression with nothing on the left side or right side (Example: = 5..f'f)

.An expression in which a relational operator is inside of a fraction or function

(Example: 1 =1, cos (8 ;a 9»

.Anexpression inwhicha relationaloperator is enclosed in parentheses

(Example:8 < (9 < 10»

.An expression in which multiple relational operators that are not oriented

in the same direction (Example: 5 ;a 6 e; 4)

.An expression that contains two of the following operators in any combination

(Example: 4 < 6 '" 8)

. An expression that contains consecutive relational operators

(Example: 5 e; > 9)

E-46

VERIFYMode Calculation Examples

"To verifylog2< log3 < log4

§2ml!i!j)[ID (VERIFY)@ «)

§ 31I11!i!!1[ID(VERIFY)@«) ~4II1§)[

TRUEI

"Toverifyo«t)'-t rmm

o I!!!J [ID (VERIFY) @ «)

8(ji)9<E>@lE!8(ji)9§) [

FALSEI

"To verify 52 =25 =>'625 rmm

5@11!i!!1[ID(VERIFY) m (=)

251!i!!1[ID(VERIFY) m (=) ~ 625 151

[

TRUEI

~Diitrja!ttPonca[q~ationi~'.$'Ill.-~J

Youcanuse the proceduresbelowtoperformsevendifferenttypesof

distribution calculations.

1. Press @!i!)IID(DIST)to enter the DIST Mode.

2. On the menu that appears, select a distribution calculation type.

3. Input values for the variables.

.With Binomial PO, Binomial CD, Poisson PO, and Poisson CD, you can

input sample data and then perfonn calculations.

4. After inputting values for all of the variables, press 151.

.This displays the calculation results.

.Pressing 151 or @ while a calculation result is displayed will retum to

the input screen of the first variable

Note:

.To change the distribution calculation type after you enter the DIST

Mode, press I!i!!Im(STAT/DIST)m(Type) and then select the distribution type you want.

.Distribution calculation accuracy is up to five significant

dig~s.

E-47

Variables that Accept Input

The following are distribution calculation variablesthataccept inputvalues. Nonnal PO x, a, p

Normal CO Lower, Upper, a, p

InverseNonnal Area, a,p (Tailsettingalwaysleft.)

Binomial PO, Binomial CO... x (or List), N, p Poisson PO, Poisson CD x (or List),p

x: data, a: standard deviation (a > O),p: mean, Lower. lower boundary, Upper.

upper boundary, Tail: probability value tail specification, Area: probability value (0 ;a Area ;a 1), List: sample data list, N: number of trials, p: success probability (0 :; p ;a 1)

List Screen (Binomial PD, Binomial CD, Poisson PD, Poisson CD)

With Binomial PO, Binomial CD, Poisson PO,and Poisson CD, usethe List

Screenforsampledata input.Youcan inputup to25 data samplesforeach

variable. Calculation results are also displayedon theList Screen.

Distributioncalculation type

Value at current cursor position

I I

X:Sample data Ans:Calculation results

edit sample data: Movethe cursor to the cell that contains the sample

data you want to edit,input the new sample data, and then press 151. To delete sample data: Move the cursor to the sample data you want to

delete and then press i!ID.

To insert sampfe data: Move the cursor to the position where you want to

insert the sample data, press I!!!J m(ST A T/DIST) m (Edit)m (Ins), and

then input thesample

data.

To delete all sample data: Press @!!JmiST AT/DIST)m (Edit)m (Del-A).

DIST Mode Calculation Examples

To calculate the nonnal probabil~y dens~ when x=36, a=2, p=35

~IID(DIST) I ~;~~~~~t ~g

3: Inverse Normal

4:BinomialPD

m(Nonnal PO)' ormal

PD:x?

36151

Normal PD:cr?

2151

Normal PD:J.\?

E-48

To select this type of calculation:

Press thfs key:

Nonnal probability density

m(Nonnal PO)

Nonnal cumulative distribution

rn(Nonnal CD)

Inverse normal cumulative distribution

lID(Inverse Nonnal)

Binomial probability

@(Binomial PO)

Binomial cumulative distribution

m(Binomial CD)

Poisson probability

m(Poisson PO)

Poisson cumulative distribution

lID(Poisson CD)

35@

0.1760326634

Result: 0.1760326634

.Pressing @ or @ retums to the x inputscreen.

To calculate binomialprobability for the sample data pO, 11,12, 13,

14}when N=15 andp=0.6

[

UList 2tVar

I!2ID ~ III (DIST)t!I (Binomial PO)

Display the List Screen:

(])(List) I ~I~I.'~ IBlOC!

.To specify data using parameter format, press rn(Var).

il.JuI.'S IBlOC!

10@11@12@13@14@

. "

@' lnomial PD:N?

15@' lnomial PD:p?

0.6@

Q~?~s'

BlOC!

2 II 0.12&'1 :I Ii! a.D&33

x 1~

D~B~33

BlOC!

5 I"~

Results:

x = binomial probability of 10 0.18594 x = binomial probability of 11 0.12678

x = binomial probability of 12 0.063388

x = binomial probability of 13 0.021942 x = binomial probability of 14 4.7018 x 10-3

.Pressing @ retums to the N input screen. Pressing @ retumsto the List

Screen (input data samples are stored).

Note .The following cannot be used in the distribution calculations:

Pol, Rec, +R, J. d/dx. .When data is specified using parameter tormat,

calculation resulls are stored in Ans memory. .An error message appears

if the input value is outsidethe allowable range. "ERROR" will appear inthe

E-49

Ans column of the List Screen when the value input for the corresponding

sample data is outsidethe allowable range.

.1Jj;i~t~fiij:1i..!U$ =",::""..2:=C1' .-1

Yourcalculator comeswith 40 built-in scientific constantsthatcan beused in

anymode besides BASE-N. Eachscientificconstantis displayed asaunique

symbol (such as tt), which can be usedinside of calculations. To input a scientific constant intoa calculation, press

lID IZ)(CONST)and

then input the two-digit number that corresponds to the constant you want.

"To input the scientific constant Co(speed of light in a vacuum), and

display its value

@IIDIZ)(CONST)

CONSTANT

Number 01--40?

L_]

m Malll..

rnf1)(Co)@ ,CO

299792458

"To calculate Co= {£;ii'. Em

MllftA

@~ 1~~IIDIZ)(CONST)lIIrn(€o)

~~~"o

lIDIZ)(CONST)IIIIII(,uo)@ 299792458

The following shows the two-digit numbers for each of the scientific constants.

E.50

01: (mp) proton mass

02; (mn)neutron mass

03; (me) electron mass

04; (mp) muon mass

05: (ao)Bohr radius

06: (h)Planck constant

07: (,uN)nuclearmagneton 08: (,uB)Bohr magneton 09; (tl) Planckconstant,

10;(ex)fine-structure constant

rationalized

11:(re) classical electron radius 12; (Ac)Compton wavelength

13:(w) proton gyromagnetic ratio

14: (Acp)prolon Compton

wavelength

15:(Acn) neutron Compton

16;(R) Rydberg constant

wavelength

17:(u) atomic mass constant

18;(,up)proton magnetic

moment

19:(,ue)electron magneticmoment

20: (,un)neutron magnetic

moment

21; (,up)muon magnetic moment 22; (F)Faraday constant

The values are based on CODATA (2010) recommended values.

~e.!l'ic convetsion:--__ _ ---

The calculator's built-in metric conversion commands make fi simple to convert values from one unit to another. You can use the metric conversion commands in any calculation mode except for BASE-N andTABLE. To input a metric conversion command into a calculation, press

I!!!I(iJ(CONV)and then inputthe two-digfi number that corresponds to

the command you want.

To convert 5 em into inches _

CONVERSION

@5@(iJ(CONV) INumber 01~40?

[__J

@)(I)(cm~in)§] ,5cmHn

1.968503937

/ To convert 100 9 intoounces _

@ 1001!!!J(iJ(CONV)(I)(I)(9~oz)§] 11009~OZ

3.527396584

/ To convert -31.C into Fahrenheit -

@1BI311!!!J(iJ(CONV)IID(iJ(.C~.F)§] 1-31°C~OF m

E-51

Thefollowing shows thetwo-digfi numbersfor each of the metricconversion commands.

Conversion formula data is based on the .NIST Special Publication 811

(1995)..

Note: TheJ~cal commandperformsconversionfor valuesatatemperature

of 15.C.

Calculation Ranges, Number of Digits,~

and P~cision _ !

The calculation range, number of digfis used for internal calculation, and calculation precisiondepend on the type of calculation you are performing.

Calculation Range and Precision

Function Calculation Input Ranges and Precision

-23.8

E-52

23: (e) elementary charge

24: (NA) Avogadro constant

25: (k) Boltzmann constant

26: (Vm) molar volume of ideal

gas (273.15K, l00kPa)

27: (R) molar gas constant

28: (Co)speed of light in vacuum

29: (C,)first radiation constant

30: (C,)second radiation

constant

31: (0) Stefan-Boltzmann constant

32: (eo)electricconstant

33: (po)magnetic constant

34: () magnetic flux quantum

35: (g)standard acceleration of

36: (Go)conductance quantum

gravity

37: (20)characteristic impedance of

38: (t) Celsius temperature

vacuum

39: (G) Newtonian constant of

40: (atm)standard atmosphere

gravitation

01: incm 02: cmin

03:ftm 04:mft

05: ydm

06:myd

07: mile km 08: km mile

09: n milem 10: mn mile

11:acrem' 12: m'acre

13:gal (US) I 14: I gal (US) 15:gal (UK) I 16: I gal (UK) 17:pckm

18:kmpc

19:krn/h mls

20: mls kmlh

21: ozg 22: goz 23: Ibkg 24: kglb 25: atm Pa 26: Paatm

27: mmHgPa 28: Pa mmHg

29: hpkW 30: kWhp 31: kgf/cm' Pa

32: Pa kgf/cm'

33: kg!. mJ 34: Jkgf. m

35: Ibflin' kPa

36: kPa Ibflin'

37: .FOC

38: .C.F 39: J cal 40: calJ

Calculation Range

:1:1x lo-"'to:l:9.999999999 x 10" orO

Numberof Digits forInternal

15digits

Calculation

Precision

Ingeneral,:l:1 at the 10thdigit fora single calculation. Precisionfor exponential

display is:l:l at the least significant digit. Errors are cumulative in the case of

consecutive calculations.

Functions

Input Range

DEG

0"iiXI<9xI0'

silU

RAD

O:ii

iXI< 157079632.7

GRA

O:iiLxl < 1 x10"

DEG

0:5 LxI< 9 X 10'

coax

RAD

O:ii iXI< 157079632.7

GRA

0;; LxI< 1X 10"

DEG

Same as sinr, except when iXI= (211-1)x 90.

tanr RAD

Same as sinr, except when iXI= (211-1)x1tl2.

GRA

Same as sinr, except when LxI= (2n-l) x 100.

E-53

.Precision is basically the same as that described under "Calculation Range

and Precision", above.

. x', -!./y, 'r, xl, nPr, nCr type functions require consecutive internal

calculation, which can cause accumulation of errors that occur with each

calculation.

.Error is cumulative and tends to be large in the vicinity of a function's singular

point and inflection point.

.The range for calculation results that can be displayed in "form when using

Natural Display is'Ixl < 10". Note, however, that internal calculation error

can make itimpossible to display some calculation results in "form. It also

can cause calculation results that should be in decimal form to appear in

"form.

The calculator willdisplay an error message whenever an error occurs for any reason during a calculation. There are two ways to exit an error message

display: Pressing @ or @;) to display the location of the error, or pressing

1!9 to clear the message and calculation.

Displaying the Location of an Error

While an error message is displaYed, press @> or @;) to return to the calculation screen. The cursor will be positioned at the location where the error occurred, ready for input. Make the necessary corrections to the

calculation and execute it again.

"When you input 14 + 0 x 2 =by mistake instead of 14 + 10 x 2 =

em I m -

Math ERROR

141Z101&!2§J

[ACJ : Cancel [~J[.J:Goto

Clearing the Error Message

Whilean errormessage isdisplayed,press 1!9to returntothe calculation

screen. Notethat thisalso clears the calculationthatcontainedthe error.

Error Messages

MathERROR

Cause:

.The intermediate or final result of the calculation you are performing

exceeds the allowable calculation range. .Your input exceeds the allowable

input range (particularty when using functions). .The calculation you are

performingcontains an illegalmathematicaloperation (such as division

byzero).

E-54

sin-1x

cos-1x

0;:;::;1

tarr'x

o ;:; ;; 9.999999999x 10'"

sinhx

o ;:i ;; 230.2585092

coshx

sinh-1x o :ii ;:ii4.999999999x 10'"

cosh-'x 1;:ix ;:;4.999999999x 10'"

tanhx

o:ii :i 9.999999999x10'"

tanlr'x

O:ii ;; 9.999999999x 10-'

Iogx/Inx

o < x ;:;9.999999999x 10'"

10'

-9.999999999x 10":ii X 99.99999999

-9.999999999x 10";; x;; 230.2585092

0:iix<1x10''''

<1x10'"

x-'

< 1x 10'00;xO

3.fX

< 1x 10'00

o ;; x ,:;69 (xisan integer)

nPr

0;:;n < 1x 10'., 0 ;:iir:ii n (n, r are integers)

1 :ii(nV(n-r)I)< 1x 10''''

nCr

0;; n < 1 x 10'., O;:iir:ii n (n,r are integers)

1 ,:;nVrl< 1x 10'''' or 1;; nV(n-r)1< 1x 10'00

Pol(x,y)

,IYI;; 9.999999999x 10'"

:ii 9.999999999 x 10"

o ;:ir:ii 9.999999999x 10"

Rec(r,8)

8: Same as sinx lal,b, C< 1x 10'''' ;0 ;:;b, C

" "

The displayseconds valueissubjecttoan errorof:I:1 at the second decimalplace.

<1x10''''

" "

Decimal... SexagesimalConversions

0'0 '0-;; ::i9999999'59'59- x> 0:-1 x 10'''' < ylogx< 100

x=O:y>O x < 0:y = n, 2:::'1 (m, n are integers)

However:-1 x 10'''' < ylog < 100

y> O:x 0, -1 x 10''''< 1/xlogy< 100

fly

y=O:x>O y < 0:x = 2n+1,2n+1(m 0;m, n areintegers)

However:-1 x 10'''' < 1/xlogIYI< 100

able

Totalofinteger,numerator,and denominatormust be 10

digits or less (including division marks).

Ranlntl/(a,b)

a < b;lal.lbI< 1 x 10'";b

-a < 1x 10'.

- --

@;)(or @) [14+1J<2

l!f

@>1§J r+ IOx2-;

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

the numeric stack or the command stack to be exceeded.

.The calculation

you are performing has caused the capacity of the matrix or vector stack to be exceeded.

Action:

.Simplify the calculation expression so it does not exceed the

capacity of 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 are performing. Action: Make necessary corrections.

Argument ERROR Cause: There is a problem with the argument of the calculation you are performing. Action: Make necessary corrections.

Dimension ERROR (MATRIXand VECTOR Modes only) Cause:

.The matrix or vector you are trying to use in a calculation was input

without specifying its dimension.

.You are tryingto perform a calculation with

matrices or vectors whose dimensions do not allow that type of calculation.

Action: .Specify the dimension of the matrix or vector and then perform

the calculation again. .Check the dimensions specified for the matrices or

vectors to see if they are compatible with the calculation. Variable ERROR (SOLVE feature only)

Cause:

.You did not specify a solution variable, and there is no X variable

in the equation you input.

.The solution variable that you specified is not

included in the equation you input. Action:

.The equation you input must include an X variable when you do

not specify the solution variable.

.Specify a variable that is included in the

equation you input as the solution variable. Can't Solve Error (SOLVE feature only)

Cause: The calculator could not obtain a solution.

Action:

.Check .lor errors in the equation that you input. .Input a value

for the solution variable that is close to the expected solution and try again.

Insufficient MEM Enror Cause: An attempt to generate a number table in th€ TABLE Mode whose

conditions cause itto exceed the maximum number of allowable rows. The

maximum number of rows is 30 when "f(x)" is selected for the setup menu table setting and 20 when '1(x),g(x)" is selected. Action: Narrow the table calculation range by changing the Start, End, and

Step values, and try again. Time Out Error

Cause: The current differential or integration calculation ends without the ending condition being fulfilled. The current distribution calculation ends without the ending condition being fullilled. Action: Differential or integration calculation: Try increasing the tol value.

Note that this also decreases solution precision.

E-55

I Before Assuming Malfunction of the --;

Calculator... _ J

Perform the following steps whenever an error occurs during a calculation or when calculation results are not what you expected. Ifone 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 itdoes not contain any

errors.

2. Make sure that you are using the correct mOde for the type of calculation you are trying to perform.

3.11the above steps do not correct your problem, press the

@ID key. This will

cause the calculator to perform a routine that checks whether calculation functions are operating correctly. Ifthe calculator discovers any abnormality,

itautomatically initializes the calculation mode and clears memory contents. For details about initialized settings. see 'Configuring the Calculator

Setup".

4. Initialize all mOdes and settings by performing the following operation: I!!1IIID(CLR) (I)(Setup)@(Yes).

Re~Cin!Lthe Batt~ry __

A low battery is indicated by a dim display, even ifcontrast is adjusted, or by failure of figures to appear on the display immediately after you tum on the

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 1!!11@(OFF) to tum off the calculator.

" To ensure that you do not accidentally tum on power while replacing the

battery, slide the hard case onto the front of the calculator.

2. Remove the cover as shown in the illustration and Screw replace the battery, taking care that its plus (+) and

minus H ends are facing correctiy.

3. Replace the cover.

4.lnmalize the calculator. "0 @1!!1I1ID(CLR)[!)(AII)@(Yes)

.Do not skip the above stepl

E-56

SP8.£~~

Power Requirements:

Built-insolar cell; button battery lR44 (GPA76) x 1

Approximate Battery life:

3 years (based on one hour of operation per day) Operating Temperature: O°C to 4Q°C (32°F to 104°F) Dimensions: 11.1 (H) x 80 (W) x 162 (D) mm

'/," (H) x 3'/," (W) x 6'10"(D)

Approximate Weight: 95 g (3.4 oz) including the battery

.....

.Frequently Asked Questions _ ___-==

. How can I perform inpu1 and display results the same way Idid on a

model that does not have Natural Textbook Display? Perform the following key operation: IIDI!!iiI(SETUP)IIJ(lineIO). See

"Configuring the Calculator Setup" on page E-5 for more information.

. How can I change a fraction form result to decimal form?

How can I change a fraction form result produced by a division

operation to decimal form?

See "Toggling Calculation Results" on page E-14 for the procedure.

. What Is the difference between Ans memory, PreAns memory,

Independent memory, and variable memory?

Eachofthese types of memoryactslike"containers"for temporarystorage

of asingle value. Ans Memory: Stores the result of the lastcalculationperformed. Usethis memory to carry the result of one calculation on to the next.

PreAns Memory: Stores the result of calculation before the last one. PreAns memory can be used onlyin the COMP Mode.

Independent Memory: Usethis memorytototalizethe results of multiple

calculations. Variables: This memory ishelpfulwhenyou needto usesthe samevalue

multiple times in one or more calculations.

. Whatisthekeyoperationtotakeme from the STAT Mode or TABLE

Modeto a mode where Ican perform arithmetic calculations?

Press I!i!!II) (COMP).

. HowcanIreturnthecalculatorto Its Initialdefault settings?

Perform the fQllowing operation; I!!iJ(IJ(ClR)II)(Setup)@(Yes)

. WhenIexecu1e

a function calculation, why do I get a calculation result

that Is completely different from older CASIO calculator models? Witha Natural

Textbook Display model, the argument of a function that

uses parentheses must be followed by a closing parenthesis. Failing to

press malterthe argumenttoclosethe parenthesesmaycause unwanted

values or expressions to be included as part ofthe argument.

Example: (sin 30) + 15 1m

Older(S-VPAM)Model: @301E 15@ 15.5

NaturalTextbook Display Model: I!ImI @ 30m IE 15@ 15.5

Failure to press rn here as shown below will resutt In calculation of sin 45.

@301E 15@ 0.7071067812

E-57

CAS I0 $

CASIO COMPUTER CO., LTD.

6-2, Hon-machi 1-chome

Shibuya-ku, Tokyo 151-8543, Japan

SA1111-A Printed in China

@2012 CASIO COMPUTER CO., LTD.

Casio fx-991ES PLUS C User Manual

Specifications and Main Features

Frequently Asked Questions

User Manual