Casio Scientific Calculator fx 83ES User Manual

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fx-82ES  
fx-83ES  
fx-85ES  
fx-300ES  
fx-350ES  
User's Guide  
RCA502136-001V01  
A
About this Manual  
• The MATH mark indicates an example that uses Math format,  
while the LINE mark indicates Linear format. For details about  
input/output formats, see “Specifying the Input/Output Format”.  
• Keycap markings indicate what a key inputs or what function it  
performs.  
Example: 1, 2, +, -, !, A, etc.  
• Pressing the 1 or S key followed by a second key performs  
the alternate function of the second key. The alternate function is  
indicated by the text printed above the key.  
Alternate function  
sin–1  
D
Keycap function  
s
• The following shows what the different colors of the alternate  
function key text mean.  
If key marking  
text is this color:  
It means this:  
Press 1 and then the key to access  
the applicable function.  
Yellow  
Press S and then the key to input the  
applicable variable, constant, or symbol.  
Red  
• The following shows an example of how an alternate function  
operation is represented in this User’s Guide.  
–1  
Example: 1s(sin )1=  
Indicates the function that is accessed by the key  
operation (1s) before it. Note that this is not part  
of the actual key operation you perform.  
• The following shows an example of how a key operation to select  
an on-screen menu item is represented in this User’s Guide.  
Example: 1(Setup)  
Indicates the menu item that is selected by the number  
key operation (1) before it. Note that this is not part  
of the actual key operation you perform.  
E-1  
The cursor key is marked with four arrows,  
indicating direction, as shown in the  
illustration nearby.In this User’s Guide, cursor  
key operation is indicated as f, c, d,  
and e.  
REPLAY  
• The displays and illustrations (such as key markings) shown in  
this User’s Guide and the separate Appendix are for illustrative  
purposes only, and may differ somewhat from the actual items  
they represent.  
• The contents of this manual are subject to change without notice.  
• In no event shall CASIO Computer Co., Ltd. be liable to anyone for  
special, collateral, incidental, or consequential damages in  
connection with or arising out of the purchase or use of this product  
and items that come with it. Moreover, CASIO Computer Co., Ltd.  
shall not be liable for any claim of any kind whatsoever by any  
other party arising out of the use of this product and the items that  
come with it.  
k Using the Separate Appendix  
Whenever you see the symbol Appendix in this manual, it  
means you should refer to the separate Appendix.  
Example numbers (like “<#021>”) in this User’s Guide refer to the  
corresponding example number in the Appendix.  
Specify the angle unit in accordance with the marks in the Appendix:  
Deg : Specify Degree for the angle unit.  
Rad : Specify Radian for the angle unit.  
Initializing the Calculator  
Perform the following procedure when you want to initialize the  
calculator and return the calculation mode and setup to their initial  
default settings.Note that this operation also clears all data currently  
in calculator memory.  
19(CLR)3(All)=(Yes)  
• For information about calculation modes and setup settings, see  
“Calculation Modes and Calculator Setup”.  
• For information about memory, see “Using Calculator Memory”.  
E-2  
Safety Precautions  
Be sure to read the following safety precautions before using this  
calculator. Keep this manual handy for later reference.  
Caution  
This symbol is used to indicate information that can result in  
personal injury or material damage if ignored.  
Battery  
• After removing the battery from the calculator, put it in a safe  
place where it will not get into the hands of small children and  
accidentally swallowed.  
• Keep batteries out of the reach of small children.If accidentally  
swallowed, consult with a physician immediately.  
• Never charge the battery, try to take the battery apart, or allow  
the battery to become shorted. Never expose the battery to  
direct heat or dispose of it by incineration.  
• Improperly using a battery can cause it to leak and damage  
nearby items, and can create the risk of fire and personal injury.  
• Always make sure that the battery’s positive  
and negative  
k
ends are facing correctly when you load it into the  
l
calculator.  
• Remove the battery if you do not plan to use the calculator  
for a long time (fx-82ES/fx-83ES/fx-350ES).  
• Use only the type of battery specified for this calculator in  
this manual.  
Disposing of the Calculator  
• Never dispose of the calculator by burning it. Doing so can  
cause certain components to suddenly burst, creating the risk  
of fire and personal injury.  
E-3  
Handling Precautions  
• Be sure to press the O key before using the calculator for  
the first time.  
• Even if the calculator is operating normally, replace the battery  
at least once every three years (LR44 (GPA76)), two years (R03  
(UM-4)), or one year (LR03 (AM4)).  
A dead battery can leak, causing damage to and malfunction of  
the calculator. Never leave a dead battery in the calculator.  
• The battery that comes with this unit discharges slightly during  
shipment and storage. Because of this, it may require  
replacement sooner than the normal expected battery life.  
• Low battery power can cause memory contents to become  
corrupted or lost completely. Always keep written records of  
all important data.  
• Avoid use and storage of the calculator in areas subjected to  
temperature extremes.  
Very low temperatures can cause slow display response, total  
failure of the display, and shortening of battery life. Also avoid  
leaving the calculator in direct sunlight, near a window, near a heater  
or anywhere else it might be exposed to very high temperatures.  
Heat can cause discoloration or deformation of the calculator’s  
case, and damage to internal circuitry.  
• Avoid use and storage of the calculator in areas subjected to  
large amounts of humidity and dust.  
Take care never to leave the calculator where it might be splashed  
by water or exposed to large amounts of humidity or dust. Such  
conditions can damage internal circuitry.  
• Never drop the calculator or otherwise subject it to strong  
impact.  
• Never twist or bend the calculator.  
Avoid carrying the calculator in the pocket of your trousers or other  
tight-fitting clothing where it might be subjected to twisting or  
bending.  
• Never try to take the calculator apart.  
• Never press the keys of the calculator with a ballpoint pen or  
other pointed object.  
• Use a soft, dry cloth to clean the exterior of the calculator.  
If the calculator becomes very dirty, wipe it off with a cloth moistened  
in a weak solution of water and a mild neutral household detergent.  
Wring out all excess liquid before wiping the calculator. Never use  
thinner, benzene or other volatile agents to clean the calculator.  
Doing so can remove printed markings and can damage the case.  
E-4  
Before Using the Calculator  
k Removing the Hard Case  
Before using the calculator, slide its hard case downwards to remove  
it, and then affix the hard case to the back of the calculator as shown  
in the illustration below.  
k Turning Power On and Off  
• Press O to turn on the calculator.  
• Press 1A(OFF) to turn off the calculator.  
k Adjusting Display Contrast  
1N(SETUP)c5(]CONT')  
This displays the contrast adjustment screen. Use d and e to  
adjust display contrast. After the setting is the way you want, press  
A.  
You can also adjust contrast using d and e while the mode  
menu (which appears when you press N) is on the display.  
Important!  
• If adjusting display contrast does not improve display readability, it  
probably means that battery power is low. Replace the battery.  
E-5  
k About the Display  
Your calculator has a 31-dot × 96-dot LCD screen.  
Example:  
Input expression  
Calculation result  
{
k Display Indicators  
Sample Display:  
STAT  
This  
Means this:  
indicator:  
The keypad has been shifted by pressing the 1  
key. The keypad will unshift and this indicator will  
disappear when you press a key.  
S
A
The alpha input mode has been entered by pressing  
the S key. 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 assign a value to the variable.This indicator  
appears after you press 1t(STO).  
STO  
The calculator is standing by for input of a variable  
name to recall the variable’s value. This indicator  
appears after you press t.  
RCL  
STAT  
7
The calculator is in the STAT Mode.  
The default angle unit is degrees.  
8
The default angle unit is radians.  
9
The default angle unit is grads.  
FIX  
SCI  
Math  
A fixed number of decimal places is in effect.  
A fixed number of significant digits is in effect.  
Math style is selected as the input/output format.  
Calculation history memory data is available and can  
be replayed, or there is more data above/below the  
current screen.  
$`  
The display currently shows an intermediate result  
of a multi-statement calculation.  
Disp  
E-6  
Important!  
• For a very complex calculation or some other type of calculation  
that takes a long time to execute, the display may show only the  
above indicators (without any value) while it performs the calculation  
internally.  
Calculation Modes and  
Calculator Setup  
k Calculation Modes  
When you want to perform this type of  
operation:  
Select this  
mode:  
General calculations  
COMP  
STAT  
Statistical and regression calculations  
Generation of a number table based on an  
expression  
TABLE  
Specifying the Calculation Mode  
(1) Press N to display the mode  
menu.  
(2) Press the number key that corresponds to the mode you want to  
select.  
To select the STAT Mode, for example, press 2.  
k Configuring the Calculator Setup  
Pressing 1N(SETUP) displays the setup menu, which you can  
use to control how the calculations are executed and displayed.The  
setup menu has two screens, which you can jump between using  
c and f.  
c
f
• See “Adjusting Display Contrast” for information about how to use  
]CONT'”.  
Specifying the Input/Output Format  
For this input/output format: Perform this key operation:  
Math  
1N1(MthIO)  
Linear  
1N2(LineIO)  
E-7  
• Math format causes fractions, irrational numbers, and other  
expressions to be displayed as they are written on paper.  
• Linear format causes fractions and other expressions to be  
displayed in a single line.  
Math  
Math Format  
Linear Format  
Specifying the Default Angle Unit  
To specify this as the default  
Perform this key operation:  
angle unit:  
Degrees  
1N3(Deg)  
1N4(Rad)  
1N5(Gra)  
Radians  
Grads  
π
2
90° =  
radians = 100 grads  
Specifying the Number of Display Digits  
To specify this:  
Perform this key operation:  
Number of Decimal Places  
Number of Significant Digits  
1N6(Fix)09  
1N7(Sci)09  
1N8(Norm)1(Norm1)  
or 2(Norm2)  
Exponential Display Range  
Calculation Result Display Examples  
• 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: 100 ÷ 7 = 14.286 (Fix3)  
14.29 (Fix2)  
• Sci: The value you specify (from 1 to 10) controls the number of  
significant digits for displayed calculation results.Calculation results  
are rounded off to the specified digit before being displayed.  
–1  
Example: 1 ÷ 7 = 1.4286 × 10 (Sci5)  
–1  
1.429 × 10 (Sci4)  
• Norm: Selecting one of the two available settings (Norm1, Norm2)  
determines the range in which results will be displayed in non-  
exponential format. Outside the specified range, results are  
displayed using exponential format.  
–2  
10  
Norm1: 10 > x, x> 10  
–9  
10  
Norm2: 10 > x, x> 10  
–3  
Example: 1 ÷ 200 = 5 × 10  
(Norm1)  
(Norm2)  
E-8  
0.005  
Specifying the Fraction Display Format  
To specify this fraction  
Perform this key operation:  
display format:  
Mixed  
1Nc1(ab/c)  
Improper  
1Nc2(d/c)  
Specifying the Statistical Display Format  
Use the following procedure to turn display of the frequency (FREQ)  
column of the STAT Mode STAT editor screen on or off.  
To specify this:  
Perform this key operation:  
1Nc3(STAT)1(ON)  
1Nc3(STAT)2(OFF)  
Show FREQ Column  
Hide FREQ Column  
Specifying the Decimal Point Display Format  
To specify this decimal  
Perform this key operation:  
point display format:  
Dot (.)  
1Nc4(Disp)1(Dot)  
Comma (,)  
1Nc4(Disp)2(Comma)  
• The setting you configure here is applied for calculation results  
only. The decimal point for input values is always a dot (.).  
k Initializing the Calculation Mode and Other  
Settings  
Performing the following procedure initializes the calculation mode  
and other setup settings as shown below.  
19(CLR)1(Setup)=(Yes)  
This setting:  
Is initialized to this:  
Calculation Mode  
Input/Output Format  
Angle Unit  
COMP  
MthIO  
Deg  
Display Digits  
Norm1  
d/c  
OFF  
Fraction Display Format  
Statistical Display  
Decimal Point  
Dot  
To cancel initialization without doing anything, press A(Cancel)  
instead of =.  
E-9  
Inputting Expressions and  
Values  
k Inputting a Calculation Expression Using  
Standard Format  
Your calculator lets you input calculation expressions just as they  
are written.Then simply press the = key to execute it.The calculator  
automatically judges the calculation priority sequence for addition,  
subtraction, multiplication, and division, functions, and parentheses.  
Example: 2 (5 + 4) – 2 × (–3) =  
LINE  
2(5+4)-  
2*y3=  
Inputting a Function with Parenthesis  
When you input any of the functions shown below, it is automatically  
input with the open parenthesis (() character. Next, you need to  
input the argument and the closing parenthesis ()).  
–1  
–1  
–1  
–1  
sin(, cos(, tan(, sin (, cos (, tan (, sinh(, cosh(, tanh(, sinh (,  
3
–1  
–1  
cosh (, tanh (, log(, ln(, e^(, 10^(, '(, '(, Abs(, Pol(, Rec(,  
Rnd(  
Example: sin 30 =  
LINE  
s30)=  
Pressing s inputs “sin(”.  
• Note that the input procedure is different if you want to use Math  
format. For more information, see “Inputting with Math Format”.  
Omitting the Multiplication Sign  
You can omit the multiplication sign (×) in any of the following cases.  
• Before an open parentheses ((): 2 × (5 + 4), etc.  
• Before a function with parenthesis: 2 × sin(30), 2 × '(3), etc.  
• Before a variable name, constant, or random number:  
20 × A, 2 × π, etc.  
Final Closed Parenthesis  
You can omit one or more closed parentheses that come at the end  
of a calculation, immediately before the = key is pressed. For  
details, see “Omitting a Final Closed Parenthesis”.  
E-10  
Displaying a Long Expression  
The display can show up to 14 characters at a time. Inputting the  
15th character causes the expression to shift to the left.At this time,  
the ] indicator appears to the left of the expression, indicating that  
it runs off the left side of the screen.  
Input expression: 1111 + 2222 + 3333 + 444  
Math  
Displayed portion:  
Cursor  
• When the ] indicator is displayed, you can scroll left and view the  
hidden part by pressing the d key. This will cause the ' indicator  
to appear to the right of the expression. At this time, you can use  
the e key to scroll back.  
Number of Input Characters (Bytes)  
You can input up to 99 bytes of data for a single expression.  
Basically, each key operation uses up one byte. A function that  
–1  
requires two key operations to input (like 1s(sin )) also uses  
only one byte.Note, however, that when you are inputting functions  
with Math format, each item you input uses up more than one  
byte. For more information, see “Inputting with Math Format”.  
• Normally the input cursor appears as a straight vertical ( ) or  
I
horizontal ( ) flashing line on the display screen.When there are  
10 or fewer bytes of input remaining in the current expression, the  
cursor changes shape to  
appears, terminate the expression at a convenient point and  
calculate the result.  
to let you know. If the  
cursor  
I
I
k Correcting an Expression  
This section explains how to correct an expression as you are  
inputting it.The procedure you should use depends on whether you  
have insert or overwrite selected as the input mode.  
About the Insert and Overwrite Input Modes  
With the insert mode, the displayed characters shift to the left to  
make room when you input a new character.With the overwrite mode,  
any new character you input replaces the character at the current  
cursor position.The initial default input mode is insert.You can change  
to the overwrite mode when you need it.  
• The cursor is a vertical flashing line ( ) when the insert mode is  
I
selected. The cursor is a horizontal flashing line ( ) when the  
overwrite mode is selected.  
• The initial default for Linear format input is the insert mode. You  
can switch to the overwrite mode by pressing 1Y(INS).  
E-11  
• With Math format, you can only use the insert mode. Pressing  
1Y(INS) when the Math format is selected does not switch to  
the overwrite mode. See “Incorporating aValue into a Function” for  
more information.  
• The calculator automatically changes to the insert mode whenever  
you change the input/output format from Linear to Math.  
Changing the Character or FunctionYou Just Input  
Example: To correct the expression 369 × 13 so it becomes  
369 × 12  
LINE  
369*13  
Y
2
Deleting a Character or Function  
Example: To correct the expression 369 × × 12 so it becomes  
369 × 12  
LINE  
Insert Mode: 369**12  
dd  
Y
Overwrite Mode:  
369**12  
ddd  
Y
Correcting a Calculation  
Example: To correct cos(60) so it becomes sin(60)  
LINE  
Insert Mode:  
c60)  
E-12  
dddY  
s
Overwrite Mode:  
c60)  
dddd  
s
Inserting Input into a Calculation  
Always use the insert mode for this operation. Use d or e to  
move the cursor to the location where you want to insert new input,  
and then input what you want.  
k Displaying the Location of an Error  
If an error message (like “Math ERROR” or “Syntax ERROR”)  
appears when you press =, press d or e. This will display the  
part of the calculation where the error occurred, with the cursor  
positioned at the error location. You can then make necessary  
corrections.  
Example: When you input 14 ÷ 0 × 2 = by mistake instead of 14 ÷  
10 × 2 =  
Use the insert mode for the following operation.  
LINE  
14/0*2=  
Press e or d.  
This is causing the error.  
d1  
=
You can also exit the error screen by pressing A, which clears the  
calculation.  
E-13  
k Inputting with Math Format  
When inputting with Math format, you can input and display fractions  
and some functions using the same format as they appear in your  
textbook.  
Important!  
• Certain types of expressions can cause the height of a calculation  
formula to be greater than one display line.The maximum allowable  
height of a calculation formula is two display screens (31 dots × 2).  
Further input will become impossible if the height of the calculation  
you are inputting exceeds the allowable limit.  
• Nesting of functions and parentheses is allowed. Further input will  
become impossible if you nest too many functions and/or  
parentheses. If this happens, divide the calculation into multiple  
parts and calculate each part separately.  
Functions and Symbols Supported for Math Format  
Input  
• The “Bytes” column shows the number of bytes of memory that  
are used up by input.  
Function/Symbol  
Improper Fraction  
Key Operation  
Bytes  
'
9
13  
6
Mixed Fraction  
log(a,b) (Logarithm)  
10^x (Power of 10)  
e^x (Power of e)  
Square Root  
Cube Root  
1'(()  
&
1l($)  
1i(%)  
!
4
4
4
1!(#)  
w, W  
E
9
Square, Cube  
Reciprocal  
4
5
Power  
6
4
Power Root  
16(")  
D
9
Absolute Value  
Parentheses  
4
( or )  
1
Math Format Input Examples  
• The following operations are all performed while Math format is  
selected.  
• Pay close attention to the location and size of the cursor on the  
display when you input using Math format.  
3
Example 1: To input 2 + 1  
Math  
MATH  
263  
E-14  
Math  
e+1  
'
Example 2: To input 1 + 2 + 3  
Math  
Math  
MATH  
1+!2  
e+3  
2
5
2
Example 3: To input (1 +  
)
× 2 =  
MATH  
Math  
(1+'2c5e)  
w*2=  
• When you press = and obtain a calculation result using Math  
format, part of the expression you input can be cut off as shown in  
the Example 3 screen shot. If you need to view the entire input  
expression again, press A and then press e.  
Incorporating a Value into a Function  
When using Math format, you can incorporate part of an input  
expression (a value, an expression within parentheses, etc.) into a  
function.  
Example: To incorporate the expression inside of the parentheses  
of 1 + (2 + 3) + 4 into the ' function  
MATH  
Math  
Move the cursor to here.  
Math  
1Y(INS)  
This changes the shape of the cursor as shown here.  
Math  
!
This incorporates the expression in the  
parentheses into the function '.  
• If the cursor is located left of a particular value or fraction (instead  
of an open parentheses), that value or fraction will be incorporated  
into the function specified here.  
• If the cursor is located left of function, the entire function is  
incorporated into the function specified here.  
E-15  
The following examples show the other functions that can be used  
in the above procedure, and the required key operations to use them.  
Original Expression:  
Function  
Fraction  
Key Operation  
Resulting Expression  
'
log(a,b)  
&
Power Root  
16(")  
You can also incorporate values into the following functions.  
1l($), 1i(%), !, 6, 1!(#), D  
Displaying Calculation Results  
in a Form that Includes '2, π,  
etc. (Irrational Number Form)  
When “MthIOis selected for the input/output format, you can specify  
whether calculation results should be displayed in a form that includes  
expressions like '2 and π (irrational number form).  
• Pressing = after inputting a calculation displays the result using  
irrational number form.  
• Pressing 1= after inputting a calculation displays the result  
using decimal values.  
Note  
• When “LineIO” is selected for the input/output format, calculation  
results are always displayed using decimal values (no irrational  
number form) regardless of whether you press = or 1=.  
π form (form that includes π within irrational number display) display  
conditions are the same as those for S-D conversion. For details,  
see “Using S-D Transformation”.  
Example 1: '2 +'8 = 3'2  
Math  
MATH  
1
!2e+!8=  
Math  
2
!2e+!81=  
E-16  
'3  
Example 2: sin (60) =  
(Angle Unit: Deg)  
2
Math  
MATH  
s60=  
1
6
Example 3: sin–1 (0.5) =  
π
(Angle Unit: Rad)  
Math  
MATH  
1s(sin–1)0.5=  
• The following are the calculations for which ' form (form that  
includes ' within irrational number display) results can be  
displayed.  
a.Arithmetic calculations of values with square root symbol ('),  
x2, x3, x–1  
b. Trigonometric function calculations  
The following are the input value ranges for which ' form is always  
used for display of trigonometric calculation results.  
Input Value Range  
Angle Unit  
Angle Value Input  
for ' Form  
Calculation Result  
Setting  
9
Deg  
Units of 15°  
ȊxȊ < 9 × 10  
1
Rad  
Multiples of  
Multiples of  
π radians  
ȊxȊ < 20π  
12  
50  
3
Gra  
grads  
ȊxȊ < 10000  
Calculation results may be displayed in decimal form for input values  
outside of the above ranges.  
k ' Form Calculation Range  
Results that include square root symbols can have up to two terms  
(an integer term is also counted as a term).  
' form calculation results use display formats like those shown  
below.  
a'b d'e  
a'b,  
d
a'b,  
c
f
The following shows the range for each of the coefficients (a, b, c, d,  
e, f).  
1 < a < 100, 1 < b < 1000, 1 < c < 100  
0 < d < 100, 0 < e < 1000, 1 < f < 100  
E-17  
Example:  
2'3 × 4 = 8'3  
' form  
35'2 × 3 = 148.492424  
decimal form  
(= 105'2)  
150'2  
= 8.485281374  
25  
2 × (3 – 2'5 ) = 6 – 4'5  
' form  
23 × (5 – 2'3 ) = 35.32566285  
decimal form  
(= 115 – 46'3 )  
10'2 + 15 × 3'3 = 45'3 + 10'2  
' form  
15 × (10'2 + 3'3 ) = 290.0743207  
decimal form  
(= 45'3 + 150'2 )  
'2 + '3 + '8 = '3 + 3'2  
' form  
'2 + '3 + '6 = 5.595754113  
decimal form  
The underlined areas in the above examples indicate what caused  
decimal form to be used.  
Reasons why the results of the examples are displayed in  
decimal form  
- Value outside of the allowable range  
- More than two terms in the calculation result  
• Calculation results displayed in ' form are reduced to a common  
denominator.  
a'b d'e  
a'b + d'e  
+
c
f
c′  
cis the least common multiple of c and f.  
• Since calculation results are reduced to a common denominator,  
they are displayed in ' form even if coefficients (a, c, and d)  
are outside the corresponding ranges of coefficients (a, c, and d).  
'3 '2 10'3 + 11'2  
+
=
Example:  
11  
10  
110  
• The result is displayed in decimal form even when any intermediate  
result has three or more terms.  
Example: (1 + '2 + '3 )(1 – '2 – '3 )(= –4 – 2'6 )  
= –8.898979486  
• If a term is encountered during the calculation cannot be displayed  
as a root (') form or a fraction, the calculation result is displayed  
in decimal form.  
Example: log3 + '2 = 1.891334817  
E-18  
Basic Calculations  
(COMP)  
This section explains how to perform arithmetic, fraction, percent,  
and sexagesimal calculations.  
All calculations in this section are performed in the COMP Mode  
(N1).  
k Arithmetic Calculations  
Use the +, -, *, and / keys to perform arithmetic calculations.  
Example: 7 × 8 – 4 × 5 = 36  
LINE  
7*8-4*5=  
• The calculator automatically judges the calculation priority  
sequence. For more information, see “Calculation Priority  
Sequence”.  
Number of Decimal Places and Number of  
Significant Digits  
You can specify a fixed number of decimal places and significant  
digits for the calculation result.  
Example: 1 ÷ 6 =  
LINE  
Initial default setting (Norm1)  
FIX  
3 decimal places (Fix3)  
SCI  
3 significant digits (Sci3)  
• For more information, see “Specifying the Number of Display Digits”.  
Omitting a Final Closed Parenthesis  
You can omit any closed parenthesis ()) immediately preceding  
operation of the = key at the end of a calculation.  
This is true only in the case of Linear format.  
E-19  
Example: (2 + 3) × (4 – 1) = 15  
LINE  
(2+3)*  
(4-1=  
k Fraction Calculations  
How you should input fractions depends on the input/output format  
that is currently selected.  
Improper Fraction  
Mixed Fraction  
1
2
7
3
Math  
Format  
3
('7c3)  
(1'(()2e1c3)  
7 { 3  
2 { 1 { 3  
Linear  
Format  
Numerator Denominator Integer Part  
Denominator  
Numerator  
(7'3)  
(2'1'3)  
• Under initial default settings, fractions are displayed as improper  
fractions.  
• Fraction calculation results are always reduced before being  
displayed.  
Appendix  
2
3
1
2
7
6
<#001> — + — = —  
1
4
2
3
11  
<#002> 3 — + 1 — = 4  
(Fraction Display Format: ab/c)  
12  
1
1
2
4 – 3 — =  
2
(Fraction Display Format: ab/c)  
• If the total number of digits used for a mixed fraction (including  
integer, numerator, denominator, and separator symbols) is greater  
than 10, the value is automatically displayed in decimal format.  
• The result of a calculation that involves both fraction and decimal  
values is displayed in decimal format.  
Switching between Improper Fraction and Mixed  
Fraction Format  
b
a—  
c
d
c
Pressing the 1f(  
between mixed fraction and improper fraction format.  
) key toggles the display fraction  
E-20  
Switching between Fraction and Decimal Format  
f
• The format of the fraction depends on the currently selected fraction  
display format setting (improper fraction or mixed fraction).  
You cannot switch from decimal format to mixed fraction format if  
the total number of digits used in the mixed fraction (including  
integer, numerator, denominator, and separator symbols) is greater  
than 10.  
• For details about the f key, see “Using S-D Transformation”.  
k Percent Calculations  
Inputting a value and pressing 1((%) causes the input value to  
become a percent.  
Appendix  
2
100  
<#003> 2% = 0.02  
——  
(
)
20  
100  
<#004> 150 × 20% = 30  
150 × —  
(
)
<#005> Calculate what percentage of 880 is 660.  
(75%)  
<#006> Increase 2500 by 15%.  
<#007> Discount 3500 by 25%.  
(2875)  
(2625)  
<#008> Discount the sum of 168, 98, and 734 by 20%.  
(800)  
<#009> If 300 grams are added to a test sample originally weighing  
500 grams, what is the percentage increase in weight?  
(160%)  
<#010> What is the percentage change when a value is increased  
from 40 to 46? How about to 48?  
(15%, 20%)  
k Degree, Minute, Second (Sexagesimal)  
Calculations  
You can perform calculations using sexagesimal values, and convert  
values between sexagesimal and decimal.  
Inputting Sexagesimal Values  
The following is the syntax for inputting a sexagesimal value.  
{Degrees}e{Minutes}e{Seconds}e  
Appendix <#011> Input 2°0´30˝.  
• Note that you must always input something for the degrees and  
minutes, even if they are zero.  
E-21  
Sexagesimal Calculations  
• Performing the following types of sexagesimal calculations  
produces a sexagesimal result.  
-
-
Addition or subtraction of two sexagesimal values  
Multiplication or division of a sexagesimal value and a  
decimal value  
Appendix <#012> 2°20´30˝ + 39´30˝ = 3°00´00˝  
Converting Values between Sexagesimal and  
Decimal  
Pressing e while a calculation result is displayed toggles the value  
between sexagesimal and decimal.  
Appendix <#013> Convert 2.255 to its sexagesimal equivalent.  
Using Multi-statements in  
Calculations  
You can use the colon character (:) to connect two or more  
expressions and execute them in sequence from left to right when  
you press =.  
Example: To create a multi-statement that performs the following  
two calculations: 3 + 3 and 3 × 3  
LINE  
3+3SW(:)3*3  
Disp  
=
“Disp” indicates this is an intermediate result of a multi-statement.  
=
E-22  
Using Calculation History  
Memory and Replay  
(COMP)  
Calculation history memory maintains a record of each calculation  
expression you input and execute, and its result.  
You can use calculation history memory in the COMP Mode  
(N1) only.  
Recalling Calculation History Memory Contents  
Press f to back-step through calculation history memory contents.  
Calculation history memory shows both calculation expressions and  
results.  
Example:  
LINE  
1+1=  
2+2=  
3+3=  
f
f
• Note that calculation history memory contents are cleared  
whenever you turn off the calculator, press the O key, change to  
the calculation mode or the input/output format, or perform any  
reset operation.  
• Calculation history memory is limited. When the calculation you  
are performing causes calculation history memory to become full,  
the oldest calculation is deleted automatically to make room for  
the new calculation.  
Replay Function  
While a calculation result is on the display, you can press A and  
then d or e to edit the expression you used for the previous  
calculation. If you are using Linear format, you can display the  
expression by pressing d or e, without pressing A first.  
Appendix <#014>  
E-23  
Using Calculator Memory  
Memory Name  
Description  
Answer Memory Stores the last calculation result obtained.  
Calculation results can be added to or subtracted  
from independent memory. The “M” display  
indicator indicates data in independent memory.  
Independent  
Memory  
Six variables named A, B, C, D, X, and Y can  
Variables  
be used for storage of individual values.  
This section uses the COMP Mode (N1) to demonstrate how  
you can use memory.  
k Answer Memory (Ans)  
Answer Memory Overview  
• Answer Memory contents are updated whenever you execute a  
calculation using any one of the following keys: =, 1=, m,  
1m(M), t,1t(STO). Answer Memory can hold up to  
15 digits.  
• Answer Memory contents are not change if an error occurs during  
the current calculation.  
• Answer Memory contents are maintained even if you press the  
A key, change the calculation mode, or turn off the calculator.  
Using Answer Memory to Perform a Series of  
Calculations  
Example: To divide the result of 3 × 4 by 30  
LINE  
3*4=  
(Continuing)/30=  
Pressing / automatically inputs  
“Ans” command.  
• With the above procedure, you need to perform the second  
calculation immediately after the first one. If you need to recall  
Answer Memory contents after pressing A, press the G key.  
E-24  
Inputting Answer Memory Contents into an Expression  
Example: To perform the calculations shown below:  
123 + 456 = 579  
789 – 579 = 210  
LINE  
123+456=  
789-G=  
k Independent Memory (M)  
You can add calculation results to or subtract results from  
independent memory. The “M” appears on the display when  
independent memory contains a value.  
Independent Memory Overview  
• The following is a summary of the different operations you can  
perform using independent memory.  
To do this:  
Perform this key operation:  
Add the displayed value or  
result of the expression to  
independent memory  
m
Subtract the displayed value  
or result of the expression from 1m(M–)  
independent memory  
Recall current independent  
tm(M)  
memory contents  
You can also insert the M variable into a calculation, which tells  
the calculator to use the current independent memory contents at  
that location.The following is the key operation for inserting the M  
variable.  
Sm(M)  
• The “M” indicator appears in the upper left of the display when  
there is any value other than zero stored in independent memory.  
• Independent memory contents are maintained even if you press  
the A key, change the calculation mode, or turn off the calculator.  
E-25  
Calculation Examples Using Independent Memory  
• If the “M” indicator is on the display, perform the procedure under  
“Clearing Independent Memory” before performing this example.  
Example: 23 + 9 = 32  
53 – 6 = 47  
23+9m  
53-6m  
–)45 × 2 = 90  
99 ÷ 3 = 33  
45*21m(M–)  
99/3m  
(Total) 22  
tm(M)  
Clearing Independent Memory  
Press01t(STO)m. This clears independent memory and  
causes the “M” indicator to disappear from the display.  
k Variables (A, B, C, D, X,Y)  
Variable Overview  
You can assign a specific value or a calculation result to a variable.  
Example: To assign the result of 3 + 5 to variable A.  
3+51t(STO)y(A)  
• Use the following procedure when you want to check the contents  
of a variable.  
Example: To recall the contents of variable A  
ty(A)  
• The following shows how you can include variables inside of an  
expression.  
Example: To multiply the contents of variable A by the contents of  
variable B  
Sy(A)*Se(B)=  
• Variable contents are maintained even if you press the A key,  
change the calculation mode, or turn off the calculator.  
Appendix <#015>  
Clearing the Contents of a Specific Variable  
Press 01t(STO) and then press the key for the name of the  
variable whose contents you want to clear. To clear the contents of  
variable A, for example, press 01t(STO)y(A).  
k Clearing the Contents of All Memories  
Use the following procedure to clear the contents of Answer Memory,  
independent memory, and all of the variables.  
Press 19(CLR)2(Memory)=(Yes).  
To cancel the clear operation without doing anything, press  
A(Cancel) instead of =.  
E-26  
Function Calculations  
This section explains how to use the calculator’s built-in functions.  
The functions available to you depends on the calculation mode  
you are in.The explanations in this section are mainly about the  
functions that are available in all calculation modes. All of the  
examples in this section show operation in the COMP Mode  
(N1).  
• Certain function calculations may take some time to display  
calculation results.Before performing an operation, be sure to wait  
until execution of the current operation is complete.You can interrupt  
an ongoing operation by pressing A.  
k Pi (π) and Natural Logarithm Base e  
You can input pi (π) or natural logarithm base e into a calculation.  
The following shows the required key operations and the values this  
calculator uses for pi (π) and e.  
π = 3.14159265358980 (15(π))  
e = 2.71828182845904 (S5(e))  
k Trigonometric and Inverse Trigonometric  
Functions  
• The angle unit required by trigonometric and inverse trigonometric  
functions is one specified as the calculator’s default angle unit.  
Before performing a calculation, be sure to specify the default angle  
unit you want to use. See “Specifying the Default Angle Unit” for  
more information.  
–1  
Appendix <#016> sin 30 = 0.5, sin 0.5 = 30  
k Hyperbolic and Inverse Hyperbolic  
Functions  
Pressing the w key displays a menu of functions.Press the number  
key that corresponds to the function you want to input.  
–1  
Appendix <#017> sinh 1 = 1.175201194, cosh 1 = 0  
E-27  
k Converting an Input Value to the  
Calculator’s Default Angle Unit  
After inputting a value, press 1G(DRG') to display the angle  
unit specification menu shown below. Press the number key that  
corresponds to the angle unit of the input value. The calculator will  
automatically convert it to the calculator’s default angle unit.  
Example: To convert the following values to degrees:  
π
2
radians = 90°, 50 grads = 45°  
The following procedure assumes that the calculator’s default angle  
unit is degrees.  
LINE  
(15(π)/2)  
r
1G(DRG')2( )=  
501G(DRG')  
g
3( )=  
Appendix  
<#018> cos (π radians) = –1, cos (100 grads) = 0  
–1  
<#019> cos (–1) = 180  
–1  
cos (–1) = π  
k Exponential Functions and Logarithmic  
Functions  
• For the logarithmic function “log(”, you can specify base m using  
the syntax “log (m, n)”.  
If you input only a single value, a base of 10 is used for the  
calculation.  
• “ln(” is a natural logarithm function with base e.  
You can also use the & key when inputting an expression with  
the form of “logmn” while using Math format. For details, see  
Appendix <#020>. Note that you must input the base (base m)  
when using the & key for input.  
Appendix <#021> to <#023>  
*1 A base of 10 (common logarithm) is used if no base is specified.  
E-28  
k Power Functions and Power Root  
Functions  
2
3
–1  
3
X , X , X , X^, '(, '(, ^'(  
Appendix <#024> to <#028>  
k Rectangular-Polar Coordinate Conversion  
Rectangular  
Coordinates (Rec)  
Polar Coordinates  
(Pol)  
• Coordinate conversion can be performed in the COMP and STAT  
calculation modes.  
Converting to Polar Coordinates (Pol)  
Pol(X, Y)  
X: Specifies the rectangular coordinate X value  
Y: Specifies the rectangular coordinate Y value  
• Calculation result θ is displayed in the range of –180° < θ < 180°.  
• Calculation result θ is displayed using the calculator’s default angle  
unit.  
• Calculation result r is assigned to variable X, while θ is assigned  
toY.  
Converting to Rectangular Coordinates (Rec)  
Rec(r,θ)  
r : Specifies r value of polar coordinate  
θ : Specifies θ value of polar coordinate  
• Input value θ is treated as an angle value, in accordance with the  
calculator’s default angle unit setting.  
• Calculation result x is assigned to variable X, while y is assigned  
to Y.  
• If you perform coordinate conversion inside of an expression instead  
of a stand-alone operation, the calculation is performed using only  
the first value (either the r-value or the X-value) produced by the  
conversion.  
Example: Pol ('2, '2) + 5 = 2 + 5 = 7  
Appendix <#029> to <#030>  
E-29  
k Other Functions  
This section explains how to use the functions shown below.  
!, Abs(, Ran#, nPr, nCr, Rnd(  
Factorial (!)  
This function obtains the factorials of a value that is zero or a positive  
integer.  
Appendix <#031> (5 + 3)! = 40320  
Absolute Value Calculation (Abs)  
When you are performing a real number calculation, this function  
simply obtains the absolute value.  
Appendix <#032> Abs (2 – 7) = 5  
Random Number (Ran#)  
This function generates a 3-digit pseudo random number that is less  
than 1.  
Appendix  
<#033> Generate three 3-digit random numbers.  
The random 3 digit decimal values are converted to 3-digit  
integer values by multiplying by 1000.  
Note that the values shown here are examples only.Values  
actually generated by your calculator will be different.  
Permutation (nPr) and Combination (nCr)  
These functions make it possible to perform permutation and  
combination calculations.  
n and r must be integers in the range of 0 < r < n < 1 × 10  
10  
.
Appendix  
<#034> How many four-person permutations and combinations are  
possible for a group of 10 people?  
Rounding Function (Rnd)  
This function rounds the value or the result of the expression in the  
function’s argument to the number of significant digits specified by  
the number of display digits setting.  
Display Digits Setting: Norm1 or Norm2  
The mantissa is rounded to 10 digits.  
E-30  
Display Digits Setting: Fix or Sci  
The value is rounded to the specified number of digits.  
Example: 200 ÷ 7 × 14 = 400  
LINE  
200/7*14=  
(Specifies three decimal places.)  
FIX  
1N6(Fix)3  
(Calculation is performed internally using 15 digits.)  
FIX  
FIX  
200/7=  
*14=  
The following performs the same calculation with rounding.  
FIX  
200/7=  
(Round the value to the specified number of digits.)  
FIX  
10(Rnd)=  
(Check rounded result.)  
FIX  
*14=  
E-31  
Transforming Displayed  
Values  
You can use the procedures in this section to transform a displayed  
value to engineering notation, or to transform between standard form  
and decimal form.  
k Using Engineering Notation  
A simple key operation transforms a displayed value to engineering  
notation.  
Appendix  
<#035> Transform the value 1,234 to engineering notation, shifting  
the decimal point to the right.  
<#036> Transform the value 123 to engineering notation, shifting  
the decimal point to the left.  
k Using S-D Transformation  
You can use S-D transformation to transform a value between its  
decimal (D) form and its standard (S) form (fraction, π).  
Formats Supported for S-D Transformation  
S-D transformation can be used to transform a displayed decimal  
calculation result to one of the forms described below. Performing  
S-D transformation again converts back to the original decimal value.  
Note  
• When you transform from decimal form to standard form, the  
calculator automatically decides the standard form to use. You  
cannot specify the standard form.  
Fraction: The current fraction display format setting determines  
whether the result is an improper fraction or mixed  
fraction.  
π:  
The following are the π forms that are supported.  
This is true only in the case of Math format.  
nπ (n is an integer.)  
d
c
b
c
(depending on fraction display format  
setting)  
a
π
π
or  
• Transformation to a fractional π form is limited to inverse  
trigonometric function results and values that are normally  
expressed in radians.  
• After obtaining a calculation result in ' form, you can convert it  
to decimal form by pressing the f key. When the original  
calculation result is in decimal form, it cannot be converted to '  
form.  
E-32  
Examples of S-DTransformation  
Note that S-D transformation can take some time to perform.  
Example: Fraction Decimal  
Math  
MATH  
'5c6=  
• Each press of the f key toggles between the two forms.  
f
f
Appendix  
<#037> π Fraction Decimal  
<#038> ' Decimal  
Statistical Calculation  
(STAT)  
All calculations in this section are performed in the STAT Mode  
(N2).  
Selecting a Statistical CalculationType  
In the STAT Mode, display the statistical calculation type selection  
screen.  
k Statistical Calculation Types  
Key  
1
2
3
4
5
6
7
8
Menu Item  
1-VAR  
Statistical Calculation  
Single-variable  
A+BX  
Linear regression  
2
_+CX  
Quadratic regression  
Logarithmic regression  
e exponential regression  
ab exponential regression  
Power regression  
In X  
e^X  
A•B^X  
A•X^B  
1/X  
Inverse regression  
E-33  
k Inputting Sample Data  
Displaying the STAT Editor Screen  
The STAT editor screen appears after you enter the STAT Mode  
from another mode. Use the STAT menu to select a statistical  
calculation type.To display the STAT editor screen from another STAT  
Mode screen, press 11(STAT)2(Data).  
STAT Editor Screen  
There are two STAT editor screen formats, depending on the type of  
statistical calculation you selected.  
STAT  
STAT  
Single-variable Statistics  
Paired-variable Statistics  
• The first line of the STAT editor screen shows the value for the first  
sample or the values for their first pair of samples.  
FREQ (Frequency) Column  
If you turn on the Statistical Display item on the calculator’s setup  
screen, a column labeled “FREQ” will also be included on the STAT  
editor screen.  
You can use the FREQ column to specify the frequency (the number  
of times the same sample appears in the group of data) of each  
sample value.  
Rules for Inputting Sample Data on the STAT Editor  
Screen  
• Data you input is inserted into the cell where the cursor is located.  
Use the cursor keys to move the cursor between cells.  
STAT  
Cursor  
• The values and expressions you can input on the STAT editor  
screen are the same as those you can input in the COMP Mode  
with Linear format.  
• Pressing A while inputting data clears your current input.  
• After inputting a value, press =. This registers the value and  
displays up to six of its digits in the currently selected cell.  
E-34  
Example: To input the value 123.45 in cell X1  
(Move the cursor to cell X1.)  
STAT  
123.45  
The value you input appears  
in the formula area.  
STAT  
=
Registering a value causes the cursor to move down one cell.  
STAT Editor Screen Input Precautions  
• The number of lines in STAT editor screen (the number of sample  
data values you can input) depends on the type of statistical data  
you selected, and on the Statistical Display setting of the calculator’s  
setup screen.  
Statistical  
OFF  
ON  
Display  
(No FREQ column)  
(FREQ column)  
Statistic Type  
Single-variable  
Paired-variable  
80 lines  
40 lines  
40 lines  
26 lines  
• The following types of input are not allowed on the STAT editor  
screen.  
m, 1m(M–) operations  
• Assignment to variables (STO)  
Precautions Concerning Sample Data Storage  
Sample data you input is deleted automatically whenever you change  
to another mode from the STAT Mode or change the Statistical  
Display setting (which causes the FREQ column to be shown or  
hidden) on the calculator’s setup screen.  
Editing Sample Data  
Replacing the Data in a Cell  
(1) On the STAT editor screen, move the cursor to the cell you want  
to edit.  
(2) Input the new data value or expression, and then press =.  
Important!  
• Note that you must totally replace the existing data of the cell with  
new input.You cannot edit parts of the existing data.  
Deleting a Line  
(1) On the STAT editor screen, move the cursor to the line you want  
to delete.  
(2) Press Y.  
E-35  
Inserting a Line  
(1) On the STAT editor screen, move the cursor to the line that will  
be under the line you will insert.  
(2) Press 11(STAT)3(Edit).  
(3) Press 1(Ins).  
Important!  
• Note that the insert operation will not work if the maximum number  
of lines allowed for the STAT editor screen are already used.  
Deleting All STAT Editor Contents  
(1) Press 11(STAT)3(Edit).  
(2) Press 2(Del-A).  
• This clears all of the sample data on the STAT editor screen.  
Note  
• Note that you can perform the procedures under “Inserting a Line”  
and “Deleting All STAT Editor Contents” only when the STAT editor  
screen is on the display.  
k STAT Calculation Screen  
The STAT calculation screen is for performing statistical calculations  
with the data you input with the STAT editor screen. Pressing the  
A key while the STAT editor screen is displayed switches to the  
STAT calculation screen.  
The STAT calculation screen also uses Linear format, regardless of  
the current input/output format setting on the calculator’s setup  
screen.  
k Using the STAT Menu  
While the STAT editor screen or STAT calculation screen is on the  
display, press 11(STAT) to display the STAT menu.  
The content to the STAT menu depends on whether the currently  
selected statistical operation type uses a single variable or paired  
variables.  
Single-variable Statistics  
Paired-variable Statistics  
E-36  
STAT Menu Items  
Common Items  
Select this  
menu item:  
When you want to do this:  
Display the statistical calculation type selection  
screen  
1Type  
2Data  
Display the STAT editor screen  
Display the Edit sub-menu for editing STAT editor  
screen contents  
3Edit  
Display the Sum sub-menu of commands for  
calculating sums  
4Sum  
5Var  
Display the Var sub-menu of commands for  
calculating the mean, standard deviation, etc.  
Display the MinMax sub-menu of commands for  
obtaining maximum and minimum values  
6MinMax  
Paired-variable Menu Item  
Select this  
When you want to do this:  
menu item:  
Display the Reg sub-menu of commands for  
regression calculations  
• For details see “Commands when Linear  
Regression Calculation (A+BX) Is Selected” and  
“Commands when Quadratic Regression  
7Reg  
2
Calculation (_+CX ) Is Selected”.  
Single-variable (1-VAR) Statistical Calculation  
Commands  
The following are the commands that appear on the sub-menus that  
appear when you select 4(Sum), 5(Var), or 6(MinMax) on the  
STAT menu while a single-variable statistical calculation type is  
selected.  
See Appendix <#039> for information about the calculation  
formula used for each command.  
Sum Sub-menu (11(STAT)4(Sum))  
Select this  
menu item:  
When you want to obtain this:  
1Σx2  
2Σx  
Sum of squares of the sample data  
Sum of the sample data  
E-37  
Var Sub-menu (11(STAT)5(Var))  
Select this  
When you want to obtain this:  
menu item:  
1n  
Number of samples  
2o  
3xσn  
4xσn–1  
Mean of the sample data  
Population standard deviation  
Sample standard deviation  
MinMax Sub-menu (11(STAT)6(MinMax))  
Select this  
When you want to obtain this:  
menu item:  
1minX  
Minimum value  
Maximum value  
2maxX  
Appendix Single-variable Statistical Calculation  
<#040> Select single-variable (1-VAR) and input the following data:  
{1, 2, 3, 4, 5, 6, 7, 8, 9, 10}  
(FREQ: ON)  
<#041> Edit the data to the following, using insert and delete:  
{0, 1, 2, 3, 4, 5, 6, 7, 9, 10}  
<#042> Edit the FREQ data to the following:  
{1, 2, 1, 2, 2, 2, 3, 4, 2, 1}  
(FREQ: ON)  
(FREQ: ON)  
• Examples <#043> through <#045> all use the same data as  
Example <#042>.  
<#043> Calculate sum of squares of the sample data and sum of  
the sample data.  
<#044> Calculate number of samples, mean, and population  
standard deviation.  
<#045> Calculate minimum value and maximum value.  
Commands when Linear Regression Calculation  
(A+BX) Is Selected  
With linear regression, regression is performed in accordance with  
the following model equation.  
y
=
A
+
BX  
The following are the commands that appear on the sub-menus that  
appear when you select 4(Sum), 5(Var), 6(MinMax), or  
7(Reg) on the STAT menu while linear regression is selected as  
the statistical calculation type.  
See Appendix <#046> for information about the calculation  
formula used for each command.  
E-38  
Sum Sub-menu (11(STAT)4(Sum))  
Select this  
menu item:  
When you want to obtain this:  
1Σx2  
2Σx  
Sum of squares of the X-data  
Sum of the X-data  
3Σy2  
4Σy  
Sum of squares of the Y-data  
Sum of the Y-data  
5Σxy  
6Σx3  
7Σx2y  
8Σx4  
Sum of products of the X-data and Y-data  
Sum of cubes of the X-data  
Sum of (X-data squares × Y-data)  
Sum of biquadrate of the X-data  
Var Sub-menu (11(STAT)5(Var))  
Select this  
When you want to obtain this:  
menu item:  
1n  
Number of samples  
2o  
Mean of the X-data  
3xσn  
4xσn–1  
5p  
Population standard deviation of the X-data  
Sample standard deviation of the X-data  
Mean of the Y-data  
6yσn  
7yσn–1  
Population standard deviation of the Y-data  
Sample standard deviation of the Y-data  
MinMax Sub-menu (11(STAT)6(MinMax))  
Select this  
When you want to obtain this:  
menu item:  
1minX  
2maxX  
3minY  
4maxY  
Minimum value of the X-data  
Maximum value of the X-data  
Minimum value of the Y-data  
Maximum value of the Y-data  
Reg Sub-menu (11(STAT)7(Reg))  
Select this  
When you want to obtain this:  
menu item:  
1A  
2B  
3r  
4m  
5n  
Regression coefficient constant term A  
Regression coefficient B  
Correlation coefficient r  
Estimated value of x  
Estimated value of y  
E-39  
Appendix Linear Regression Calculation: <#047> to <#050>  
• Examples <#048> through <#050> all use the data input in Example  
<#047>.  
*1 Estimated Value (y = –3 m = ?)  
*2 Estimated Value (x = 2 n = ?)  
Commands when Quadratic Regression Calculation  
(_+CX2) Is Selected  
With quadratic regression, regression is performed in accordance  
with the following model equation.  
y
=
A
+
BX  
CX2  
+
See Appendix <#051> for information about the calculation  
formula used for each command.  
Reg Sub-menu (11(STAT)7(Reg))  
Select this  
When you want to obtain this:  
menu item:  
1A  
Regression coefficient constant term A  
2B  
Linear coefficient B of the regression coefficients  
Quadratic coefficient C of the regression  
coefficients  
3C  
4m1  
5m2  
6n  
Estimated value of x1  
Estimated value of x2  
Estimated value of y  
• Sum sub-menu (sums), Var sub-menu (number of samples, mean,  
standard deviation), and MinMax sub-menu (maximum value,  
minimum value) operations are the same those for linear regression  
calculations.  
Appendix Quadratic Regression Calculation:<#052> to <#054>  
Examples <#052> through <#054> all use the data input in  
Example <#047>.  
Comments for Other Types of Regression  
For details about the calculation formula of the command included  
in each regression type, refer to the indicated calculation formulas  
( Appendix <#055> to <#059>).  
E-40  
Statistical Calculation  
Type  
Calculation  
Formula  
Model Equation  
Logarithmic Regression  
(ln X)  
y = A + BlnX  
<#055>  
<#056>  
<#057>  
<#058>  
<#059>  
e Exponential Regression  
(e^X)  
y
y
y
y
=
AeBX  
ABX  
AXB  
ab Exponential Regression  
(A•B^X)  
=
=
=
Power Regression (A•X^B)  
Inverse Regression (1/X)  
B
X
A
+
Appendix Comparison of Regression Curves  
• The following example uses the data input in Example <#047>.  
<#060> Compare the correlation coefficient for logarithmic, e  
exponential, ab exponential, power, and inverse regression.  
(FREQ: OFF)  
Appendix Other Types of Regression Calculation: <#061> to  
<#065>  
Command Usage Tips  
• The commands included in the Reg sub-menu can take a long  
time to execute in logarithmic, e exponential, ab exponential, or  
power regression calculation when there are a large number of  
data samples.  
Generating a Number Table  
from a Function  
(TABLE)  
All calculations in this section are performed in theTABLE Mode  
(N3).  
k Configuring a Number Table Generation  
Function  
The procedure below configures the number table generation  
function with the following settings.  
1
Function:  
f(x) = x2  
+
2
Start Value: 1, End Value: 5, Step Value: 1  
LINE  
E-41  
(1) Press N3(TABLE).  
(2) Input the function.  
(3) After making sure the function is the way you want, press =.  
• This displays the start value input screen.  
Indicates the initial default start  
value of 1.  
• If the initial value is not 1, press 1 to specify the initial start  
value for this example.  
(4) After specifying the start value, press =.  
• This displays the end value input screen.  
Indicates the initial default end  
value of 5.  
• Specify the end value.  
(5) After specifying the end value, press =.  
• This displays the step value input screen.  
Indicates the initial default step  
value of 1.  
• Specify the step value.  
• For details about specifying the start, end, and step values,  
see “Start, End, and Step Value Rules”.  
(6) After specifying the step value, press =.  
• Pressing the A key returns to the function editor screen.  
k Supported Function Types  
• Except for the X variable, other variables (A, B, C, D, Y) and  
independent memory (M) are all treated as values (the current  
variable assigned to the variable or stored in independent memory).  
E-42  
• Only variable X can be used as the variable of a function.  
• The coordinate conversion (Pol, Rec) functions cannot be used  
for a number table generation function.  
• Note that the number table generation operation causes the  
contents of variable X to be changed.  
k Start, End, and Step Value Rules  
• Linear format is always used for value input.  
You can specify either values or calculation expressions (which  
must produce a numeric result) for Start, End, and Step.  
• Specifying an End value that is less than the Start value causes  
an error, so the number table is not generated.  
• The specified Start, End, and Step values should produce a  
maximum of 30 x-values for the number table being generated.  
Executing a number generation table using a Start, End, and Step  
value combination that produces more than 30 x-values causes  
an error.  
Note  
• Certain functions and Start, End, Step value combinations can  
cause number table generation to take a long time.  
k Number Table Screen  
The number table screen shows x-values calculated using the  
specified Start, End, and Step values, as well as the values obtained  
when each x-value is substituted in the function f(x).  
• Note that you can use the number table screen for viewing values  
only.Table contents cannot be edited.  
• Pressing the A key returns to the function editor screen.  
k TABLE Mode Precautions  
Note that changing the input/output format settings (Math format or  
Linear format) on the calculator’s setup screen while in the TABLE  
Mode clears the number table generation function.  
E-43  
Technical Information  
k Calculation Priority Sequence  
The calculator performs calculations according to a calculation priority sequence.  
Basically, calculations are performed from left to right.  
Expressions within parentheses have the highest priority.  
The following shows the priority sequence for each individual command.  
1. Function with parentheses:  
Pol(, Rec(  
–1  
–1  
–1  
–1  
–1  
sin(, cos(, tan(, sin (, cos (, tan (, sinh(, cosh(, tanh(, sinh (, cosh (,  
–1  
tanh  
(
3
log(, ln(, e^(, 10^(, '(, '(  
Abs(  
Rnd(  
2. Functions preceded by values, powers, power roots:  
2
3
–1  
r
g
x
x
, x , x , x!, ° ’ ”, °,  
,
, ^(, '(  
Percent %  
b
3. Fractions: a /c  
4. Prefix symbol: (–) (negative sign)  
5. Statistical estimated value calculation: m, n, m1, m2  
6. Permutations, combinations: nPr, nCr  
7. Multiplication and division: ×, ÷  
Multiplication where sign is omitted: Multiplication sign omitted immediately  
before π, e, variables (2π, 5A, πA, etc.), functions with parentheses (2'(3),  
Asin(30), etc.)  
8. Addition and subtraction: +, –  
If a calculation contains a negative value, you may need to enclose the negative  
value in parentheses. If you want to square the value –2, for example, you need to  
2
2
input: (–2) . This is because x is a function preceded by a value (Priority 2,  
above), whose priority is greater than the negative sign, which is a prefix symbol  
(Priority 4).  
Example:  
2
y2w=  
–2 = –4  
2
(y2)w=  
(–2) = 4  
Multiplication and division, and multiplication where the sign is omitted are the  
same priority (Priority 7), so these operations are performed from left to right  
when both types are mixed in the same calculation. Enclosing an operation within  
parentheses causes it to be performed first, so the use of parentheses can result  
in different calculation results.  
Example:  
1/215(π)=  
1 ÷ 2π = 1.570796327  
1/(215(π))=  
1 ÷ (2π) = 0.1591549431  
E-44  
k Stack Limitations  
This calculator uses memory areas called stacks to temporarily store lower  
calculation priority sequence values, commands, and functions.The numeric stack  
has 10 levels and the command stack has 24 levels, as shown in the illustration  
below.  
1
2
3
4
5
1
2
3
4
5
6
7
Numeric Stack  
1
Command Stack  
2
1
2
3
4
5
6
7
҂
2
3
3
4
4
5
ѿ
҂
5
4
ѿ
A Stack ERROR occurs when the calculation you are performing causes the  
capacity of either stack to be exceeded.  
k Calculation Ranges, Number of Digits, and  
Precision  
The calculation range, number of digits used for internal calculation, and calculation  
precision depends on the type of calculation you are performing.  
Calculation Range and Precision  
–99  
99  
to 9.999999999 × 10 or 0  
Calculation Range  
1 × 10  
15 digits  
Number of Digits for Internal  
Calculation  
Precision  
In general, 1 at the 10th digit for a single  
calculation. Precision for exponential display  
is 1 at the least significant digit. Errors are  
cumulative in the case of consecutive  
calculations.  
Function Calculation Input Ranges and Precision  
Functions  
Input Range  
9
DEG 0Ϲ xϽ9҂10  
sinx  
RAD  
0Ϲ xϽ157079632.7  
10  
GRA 0Ϲ xϽ1҂10  
9
cosx  
DEG 0Ϲ xϽ9҂10  
RAD  
0Ϲ xϽ157079632.7  
10  
GRA 0Ϲ xϽ1҂10  
E-45  
Functions  
Input Range  
tanx  
DEG Same as sinx, except when x= (2n–1)҂90.  
RAD  
Same as sinx, except when x= (2n–1)҂π/2.  
GRA Same as sinx, except when x= (2n–1)҂100  
.
sin1x  
cos1x  
0Ϲ xϹ1  
99  
tan1x  
0Ϲ xϹ9.999999999҂10  
sinhx  
coshx  
0Ϲ xϹ230.2585092  
sinh1x  
0Ϲ xϹ4.999999999҂10  
99  
99  
cosh1x 1Ϲ x Ϲ4.999999999҂10  
99  
tanhx  
tanh1x  
logx/lnx  
10x  
0Ϲ xϹ9.999999999҂10  
–1  
0Ϲ xϹ9.999999999҂10  
99  
0x Ϲ9.999999999҂10  
99  
–9.999999999҂10 Ϲ x Ϲ 99.99999999  
–9.999999999҂10 Ϲ x Ϲ 230.2585092  
ex  
99  
100  
'x  
0Ϲ x 1 ҂ 10  
50  
x2  
xꢀꢁ 1҂ 10  
100  
1/x  
xꢀꢁ 1҂ 10  
;
x G  
0
3
100  
'x  
xꢀꢁ 1҂ 10  
x!  
0Ϲ x Ϲ 69 (x is an integer)  
10  
0Ϲ n 1҂10 , 0Ϲ r Ϲ n (n, r are integers)  
nPr  
100  
1Ϲ {n!/(nr)!} 1҂10  
10  
0Ϲ n 1҂10 , 0Ϲ r Ϲ n (n, r are integers)  
nCr  
100  
100  
1Ϲ n!/r! 1҂10  
or 1Ϲ n!/(nr)! 1҂10  
99  
x, yϹ9.999999999҂10  
Pol(x, y)  
x2+y2 Ϲ9.999999999҂10  
99  
99  
0Ϲ r Ϲ9.999999999҂10  
θ: Same as sinx  
Rec(r, )  
100  
a, b, c 1҂10  
°’ ”  
0 Ϲ b, c  
xꢀꢁ1҂10  
100  
Decimal Sexagesimal Conversions  
0°0’0”Ϲ xϹ9999999°59’59”  
100  
xŒ0: –1҂10  
ylogx100  
x҃0: yŒ0  
x0: y҃n,  
y
m
2n+1  
^(x )  
(m, n are integers)  
100  
However: –1҂10  
ylogxꢀꢁ100  
100  
yŒ0: x G 0, –1҂10 1/x logy100  
y҃0: xŒ0  
y0: x҃2nѿ1,  
x
'
y
2n+1  
m
100  
(m G 0; m, n are integers)  
However: –1҂10  
1/x logyꢀꢁ100  
Total of integer, numerator, and denominator must be 10 digits or  
less (including division marks).  
b
a
/c  
E-46  
Precision is basically the same as that described underCalculation Range and  
Precision”, above.  
^(x ), 'y, ', x!, nPr, nCr type functions require consecutive internal  
calculation, which can cause accumulation of errors that occur with each  
calculation.  
y
x
3
Error is cumulative and tends to be large in the vicinity of a function’s singular  
point and inflection point.  
k Error Messages  
The calculator will display an error message when a result exceeds the calculation  
range, when you attempt an illegal input, or whenever any other similar problem  
occurs.  
When an error message appears...  
The following are general operations you can use when any error message  
appears.  
Pressing d or e displays to the calculation expression editing screen you  
were using before the error message appeared, with the cursor located at the  
position of the error. For more information, see “Displaying the Location of an  
Error”.  
Pressing A clears the calculation expression you input before the error message  
appeared. You can then re-input and re-execute the calculation, if you want.  
Note that in this case, the original calculation will not be retained in calculation  
history memory.  
Math ERROR  
Cause  
The intermediate or final result of the calculation you are performing exceeds  
the allowable calculation range.  
Your input exceeds the allowable input range (particularly when using  
functions).  
The calculation you are performing contains an illegal mathematical operation  
(such as division by zero).  
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.  
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.  
E-47  
Insufficient MEM Error  
Cause  
There is not enough memory to perform your calculation.  
Action  
Narrow the table calculation range by changing the Start, End, and Step values,  
and try again.  
k Before assuming malfunction of the calculator...  
Perform the following steps whenever an error occurs during a calculation or when  
calculation results are not what you expected. If one step does not correct the  
problem, move on to the next step.  
Note that you should make separate copies of important data before performing  
these steps.  
(1) Check the calculation expression to make sure that it does not contain any  
errors.  
(2) Make sure that you are using the correct mode for the type of calculation you  
are trying to perform.  
(3) If the above steps do not correct your problem, press the O key. This will  
cause the calculator to perform a routine that checks whether calculation  
functions are operating correctly. If the calculator discovers any abnormality,  
it automatically initializes the calculation mode and clears memory contents.  
For details about initialized settings, see “Initializing the Calculation Mode  
and Other Settings” under “Calculation Modes and Calculator Setup”.  
(4) Initialize all modes and settings by performing the following operation:  
19(CLR) 1(Setup) =(Yes).  
Reference  
k Power Requirements and Battery  
Replacement  
fx-85ES/fx-300ES  
Your calculator uses a TWO WAY POWER system that combines a  
solar cell with button battery (LR44 (GPA76)).  
Normally, calculators equipped with a solar cell alone can operate  
only when relatively bright light is present. The TWO WAY POWER  
system, however, lets you continue to use the calculator as long as  
there is enough light to read the display.  
Replacing the Battery  
Dim display figures when available lighting is dim or failure of anything  
to appear on the display immediately when you turn on the calculator  
indicates that button battery power is low. Note that you will not be  
able to use the calculator if its button battery is dead. When any of  
these symptoms occur, replace the button battery.  
Even if the calculator is operating normally, replace the battery at  
least once every three years.  
E-48  
Important!  
• Removing the button battery from the calculator causes  
independent memory contents and values assigned to variables  
to be cleared.  
Screw  
1 Press 1A(OFF) to turn off the  
calculator.  
• To ensure that you do not  
accidentally turn on power while  
replacing the battery, slide the hard  
case onto the front of the calculator.  
2 On the back of the calculator, remove  
the screw and the battery cover.  
3 Remove the old battery.  
4 Wipe a new battery with a dry cloth,  
and then load it into the calculator with  
its positive  
(so you can see it).  
side facing upwards  
k
5 Replace the battery cover and secure  
it in place with its screw.  
6 Perform the following key operation:  
O19(CLR)3(All)=(Yes).  
• Make sure you perform the above key operation. Do not skip it.  
fx-82ES/fx-83ES/fx-350ES  
fx-82ES/fx-83ES: This calculator is powered by a single AAA-size  
battery (R03 (UM-4)).  
fx-350ES: This calculator is powered by a single AAA-size battery  
(LR03 (AM4)).  
Replacing the Battery  
Dim figures on the display of the calculator indicate that battery power  
is low. Continued use of the calculator when the battery is low can  
result in improper operation.Replace the battery as soon as possible  
when display figures becomes dim.  
Even if the calculator is operating normally, replace the battery at  
least once every two years (R03 (UM-4)) or one year (LR03 (AM4)).  
Important!  
• Removing the battery from the calculator causes independent  
memory contents and values assigned to variables to be cleared.  
E-49  
1 Press 1A(OFF) to turn off the  
calculator.  
Screw  
Screw  
2 On the back of the calculator, remove  
the screws and the back cover.  
3 Remove the old battery.  
4 Load a new battery into the calculator  
with its positive  
ends facing correctly.  
and negative  
k
l
5 Replace the back cover and secure it  
in place with its screws.  
6 Perform the following key operation:  
O19(CLR)3(All)=(Yes).  
• Make sure you perform the above key operation. Do not skip it.  
Auto Power Off  
Your calculator will turn off automatically if you do not perform any  
operation for about six minutes. If this happens, press the O key to  
turn the calculator back on.  
E-50  
Specifications  
fx-82ES/fx-83ES  
Power Requirements:  
AAA-size battery: R03 (UM-4) × 1  
Battery Life: Approximately 6,000 hours (continuous operation)  
Approximately 17,000 hours (continuous display of  
flashing cursor)  
Power Consumption: 0.0002 W  
OperatingTemperature: 0°C to 40°C  
Dimensions: 13.7 (H) × 80 (W) × 161 (D) mm  
9
1
5
/16(H) ҂ 3 /8(W) ҂ 6 /16(D)  
Approximate Weight: 110 g (3.9 oz) including the battery  
Bundled Items: Hard Case  
fx-350ES  
Power Requirements:  
AAA-size battery: LR03 (AM4) × 1  
Battery Life: Approximately 8,700 hours (continuous operation)  
Power Consumption: 0.0002 W  
OperatingTemperature: 0°C to 40°C  
Dimensions: 13.7 (H) × 80 (W) × 161 (D) mm  
9
1
5
/16(H) ҂ 3 /8(W) ҂ 6 /16(D)  
Approximate Weight: 110 g (3.9 oz) including the battery  
Bundled Items: Hard Case  
fx-85ES/fx-300ES  
Power Requirements:  
Solar Cell: Built into the front of the calculator  
Button Battery: LR44 (GPA76) × 1  
Battery Life: Approximately 3 years (Based on one hour of  
operation per day.)  
OperatingTemperature: 0°C to 40°C  
Dimensions: 12.2 (H) × 80 (W) × 161 (D) mm  
1
1
5
/2(H) ҂ 3 /8(W) ҂ 6 /16(D)  
Approximate Weight: 105 g (3.7 oz) including the battery  
Bundled Items: Hard Case  
E-51  
CASIO COMPUTER CO., LTD.  
6-2, Hon-machi 1-chome  
Shibuya-ku, Tokyo 151-8543, Japan  
SA0412-C  
Printed in China  

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