Casio Fx 570EX_fx991EX 570_991EX 570 991EX EN
User Manual: Casio fx-570_991EX fx-570EX, fx-991EX | Calculators | Manuals | CASIO
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EN
fx-570EX
fx-991EX
User’s Guide
CASIO Worldwide Education Website
http://edu.casio.com
Be sure to keep all user documentation handy for future
reference.
RJA532432-001V01
CONTENTS
About this Manual......................................................................................2
Initializing the Calculator........................................................................... 2
Precautions................................................................................................2
Getting Started.......................................................................................... 3
Calculation Mode.......................................................................................4
Input and Output Formats......................................................................... 5
Configuring the Calculator Setup.............................................................. 6
Inputting Expressions and Values............................................................. 8
Toggling Calculation Results................................................................... 10
Basic Calculations................................................................................... 10
Calculation History and Replay............................................................... 12
Using Memory Functions.........................................................................13
Function Calculations.............................................................................. 14
QR Code Function................................................................................... 17
Complex Number Calculations................................................................18
Using CALC.............................................................................................18
Using SOLVE........................................................................................... 19
Statistical Calculations.............................................................................20
Base-n Calculations.................................................................................23
Equation Calculations..............................................................................24
Matrix Calculations.................................................................................. 25
Creating a Number Table........................................................................ 27
Vector Calculations..................................................................................28
Inequality Calculations............................................................................ 29
Ratio Calculations....................................................................................30
Distribution Calculations..........................................................................31
Using Spreadsheet..................................................................................33
Scientific Constants................................................................................. 37
Metric Conversion....................................................................................37
Errors....................................................................................................... 37
Before Assuming Malfunction of the Calculator.......................................39
Replacing the Battery.............................................................................. 39
Technical Information...............................................................................40
■■ Frequently Asked Questions ■■.........................................................42
Reference Sheet...................................................................................... 44
• 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.
1
About this Manual
• Unless specifically stated, all sample operations in this manual assume
that the calculator is in its initial default setup. Use the procedure under
“Initializing the Calculator” to return the calculator to its initial default
setup.
• The contents of this manual are subject to change without notice.
• 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.
• Company and product names used in this manual may be registered
trademarks or trademarks of their respective owners.
Initializing the Calculator
Perform the following procedure when you want to initialize the calculator
and return the calculation mode and setup (except for the Contrast setting)
to their initial default settings. Note that this operation also clears all data
currently in calculator memory.
(RESET)(Initialize All)(Yes)
Precautions
Safety Precautions
Battery
• Keep batteries out of the reach of small children.
• Use only the type of battery specified for this calculator in this manual.
Handling Precautions
• Even if the calculator is operating normally, replace the battery at least
once every three years (LR44) or two years (R03 (UM-4)). A dead battery
can leak, causing damage to and malfunction of the calculator. Never
leave a dead battery in the calculator. Do not try using the calculator
while the battery is completely dead (fx-991EX).
• The battery that comes with the calculator discharges slightly during
shipment and storage. Because of this, it may require replacement
sooner than the normal expected battery life.
• Avoid use and storage of the calculator in areas subjected to
temperature extremes, and large amounts of humidity and dust.
• Do not subject the calculator to excessive impact, pressure, or bending.
• Never try to take the calculator apart.
• Use a soft, dry cloth to clean the exterior of the calculator.
• Whenever discarding the calculator or batteries, be sure to do so in
accordance with the laws and regulations in your particular area.
2
Getting Started
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 nearby.
Turning Power On and Off
Press to turn on the calculator. Press
(OFF) to turn off the calculator.
Note: The calculator also will turn off automatically after approximately 10
minutes of non-use. Press the key to turn the calculator back on.
Adjusting Display Contrast
Display the Contrast screen by performing the key operation below:
(SETUP)(Contrast). Next, use and to adjust contrast.
After the setting is the way you want, press .
Important: If adjusting display contrast does not improve display
readability, it probably means that battery power is low. Replace the battery.
Key Markings
Pressing the or 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.
(1) Keycap function (2) Alternate function
This color:
Means this:
Yellow
Press and then the key to access the
applicable function.
Red
Press and then the key to input the
applicable variable, constant, function, or
symbol.
Purple (or enclosed in
purple brackets)
Enter the Complex Mode to access the function.
Blue (or enclosed in
blue brackets)
Enter the Base-N Mode to access the function.
Reading the Display
• If a or indicator appears on the right side of either the input
expression line or calculation result line, it means the displayed line
continues to the right. Use and to scroll the line display. Note that
if you want to scroll the input expression while both the and
indicators are displayed, you will need to press first and then use
and to scroll.
3
• The table below describes some of the typical indicators that appear at
the top of the screen.
The keypad has been shifted by pressing the key. The
keypad will unshift and this indicator will disappear when you
press a key.
The alpha input mode has been entered by pressing the
key. The alpha input mode will be exited and this indicator
will disappear when you press a key.
//
Indicates the current setting of Angle Unit (: Degree, :
Radian, or : Gradian) on the setup menu.
FIX
A fixed number of decimal places is in effect.
SCI
A fixed number of significant digits is in effect.
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 .
Indicates that MathI/MathO or MathI/DecimalO is selected for
Input/Output on the setup menu.
The display currently shows an intermediate result of a multistatement calculation.
This indicator is displayed while the calculator is being
powered directly by its solar cells, either entirely or in some
combination with the battery. (fx-991EX only)
Using Menus
Some of the operations of this calculator are performed using menus.
Menus are displayed by pressing or and then (SETUP).
General menu operation operations are described below.
• You can select a menu item by pressing the number key that
corresponds to the number to its left on the menu screen.
• A vertical scroll bar (1) indicates that the menu runs off the screen. In this
case, you can use and to scroll the menu up and down. A left
arrow (2) indicates that the currently displayed menu is a sub-menu. To
return from a sub-menu to its parent menu, press .
• To close a menu without selecting anything, press .
Calculation Mode
Specify the calculation mode that is suitable for the type of calculation you
want to perform.
1. Press to display the Main Menu.
2. Use the cursor keys to move the
highlighting to the icon you want.
4
For this:
Select this icon:
General calculations
(Calculate)
Complex number calculations
(Complex)
Calculations involving specific number
systems (binary, octal, decimal,
hexadecimal)
(Base-N)
Matrix calculations
(Matrix)
Vector calculations
(Vector)
Statistical and regression calculations
(Statistics)
Distribution calculations
(Distribution)
Spreadsheet calculations
(Spreadsheet)
Generate a number table based on one
or two functions
(Table)
Equation and function calculations
(Equation/Func)
Inequality calculations
(Inequality)
Ratio calculations
(Ratio)
3. Press to display the initial screen of the mode whose icon you
selected.
Note: The initial default calculation mode is the Calculate Mode.
Input and Output Formats
Before starting a calculation on the calculator, you should first use the
operations in the table below to specify the formats that should be applied
for calculation formula input and calculation result output.
To specify this type of input and output:
Press (SETUP)
(Input/Output) and then
press:
Input: Natural Textbook; Output: Format that
(MathI/MathO)
includes a fraction, √, or π*1
Input: Natural Textbook; Output: Converted
to decimal value
(MathI/DecimalO)
Input: Linear*2; Output: Decimal or fraction
(LineI/LineO)
5
Input: Linear*2; Output: Converted to
decimal value
(LineI/DecimalO)
*1 Decimal output is applied when these formats cannot be output for
some reason.
*2 All calculations, including fractions and functions are input in a single
line. Same output format as that for models without Natural Textbook
Display (S-V.P.A.M. models, etc.)
Input/Output Format Display Examples
MathI/MathO
MathI/DecimalO
LineI/LineO
LineI/DecimalO
Note: The initial default input/output format setting is MathI/MathO.
Configuring the Calculator Setup
To change the calculator setup
1. Press (SETUP) to display the setup menu.
2. Use and to scroll the setup menu, and then input the number
displayed to the left of the item whose setting you want to change.
Items and Available Setting Options
“◆” indicates the initial default setting.
Input/Output MathI/MathO◆; MathI/DecimalO; LineI/LineO;
LineI/DecimalO Specifies the format to be used by the calculator for
formula input and calculation result output.
Angle Unit Degree◆; Radian; Gradian Specifies degree,
radian or gradian as the angle unit for value input and calculation result
display.
Number Format Specifies the number of digits for display of a calculation
result.
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: 1007(≈)* 14.286 (Fix 3)
Sci: The value you specify (from 0 to 9) controls the number of
significant digits for displayed calculation results. Calculation results are
rounded off to the specified digit before being displayed.
6
Example: 17(≈)* 1.4286 × 10-1 (Sci 5)
Norm: Displays calculation results in exponential format when they fall
within the ranges below.
Norm 1◆: 10-2 > |x|, |x| ≧ 1010, Norm 2: 10-9 > |x|, |x| ≧ 1010
Example: 1200(≈)* 5 × 10-3 (Norm 1), 0.005 (Norm 2)
* Pressing (≈) instead of after inputting a calculation will display
the calculation result in decimal form.
Engineer Symbol On; Off◆ Specifies whether or not to display
calculation results using engineering symbols.
Note: An indicator (E) is displayed at the top of the screen while On is
selected for this setting.
Fraction Result ab/c; d/c◆ Specifies either mixed fraction or
improper fraction for display of fractions in calculation results.
Complex a+bi◆; r∠θ Specifies either rectangular coordinates or
polar coordinates for Complex Mode calculation results and Equation/Func
Mode solutions.
Note: An i indicator is displayed at the top of the screen while a+bi is
selected for the Complex setting. ∠ is displayed while r∠θ is selected.
Statistics On; Off◆ Specifies whether or not to display a Freq
(frequency) column in the Statistics Mode Statistics Editor.
Spreadsheet For configuring Spreadsheet Mode settings.
Auto Calc: Specifies whether or not formulas should be re-calculated
automatically.
On◆; Off Enables or disables auto re-calculation.
Show Cell: Specifies whether a formula in the edit box should be
displayed as it is or as its calculation result value.
Formula◆: Displays the formula as it is.
Value: Displays the calculation result value of the formula.
Equation/Func On◆; Off Specifies whether or not to use complex
numbers in solutions output in the Equation/Func Mode.
Table f(x); f(x),g(x)◆ Specifies whether to use function f(x) only or
the two functions f(x) and g(x) in the Table Mode.
Decimal Mark Dot◆; Comma Specifies whether to display a dot or
a comma for the calculation result decimal mark. A dot is always displayed
during input.
Note: When dot is selected as the decimal mark, the separator for multiple
results is a comma (,). When comma is selected, the separator is a
semicolon (;).
Digit Separator On; Off◆ Specifies whether or not a separator
character should be used in calculation results.
MultiLine Font Normal Font◆; Small Font Specifies the display
font size when LineI/LineO or LineI/DecimalO is selected for Input/Output.
Up to four lines can be displayed while Normal Font is selected, and up to
six lines can be displayed with Small Font.
QR Code Specifies the version of the QR code displayed when
(QR) is pressed.
Version 3: Indicates QR code Version 3.
Version 11◆: Indicates QR code Version 11.
To initialize calculator settings (except the Contrast setting)
(RESET)(Setup Data)(Yes)
7
Inputting Expressions and Values
Basic Input Rules
When you press the priority sequence of the input calculation will be
evaluated automatically and the result will appear on the display.
4 × sin 30 × (30 + 10 × 3) = 120
*1 Input of the closing parenthesis is required for sin and other functions
that include parentheses.
*2 These multiplication symbols (×) can be omitted.
*3 The closing parenthesis immediately before the operation can be
omitted.
Note
• The cursor will change shape to when there are 10 bytes or less of
allowed input remaining. If this happens, end calculation input and then
press .
• If you execute a calculation that includes both division and multiplication
operations in which a multiplication sign has been omitted, parentheses
will be inserted automatically as shown in the examples below.
- When a multiplication sign is omitted immediately before an open
parenthesis or after a closed parenthesis.
6 ÷ 2 1 + 2
Example: 6 ÷ 2 1 + 2
- When a multiplication sign is omitted immediately before a variable, a
constant, etc.
2÷ 2 2
Example: 2 ÷ 2 2
Calculation Priority Sequence
The priority sequence of input calculations is evaluated in accordance with
the rules below. When the priority of two expressions is the same, the
calculation is performed from left to right.
1
Parenthetical expressions
2
Functions that have parentheses (sin(, log(, etc., functions that take
an argument to the right, functions that require a closing parenthesis
after the argument)
3
Functions that come after the input value (𝑥2, 𝑥3, 𝑥-1, 𝑥!, °’ ”, °, r, g, %,
𝑡), engineering symbols (m, μ, n, p, f, k, M, G, T, P, E), powers (),
roots ()
4
Fractions
5
Negative sign ((-)), base-n symbols (d, h, b, o)
6
Metric conversion commands (cmin, etc.), Statistics Mode
estimated values (𝑥, 𝑦, 𝑥1, 𝑥2)
7
Multiplication where the multiplication sign is omitted
8
Permutation (nPr), combination (nCr), complex number polar
coordinate symbol (∠)
8
9
Dot product (•)
10 Multiplication (×), division (÷)
11 Addition (+), subtraction (−)
12 and (logical operator)
13 or, xor, xnor (logical operators)
Note: When squaring a negative value (such as -2), the value being
squared must be enclosed in parentheses (2). Since x2 has
a higher priority than the negative sign, inputting 2 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.
Inputting an Expression Using Natural Textbook
Format (MathI/MathO or MathI/DecimalO Only)
Formulas and expressions that include fractions and/or special functions
such as √ can be input in natural textbook format by using templates that
appear when certain keys are pressed.
1
3
Example: 3 + 5
2
2
1. Press ().
• This inputs a mixed fraction template.
2. Input values into the integer, numerator, and denominator areas of the
template.
312
3. Do the same to input the remainder of the expression.
() 532
Tip: While the input cursor is located within the input area of a template
(mixed fractions, integration (∫), and sum (Σ)), pressing jumps to the
position immediately following (to the right) of the template, while pressing
jumps to the position immediate before (to the left of) it.
Note
• When you press and obtain a calculation result, part of the
expression you input may be cut off. If you need to view the entire input
expression again, press and then use and to scroll the input
expression.
• Nesting of functions and parentheses is allowed. Further input will
become impossible if you nest too many functions and/or parentheses.
To undo operations (MathI/MathO or MathI/DecimalO only): To undo the
last key operation, press (UNDO). To redo a key operation you have
just undone, press (UNDO) again.
9
Using Values and Expressions as Arguments (MathI/
MathO or MathI/DecimalO only)
Example: To input 1 +
7
7
and then change it to 1 +
6
6
176(INS)
Pressing (INS) in the above example causes
7
to be the argument
6
of the function input by the next key operation (√).
Overwrite Input Mode (LineI/LineO or LineI/DecimalO
only)
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: (INS). The cursor appears as “” in the
insert mode and as “” in the overwrite mode.
Toggling Calculation Results
While MathI/MathO or MathI/DecimalO is selected for Input/Output on the
setup menu, each press of will toggle the currently displayed
calculation result between its fraction form and decimal form, its √ form
and decimal form, or its π form and decimal form.
1
𝜋 ÷ 6 = 𝜋 = 0.5235987756 (MathI/MathO)
6
1
π ←→ 0.5235987756
(π)6
6
2 + 2 × 3 = 5.913591358 = 6 + 2 3 (MathI/DecimalO)
5.913591358 ←→
6+2 3
223
Regardless of what is selected for Input/Output on the setup menu, each
press of will toggle the currently displayed calculation result between its
decimal form and fraction form.
Important
• With certain calculation results, pressing the key will not convert the
displayed value.
• You cannot switch from decimal form to mixed fraction form if the total
number of digits used in the mixed fraction (including integer, numerator,
denominator, and separator symbol) is greater than 10.
To obtain a decimal value calculation result while MathI/MathO or LineI/
LineO is selected
Press (≈) instead of after inputting a calculation.
Basic Calculations
Fraction Calculations
Note that the input method for fractions depends on the current Input/
Output setting on the setup menu.
23()
2
1
13
(MathI/MathO)
+1 =
3
2
6
112
10
13
6
23112 136
(LineI/LineO)
Note
• Mixing fractions and decimal values in a calculation while something
other than MathI/MathO is selected will cause the result to be displayed
as a decimal value.
• Fractions in calculation results are displayed after being reduced to their
lowest terms.
• To switch a calculation result between improper fraction and mixed
fraction form, press ().
Percent Calculations
Inputting a value and pressing (%) causes the input value to
become a percent.
150 × 20% = 30
15020(%)
Calculate what percentage of 880 is 660. (75%)
660880(%)
Discount 3500 by 25%. (2625)
3500350025(%)
30
75
2625
Degree, Minute, Second (Sexagesimal) Calculations
The syntax below is for inputting a sexagesimal value: {degrees}
{minutes} {seconds} . Note that you must always input something
for the degrees and minutes, even if they are zero.
2°20’30” + 9’30” = 2°30’00”
2°30’0”
220300930
Convert 2°30’0” to its decimal equivalent.
2.5
2°30’0”
(Converts decimal to sexagesimal.)
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+3:3×3
6
33(:) 33
9
Note: Inputting a colon (:) while LineI/LineO or LineI/DecimalO is selected
for the Input/Output setting on the setup menu causes a newline operation
to be performed.
Using Engineering Notation
1234
1234
1.234×103
1234×100
1.234×103
(←)
0.001234×106
(←)
Note: The calculation result shown above is what appears when Off is
selected for the Engineer Symbol setting on the setup menu.
Transform the value 1234 to engineering
notation, shifting the decimal mark to the
right, and then to the left.
Using Engineering Symbols
Your calculator supports the use of 11 engineering symbols (m, μ, n, p, f, k,
M, G, T, P, E) that you can use for input of value or for calculation result
display.
To display calculation results with engineering symbols
On the setup menu, change the Engineer Symbol setting to On.
11
Example Input and Calculations Using Engineering Symbols
To input 500k
500(Engineer Symbol)
500k
(k)
To calculate 999k (kilo) + 25k (kilo) = 1.024M (Mega) = 1024k (kilo) =
1024000
999(Engineer Symbol)(k)
1.024M
25(Engineer Symbol)(k)
1024k
1024000
1024k
(←)
Prime Factorization
In the Calculate Mode, a positive integer no more than 10 digits long can be
factored to prime factors.
To perform prime factorization on 1014
1014
1014
2×3×132
(FACT)
To re-display the unfactored value, press (FACT) or .
Note: The types of values described below cannot be factored, even if they
have 10 or fewer digits.
• One of the prime factors of the value is 1,018,081 or greater.
• Two or more of the prime factors of the value have more than three digits.
The part that cannot be factored will be enclosed in parentheses on the
display.
Calculation History and Replay
Calculation History
An and/or at the top of the display indicates that there is more
calculation history content above and/or below. You can scroll through
calculation history contents using and .
2+2=4
22
3+3=6
33
(Scrolls back.)
4
6
4
Note: Calculation history data is all cleared whenever you press , when
you change to a different calculation mode, when you change the Input/
Output setting, or whenever you perform a RESET operation (“Initialize All”
or “Setup Data”).
Replay
While a calculation result is on the display, you can press or to edit
the expression you used for the previous calculation.
4 × 3 + 2 = 14
14
432
4×3−7=5
5
(Continuing) 7
12
Using Memory Functions
Answer Memory (Ans)
The last calculation result obtained is stored in Ans (answer) memory.
To divide the result of 14 × 13 by 7
1413
182
(Continuing) 7
123 + 456 = 579
789 − 579 = 210
123456
(Continuing) 789
579
210
Variables (A, B, C, D, E, F, M, x, y)
You can assign values to variables and use the variables in calculations.
To assign the result of 3 + 5 to variable A
8
35(A)
To multiply the contents of variable A by 10
80
(Continuing) (A)10*1
To recall the contents of variable A
(Continuing) (RECALL)*2
(A)
8
To clear the contents of variable A
0(A)
0
*1 Input a variable as shown here: press and then press the key that
corresponds to the desired variable name. To input x as the variable
name, you can press (x) or .
*2 Pressing (RECALL) displays a screen that shows the values
currently assigned to variables A, B, C, D, E, F, M, x, and y. On this
screen, values are always displayed using the “Norm 1” Number
Format. To close the screen without recalling a variable value, press
.
Independent Memory (M)
You can add calculation results to or subtract results from independent
memory. The “M” appears on the display when there is any value other than
zero stored in independent memory.
To clear the contents of M
0
0(M)
To add the result of 10 × 5 to M
50
(Continuing) 105
To subtract the result of 10 + 5 from M
15
(Continuing) 105(M−)
To recall the contents of M
35
(Continuing) (RECALL)(M)
Note: Variable M is used for independent memory. You also can call M and
use it in a calculation you are inputting.
13
Clearing the Contents of All Memories
Ans memory, independent memory, and variable contents are retained even
if you press , change the calculation mode, or turn off the calculator.
Perform the procedure below when you want to clear the contents of all
memories.
(RESET)(Memory)(Yes)
Function Calculations
Note: To interrupt an ongoing calculation before its result appears, press
.
Pi π: π is displayed as 3.141592654, but π = 3.14159265358980 is used for
internal calculations.
Natural Logarithm Base e: e is displayed as 2.718281828, but e =
2.71828182845904 is used for internal calculations.
sin, cos, tan, sin-1, cos-1, tan-1: Specify the angle unit before performing
calculations.
1
1
(Angle Unit: Degree)
sin 30° =
30
2
2
-1
-1
-1
sinh, cosh, tanh, sinh , cosh , tanh : Input a function from the menu that
appears when you press (Hyperbolic Func)*1. The angle unit setting
does not affect calculations.
*1 Depending on the calculation mode, you should press .
∘ r g
: These functions specify the angle unit. ° specifies degree, r radian,
and g gradian. Input a function from the menu that appears when you
perform the following key operation: (Angle Unit)*2.
π/2 radians = 90° (Angle Unit: Degree)
90
(π)2(Angle Unit)(r)
, ,
*2 Depending on the calculation mode, you should press .
, : Exponential functions.
e5 × 2 = 296.8263182
(MathI/MathO)
296.8263182
() 52
(LineI/LineO)
296.8263182
() 52
log: Logarithmic function. Use (log) to input logab as log (a, b).
Base 10 is the default setting if you do not input anything for a.
log101000 = log 1000 = 3
3
(log) 1000
log216 = 4
4
(log) 2(,) 16
The key also can be used for input, but only while MathI/MathO or
MathI/DecimalO is selected for Input/Output on the setup menu. In this
case, you must input a value for the base.
log216 = 4
4
216
ln: Natural logarithm to base e.
4.49980967
ln 90 (= loge 90) = 4.49980967
90
x2, x3, , , , , x-1: Powers, power roots, and reciprocals.
16
(1 + 1)2+2 = 16
1122
2 3
3
15625
(5 ) = 15625
5(x )
5
32 = 2
(MathI/MathO)
2
() 532
14
(LineI/LineO)
5() 32
2
2 × 3 = 3 2 = 4.242640687...
(MathI/MathO)
(LineI/LineO)
3 2
23
4.242640687
23
, , : These functions use Gauss-Kronrod methods to perform
numerical integration, approximation of the derivative based on central
difference method, and calculation of the sum of a specific range of f(x).
Input Syntax
(1) When MathI/MathO or MathI/DecimalO is selected
(2) When LineI/LineO or LineI/DecimalO is selected
*2
*3
*1
(1)
∫
𝑎
𝑏
𝑓 𝑥 𝑑𝑥
𝑑
𝑓 𝑥
𝑑𝑥
𝑏
𝑥=𝑎
∑
𝑓 𝑥
𝑥=𝑎
𝑑
𝑓 𝑥 , 𝑎, 𝑡𝑜𝑙
∑ 𝑓 𝑥 , 𝑎, 𝑏
𝑑𝑥
*1 tol specifies tolerance, which becomes 1 × 10-5 when nothing is input
for tol.
*2 tol specifies tolerance, which becomes 1 × 10-10 when nothing is input
for tol.
*3 a and b are integers that can be specified within the range of -1 × 1010
< a ≦ b < 1 × 1010.
Integration and Differential Calculation Precautions
• When using a trigonometric function in f(x), specify “Radian” as the angle
unit.
• A smaller tol value increases precision, but it also increases calculation
time. When specifying tol, use value that is 1 × 10-14 or greater.
• Integration normally requires considerable time to perform.
• Depending on the content of f(x), positive and negative values within the
region of integration, or the region of integration, calculation error that
exceeds the allowable range may be generated, causing the calculator
to display an error message.
• With derivative calculations, 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 a differential
calculation result that approaches zero can cause poor precision or
error.
(2)
∫ 𝑓 𝑥 , 𝑎, 𝑏, 𝑡𝑜𝑙
𝑒
∫ ln 𝑥 𝑑𝑥
1
(x)1(e)
(x)(,)
1(,)(e)
To obtain the derivative at point x = π/2 for the function y = sin(x) (Angle
Unit: Radian)
()(x) …(1)
(MathI/MathO)
(Continued following (1))
(π)2
(LineI/LineO)
(Continued following (1))
(,)(π)2
(MathI/MathO)
(LineI/LineO)
5
∑
𝑥 + 1 = 20
𝑥=1
15
1
1
0
0
20
()(x)115
()(x)1
(,) 1(,) 5
20
Pol, Rec: Pol converts rectangular coordinates to polar coordinates, while
Rec converts polar coordinates to rectangular coordinates.
• Specify the angle unit before
performing calculations.
• The calculation result for r and θ
and for x and y are each
assigned respectively to
variables x and y.
• Calculation result θ is displayed
in the range of -180° < θ ≦ 180°.
To convert rectangular coordinates 2, 2 to polar coordinates (Angle
Unit: Degree)
(MathI/MathO)
(Pol)2(,)2 r=2, θ=45
(MathI/MathO)
(LineI/LineO)
To convert polar coordinates 2, 45° to rectangular coordinates (Angle
Unit: Degree)
(MathI/MathO)
(Rec)2(,) 45 x=1, y=1
x!: Factorial function.
(5 + 3) ! = 40320
40320
53(x!)
Abs: Absolute value function.
|2 − 7| × 2 = 10
(MathI/MathO)
10
(Abs) 272
(LineI/LineO)
10
(Abs) 272
Ran#: Function that generates a pseudo random number in the range of
0.000 to 0.999. The result is displayed as a fraction when MathI/MathO is
selected for Input/Output on the setup menu.
To obtain random three-digit integers
459
1000(Ran#)
(The result differs with each execution.)
RanInt#: Function that generates a pseudo random integer between a
specified start value and end value.
To generate random integers in the range of 1 to 6
2
(RanInt)1(,) 6
(The result differs with each execution.)
nPr, nCr: Permutation (nPr) and combination (nCr) functions.
To determine the number of permutations and combinations possible when
selecting four people from a group of 10
Permutations:
5040
10(nPr) 4
Combinations:
210
10(nCr) 4
Rnd: Using the Rnd function causes decimal fraction values of the
argument to be rounded in accordance with the current Number Format
setting. For example, the internal and displayed result of Rnd(10 ÷ 3) is
3.333 when the Number Format setting is Fix 3. Using the Norm 1 or Norm
2 setting cause the argument to be rounded off at the 11th digit of the
mantissa part.
To perform the following calculations when Fix 3 is selected for the number
of display digits: 10 ÷ 3 × 3 and Rnd(10 ÷ 3) × 3
(MathI/DecimalO)
(SETUP)(Number Format)(Fix)
16
1033
(Rnd) 1033
10.000
9.999
QR Code Function
Your calculator can display QR codes* that can be read by a smart device.
* QR Code is a registered trademark of DENSO WAVE INCORPORATED in
Japan and in other countries.
Important
• The operations in this section assume that the smart device being used
has a QR code reader that can read multiple QR codes installed, and it
can connect to the Internet.
• Reading a QR code displayed by this calculator with a smart device will
cause the smart device to access the CASIO website.
Note: A QR code can be displayed by pressing (QR) while the
setup screen, a menu screen, an error screen, a calculation result screen in
any calculation mode, or a table screen is displayed. For details, visit the
CASIO website (wes.casio.com).
Displaying a QR Code
Example: To display the QR code for a calculation result in the calculator’s
Calculate Mode and read it with a smart device
1. In the Calculate Mode, execute some calculation.
2. Press (QR) to display the QR code.
• The numbers in the lower right corner of the
display shows the current QR code number
and the total number of QR codes. To
display the next QR code, press or .
Note
• A indicator is displayed at the top of the screen while the
calculator is generating a QR code.
• To return to a previous QR code, press or as many times as
required to scroll forward until it appears.
3. Use a smart device to read the QR code on the calculator display.
• For information about how to read a QR code, refer to the user
documentation of the QR code reader you are using.
If you experience difficulty reading a QR code: While the QR code is
displayed use and to adjust the display contrast of the QR code.
This contrast adjustment affects QR code displays only.
Important
• Depending on the smart device and/or QR reader app being used, you
may experience problems reading the QR codes produced by this
calculator.
• When the setup “QR Code” setting is “Version 3”, the calculator modes
that can display QR codes are limited. If you try to display a QR code in
a mode that does not support QR code display, the message “Not
Supported (Version 3)” will appear. However, the QR code produced by
this setting is easier to read with a smart device.
• For more information, visit the CASIO website (wes.casio.com).
To exit the QR code display: Press or (QR).
17
Complex Number Calculations
To perform complex number calculations, first enter the Complex Mode. You
can use either rectangular coordinates (a+bi) or polar coordinates (r∠θ) to
input complex numbers. Complex number calculation results are displayed
in accordance with the Complex setting on the setup menu.
(1 + i)4 + (1 − i)2 = -4 − 2i (Complex: a+bi)*
-4 − 2i
1(i)41(i)
2∠45 = 2 + 2𝒊 (Angle Unit: Degree, Complex: a+bi)
2 + 2𝒊
2(∠) 45
2 + 2𝒊 = 2∠45 (Angle Unit: Degree, Complex: r∠θ)
2∠45
22(i)
* When raising a complex number to an integer power using the syntax (a
+bi)n, the power value can be within the following range: -1 × 1010 < n < 1
× 1010.
Note
• If you are planning to perform input and display of the calculation result
in polar coordinate format, specify the angle unit before starting the
calculation.
• The θ value of the calculation result is displayed in the range of -180°< θ
≦ 180°.
• Display of the calculation result while LineI/LineO or LineI/DecimalO is
selected will show a and bi (or r and θ) on separate lines.
Complex Mode Calculation Examples
To obtain the conjugate complex number of 2 + 3i (Complex: a+bi)
2−3i
(Conjugate) 23(i)
To obtain the absolute value and argument of 1 + i (Angle Unit: Degree)
2
(Abs) 1(i)
45
(Argument) 1(i)
To extract the real part and imaginary part of 2 + 3i
2
(Real Part) 23(i)
3
(Imaginary Part) 23(i)
Using a Command to Specify the Calculation Output
Format
2 + 2𝒊 = 2∠45, 2∠45 = 2 + 2𝒊 (Angle Unit: Degree)
22(i)(r∠θ)
2(∠) 45(a+bi)
2∠45
2 + 2𝒊
Using CALC
CALC lets you input calculation expressions that include one or more
variable, assign values to the variables, and calculate the result. CALC can
be used in the Calculate Mode and Complex Mode.
You can use CALC to save the types of expressions below.
• 2x + 3y, 2Ax + 3By + C, A + Bi, etc.
• x + y : x (x + y), etc.
• y = x2 + x + 3, etc.
Note: During the time from when you press until you exit CALC by
pressing , you should use Linear input procedures for input.
18
To store 3A + B and then substitute the following values to perform the
calculation: A = 5, B = 10
3(A)(B)
510
→
Using SOLVE
SOLVE uses Newton’s method to approximate the solution of equations.
Note that SOLVE can be used in the Calculate Mode only. SOLVE supports
input of equations of the following formats.
Examples: y = x + 5, x = sin(M), xy + C (Treated as xy + C = 0)
Note
• If an equation contains input functions that include an open parenthesis
(such as sin and log), do not omit the closing parenthesis.
• During the time from when you press (SOLVE) until you exit
SOLVE by pressing , you should use Linear input procedures for
input.
To solve x2 + b = 0 for x when b = -2
(x)(B)(=) 0
(SOLVE)
Input an initial value for x (Here,
1
input 1):
Assign -2 to B:
2
Specify the variable you want to solve for
(Here we want to solve for x, so move the
highlighting to x.):
Solve the equation:
(1) Variable solved for
(2) Solution
(3) (Left Side) − (Right Side) result
• Solutions are always displayed in decimal form.
• The closer the (Left Side) − (Right Side) result is to zero, the higher the
accuracy of the solution.
Important
• SOLVE performs convergence a preset number of times. If it cannot find
a solution, it displays a confirmation screen that shows “Continue:[=]”,
asking if you want to continue. Press to continue or to cancel the
SOLVE operation.
• Depending on what you input for the initial value for x (solution variable),
SOLVE may not be able to obtain solutions. If this happens, try changing
the initial value so they are closer to the solution.
• SOLVE may not be able to determine the correct solution, even when one
exists.
19
• SOLVE uses Newton’s method, so even if there are multiple solutions,
only one of them will be returned.
• Due to limitations in Newton’s method, solutions tend to be difficult to
obtain for equations like the following: y = sin x, 𝑦 = 𝑒𝑥, 𝑦 = 𝑥.
Statistical Calculations
Perform the steps below to start a statistical calculation.
1. Press , select the Statistics Mode icon, and then press .
2. On the Select Type screen that appears, select a statistical calculation
type.
To select this type of statistical calculation:
Press this key:
Single-variable (x)
(1-Variable)
Paired-variable (x, y), linear regression
(y=a+bx)
Paired-variable (x, y), quadratic regression
(y=a+bx+cx2)
Paired-variable (x, y), logarithmic regression
(y=a+b･ln(x))
Paired-variable (x, y), e exponential regression
(y=a･e^(bx))
Paired-variable (x, y), ab exponential regression
(y=a･b^x)
Paired-variable (x, y), power regression
(y=a･x^b)
Paired-variable (x, y), inverse regression
(y=a+b/x)
• Performing any of the above key operations displays the Statistics
Editor.
Note: When you want to change the calculation type after entering the
Statistics Mode, perform the key operation (Select Type) to display
the calculation type selection screen.
Inputting Data with Statistics Editor
Statistics Editor displays one, two, or three columns: single-variable (x),
single variable and frequency (x, Freq), paired-variable (x, y), pairedvariable and frequency (x, y, Freq). The number of data rows that can be
input depends on the number of columns: 160 rows for one column, 80
rows for two columns, 53 rows for three columns.
Note
• Use the Freq (frequency) column to input the quantity (frequency) of
identical data items. Display of the Freq column can be turned on
(displayed) or off (not displayed) using the Statistics setting on the setup
menu.
• Pressing the key while the Statistics Editor is on the screen will
display a statistical calculation screen for performing calculations based
on the input data. What you need to do to return to the Statistics Editor
from the statistical calculation screen depends on the calculation type
you selected. Press (Data) if you selected single-variable or
(Data) if you selected paired-variable.
Ex 1: To select logarithmic regression and input the following data: (170,
66), (173, 68), (179, 75)
(Select Type)(y=a+b･ln(x))
20
170173179
666875
Important: All data currently input in the Statistics Editor is deleted
whenever you exit the Statistics Mode, switch between the single-variable
and a paired-variable statistical calculation type, or change the Statistics
setting on the setup menu.
To delete a line: In the Statistics Editor, move the cursor to the line that you
want to delete and then press .
To insert a line: In the Statistics Editor, move the cursor to the location
where you want to insert the line and then perform the following key
operation: (Editor)(Insert Row).
To delete all Statistics Editor contents: In the Statistics Editor, perform
the following key operation: (Editor)(Delete All).
Displaying Statistical Values Based On Input Data
From the Statistics Editor:
(1-Variable Calc or 2-Variable Calc)
From the statistical calculation screen:
(1-Variable Calc or 2-Variable Calc)
Displaying Regression Calculation Results Based On
Input Data (Paired-Variable Data Only)
From the Statistics Editor:
(Regression Calc)
From the statistical calculation screen:
(Regression Calc)
Obtaining Statistical Values from Input Data
You can use the operations in this section to recall statistical values
assigned to variables (σx, Σx2, etc.) based on the data you input with the
Statistics Editor. You can also use the variables in calculations. The
operations in this section are performed on the statistical calculation screen
that appears when you press while the Statistics Editor is displayed.
Supported statistical variables and the keys you should press to recall them
are shown below. For single-variable statistical calculations, the variables
marked with an asterisk (*) are available.
Summation: Σx*, Σx2*, Σy, Σy2, Σxy, Σx3, Σx2y, Σx4
(Summation) to
Number of Items: n* / Mean: −
𝑥 *, −
𝑦 / Population Variance: σ2x*, σ2y /
Population Standard Deviation: σx*, σy / Sample Variance: s2x*, s2y /
Sample Standard Deviation: sx*, sy
(Variable) to , to
Minimum Value: min(x)*, min(y) / Maximum Value: max(x)*, max(y)
When the single-variable statistical calculation is selected:
(Min/Max) ,
When a paired-variable statistical calculation is selected:
(Min/Max) to
First Quartile: Q1* / Median: Med* / Third Quartile: Q3* (For single-variable
statistical calculations only)
(Min/Max) to
21
Regression Coefficients: a, b / Correlation Coefficient: r / Estimated
Values: 𝑥, 𝑦
(Regression) to
Regression Coefficients for Quadratic Regression: a, b, c / Estimated
Values: 𝑥1, 𝑥2, 𝑦
(Regression) to
• 𝑥, 𝑥1, 𝑥2 and 𝑦 are commands of the type that take an argument
immediately before them.
Ex 2: To input the single-variable data x = {1, 2, 2, 3, 3, 3, 4, 4, 5}, using the
Freq column to specify the number of repeats for each items {xn; freqn} =
{1;1, 2;2, 3;3, 4;2, 5;1}, and calculate the mean.
(SETUP)(Statistics)(On)
(Select Type)(1-Variable)
12345
1232
3
(Variable)(−
𝑥 )
Ex 3: To calculate the logarithmic regression correlation coefficients for the
following paired-variable data and determine the regression formula: (x, y) =
(20, 3150), (110, 7310), (200, 8800), (290, 9310). Specify Fix 3 (three
decimal places) for results.
(SETUP)(Statistics)(Off)
(SETUP)(Number Format)(Fix)
(Select Type)(y=a+b･ln(x))
20110200290
3150731088009310
(Regression)(r)
(Regression)(a)
(Regression)(b)
0.998
-3857.984
2357.532
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, x1 and x2, in the case of quadratic
regression) also can be calculated for a value of y in the regression formula.
Ex 4: To determine the estimate value for y when x = 160 in the regression
formula produced by logarithmic regression of the data in Ex 3. Specify Fix
3 for the result. (Perform the following operation after completing the
operations in Ex 3.)
8106.898
160(Regression)(𝑦)
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:
(Norm Dist).
22
P, Q, R: These functions take the
argument t and determine a probability
of standard normal distribution as
illustrated nearby.
t: This function is preceded by the argument x. It calculates the standard
variate for data value x using the mean value (−
𝑥 ) and population standard
deviation (σx) of data input with Statistics Editor.
𝑥−−
𝑥
x t =
𝜎𝑥
Ex 5: For the single variable data in Ex 2, to determine the normalized
variate when x = 2, and P(t) at that point.
2(Norm Dist)(t)
(Norm Dist)(P()
Base-n Calculations
When you want to perform calculations using decimal, hexadecimal, binary,
and/or octal values, enter the Base-N Mode. After entering the Base-N
Mode, press one of the following keys to switch number modes: (DEC)
for decimal, (HEX) for hexadecimal, (BIN) for binary, or (OCT) for
octal.
To calculate 112 + 12
(BIN)111
Note
• Use the following keys to input the letters A through F for hexadecimal
values: (A), (B), (C), (D), (E), (F).
• In the Base-N Mode, input of fractional (decimal) values and exponents
is not supported. If a calculation result has a fractional part, it is cut off.
• Details about input and output ranges (32 bits) are shown below.
00000000000000000000000000000000 ≦ x ≦
Positive:
01111111111111111111111111111111
Binary
10000000000000000000000000000000 ≦ x ≦
Negative:
11111111111111111111111111111111
Positive:
00000000000 ≦ x ≦ 17777777777
Octal
Negative:
20000000000 ≦ x ≦ 37777777777
-2147483648 ≦ x ≦ 2147483647
Decimal
Positive:
00000000 ≦ x ≦ 7FFFFFFF
Hexadecimal
Negative:
80000000 ≦ x ≦ FFFFFFFF
Specifying the Number Mode of a Particular Input
Value
You can input a special command immediately following a value to specify
the number mode of that value. The special commands are: d (decimal), h
(hexadecimal), b (binary), and o (octal).
To calculate 1010 + 1016 + 102 + 108 and display the result as a decimal
value
(DEC)(d) 10(h) 10
23
(b) 10(o) 10
36
Converting a Calculation Result to another Type of
Value
You can use any one of the following key operations to convert the currently
displayed calculation result to another type of value: (DEC), (HEX),
(BIN), (OCT).
To calculate 1510 × 3710 in the decimal mode, and then convert the result to
hexadecimal
555
(DEC) 1537
0000022B
(HEX)
Logical and Negation Operations
Logical and negation operations are performed by pressing and then
selecting the desired command (and, or, xor, xnor, Not, Neg) from the menu
that appears. All of the examples below are performed in the binary mode
((BIN)).
To determine the logical AND of 10102 and 11002 (10102 and 11002)
0000 0000 0000 0000
1010(and) 1100
0000 0000 0000 1000
To determine the bitwise complement of 10102 (Not(10102))
1111 1111 1111 1111
(Not) 1010
1111 1111 1111 0101
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 values, the
calculator merely adds a minus sign.
Equation Calculations
Perform the steps below to solve an equation in the Equation/Func Mode.
1. Press , select the Equation/Func Mode icon, and then press .
2. Select the type of calculation you want to perform.
To select this calculation
type:
Do this:
Simultaneous linear equations
with two, three, or four
unknowns
Press (Simul Equation), and then
use a number key ( to ) to
specify the number of unknowns.
Quadratic equations, cubic
equations, or quartic equations
Press (Polynomial), and then use
a number key ( to ) to specify
the polynomial degree.
3. Use the Coefficient Editor that appears to input coefficient values.
• To solve 2x2 + x − 3 = 0, for example, press (Polynomial) in
step 2. Use the Coefficient Editor that appears to input
213.
• Pressing will clear all of the coefficients to zero.
4. After all the values are the way you want, press .
24
• This will display a solution. Each press of will display another
solution. Pressing while the final solution is displayed will return to
the Coefficient Editor.
• A message appears to let you know when there is no solution or when
there are infinite solutions. Pressing or will return to the
Coefficient Editor.
• You can assign the currently displayed solution to a variable. While
the solution is displayed, press and then the key that
corresponds to the name of the variable to which you want to assign
it.
• To return to the Coefficient Editor while any solution is displayed,
press .
Note: Solutions that include √ are displayed only when the selected
calculation type is Polynomial.
To change the current equation type setting: Press (Simul
Equation) or (Polynomial), and then press , , or . Changing
the equation type causes the values of all Coefficient Editor coefficients to
change to zero.
Equation/Func Mode Calculation Examples
x + 2y = 3, 2x + 3y = 4
(Simul Equation)
123234
x2 + 2x − 2 = 0
(Polynomial)
(x=)
(y=)
-1
2
(x1=) -1 + 3
122
(x2=) -1 − 3
2
(Displays x-coordinate of local minimum of y = x + 2x − 2.*)
-1
(x=)
2
(Displays y-coordinate of local minimum of y = x + 2x − 2.*)
-3
(y=)
* The x- and y-coordinates of the local minimum (or local maximum) of the
function y = ax2 + bx + c are also displayed, but only when a quadratic
equation is selected for the calculation type.
Matrix Calculations
Use the Matrix Mode to perform calculations involving matrices of up to 4
rows by 4 columns. To perform a matrix calculation, use the special matrix
variables (MatA, MatB, MatC, MatD) as shown in the example below.
2 1
2 -1
×
Example:
1 1
-1 2
1. Press , select the Matrix Mode icon, and then press .
2. Press (MatA)(2 rows)(2 columns).
• This will display the Matrix Editor for
input of the elements of the 2 × 2
matrix you specified for MatA.
3. Input the elements of MatA: 2111.
25
4. Perform the following key operation: (Define
Matrix)(MatB)(2 rows)(2 columns).
5. Input the elements of MatB: 2112.
6. Press to advance to the calculation screen, and perform the
calculation (MatA × MatB): (MatA)(MatB).
• This will display the MatAns (Matrix
Answer Memory) screen with the
calculation results.
Matrix Answer Memory (MatAns)
Whenever the result of a calculation executed in the Matrix Mode is a
matrix, the MatAns screen will appear with the result. The result also will be
assigned to a variable named “MatAns”.
The MatAns variable can be used in calculations as described below.
• To insert the MatAns variable into a calculation, perform the following key
operation: (MatAns).
• Pressing any one of the following keys while the MatAns screen is
displayed will switch automatically to the calculation screen: , ,
, , , , (x3).
Assigning and Editing Matrix Variable Data
To assign new data to a matrix variable
1. Press (Define Matrix), and then, on the menu that appears,
select the matrix variable to which you want to assign data.
2. On the dialog box that appears, use a number key ( to ) to
specify the number of rows.
3. On the next dialog box that appears, use a number key ( to ) to
specify the number of columns.
4. Use the Matrix Editor that appears to input the elements of the matrix.
To edit the elements of a matrix variable
Press (Edit Matrix), and then, on the menu that appears, select the
matrix variable you want to edit.
To copy matrix variable (or MatAns) contents
1. Use the Matrix Editor to display the matrix you want to copy.
• If you want to copy MatAns contents, perform the following to display
the MatAns screen: (MatAns).
2. Press , and then perform one of the following key operations to
specify the copy destination: (MatA), (MatB), (MatC), or
(MatD).
• This will display the Matrix Editor with the contents of the copy
destination.
Matrix Calculation Examples
2 1
1 0 -1
, MatB =
.
1 1
0 -1 1
To obtain the determinant of MatA (Det(MatA))
(Determinant) MatA
To create a 2 × 2 identity matrix and add it to MatA (Identity(2) + MatA)
The following examples use MatA =
(Identity) MatA
Note: You can specify a value from 1 to 4 as the Identity command
argument (number of dimensions).
To obtain the transposition of MatB (Trn(MatB))
26
1
(Transposition) MatB
To invert, square, and cube MatA (MatA-1, MatA2, MatA3)
Note: You cannot use for this input. Use to input “-1”, to specify
squaring, and (x3) to specify cubing.
MatA
MatA
MatA (x3)
To obtain the absolute value of each element of MatB (Abs(MatB))
(Abs) MatB
Creating a Number Table
The Table Mode generates a number table based on one or two functions.
1
Example: To generate a number table for the functions 𝑓 𝑥 = 𝑥2 + and
2
1
g 𝑥 = 𝑥2 − for the range -1 ≦ 𝑥 ≦ 1, incremented in steps of 0.5
2
1. Press , select the Table Mode icon, and then press .
2. Configure settings to generate a number table from two functions.
(SETUP)(Table)(f(x),g(x))
1
3. Input 𝑥2 + .
2
(x)12
4. Input 𝑥2 −
1
.
2
(x)12
5. Press . On the Table Range dialog box that appears, input values for
Start (Default: 1), End (Default: 5), and Step (Default: 1).
110.5
6. Press to generate the number table.
• Press to return to the screen in
step 3.
Tip
• In the number table shown in step 6, you can change the value in the
currently highlighted x cell. Changing the x value causes the f(x) and g(x)
values in the same line to be updated accordingly.
• If there is value in the x cell above the currently highlighted x cell,
pressing or automatically inputs into the highlighted cell the
value equal to the value of the cell above it plus the step value. So also,
27
pressing automatically inputs the value equal to the value of the cell
above less the step value. The f(x) and g(x) values in the same line are
also updated accordingly.
Note
• After pressing in step 4 above, proceeding from step 5 onwards
without inputting anything for g(x) will generate a number table for f(x)
only.
• The maximum number of rows in the generated number table depends
on the setup menu table setting. Up to 45 rows are supported for the
“f(x)” setting, while 30 rows are supported for the “f(x),g(x)” setting.
• The number table generation operation causes the contents of variable x
to be changed.
Important: Functions input in this mode are deleted whenever the Input/
Output settings are changed in the Table Mode.
Vector Calculations
Use the Vector Mode to perform 2-dimensional and 3-dimensional vector
calculations. To perform a vector calculation, use the special vector
variables (VctA, VctB, VctC, VctD) as shown in the example below.
Example: (1, 2) + (3, 4)
1. Press , select the Vector Mode icon, and then press .
2. Press (VctA)(2 dimensions).
• This will display the Vector Editor for
input of the 2-dimensional vector for
VctA.
3. Input the elements of VctA: 12.
4. Perform the following key operation: (Define
Vector)(VctB)(2 dimensions).
5. Input the elements of VctB: 34.
6. Press to advance to the calculation screen, and perform the
calculation (VctA + VctB): (VctA)(VctB).
• This will display the VctAns (Vector
Answer Memory) screen with the
calculation results.
Vector Answer Memory
Whenever the result of a calculation executed in the Vector Mode is a
vector, the VctAns screen will appear with the 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: (VctAns).
• Pressing any one of the following keys while the VctAns screen is
displayed will switch automatically to the calculation screen: , ,
, .
Assigning and Editing Vector Variable Data
To assign new data to a vector variable
1. Press (Define Vector), and then, on the menu that appears,
select the vector variable to which you want to assign data.
2. On the dialog box that appears, press or to specify the vector
dimension.
28
3. Use the Vector Editor that appears to input the elements of the vector.
To edit the elements of a vector variable
Press (Edit Vector), and then, on the menu that appears, select the
vector variable you want to edit.
To copy vector variable (or VctAns) contents
1. Use the Vector Editor to display the vector you want to copy.
• If you want to copy VctAns contents, perform the following to display
the VctAns screen: (VctAns).
2. Press , and then perform one of the following key operations to
specify the copy destination: (VctA), (VctB), (VctC), or
(VctD).
• This will display the Vector Editor with the contents of the copy
destination.
Vector Calculation Examples
The examples below use VctA = (1, 2) and VctB = (3, 4), and VctC = (2, -1,
2).
VctA • VctB (Vector dot product)
VctA (Dot Product) VctB
VctA × VctB (Vector cross product)
VctA VctB
To obtain the absolute values of VctC
(Abs) VctC
To determine the angle formed by VctA and VctB to three decimal places
(Fix 3). (Angle Unit: Degree)
(SETUP)(Number Format)(Fix)
(Angle) VctA (,)
VctB
To normalize VctB
(Unit Vector) VctB
Inequality Calculations
You can use the procedure below to solve a 2nd, 3rd, or 4th degree
inequality.
1. Press , select the Inequality Mode icon, and then press .
2. On the dialog box that appears, use a number key ( to ) to
specify the degree of the inequality.
3. On the menu that appears, use keys through to select the
inequality symbol type and orientation.
4. Use the Coefficient Editor that appears to input coefficient values.
• To solve x2 + 2x − 3 < 0, for example, input the following for the
coefficients (a = 1, b = 2, c = -3): 123.
• Pressing will clear all of the coefficients to zero.
5. After all the values are the way you want, press .
• This will display the solutions.
29
• To return to the Coefficient Editor while the solutions are displayed,
press .
To change the Inequality Type: Pressing (Polynomial) displays a
dialog box that you can use to select an inequality degree. Changing the
degree of an inequality causes the values of all Coefficient Editor
coefficients to become zero.
Inequality Mode Calculation Examples
3x3 + 3x2 − x > 0
(Polynomial)(3rd degree inequality)(ax3+bx2+cx+d>0)
331
Note
• Solutions are displayed as shown in the
screen shot nearby when something
other than MathI/MathO is selected for
the Input/Output setting on the setup
menu.
• “All Real Numbers” appears on the solution screen when the solution of
an inequality is all numbers (such as x2 ≧ 0).
• “No Solution” appears on the solution screen when no solution exists for
an inequality (such as x2 < 0).
Ratio Calculations
The Ratio Mode lets you determine the value of X in the ratio expression A :
B = X : D (or A : B = C : X) when the values of A, B, C and D are known. The
following shows the general procedure for using Ratio.
1. Press , select the Ratio Mode icon, and then press .
2. On the menu that appears, select (A:B=X:D) or (A:B=C:X).
3. On the Coefficient Editor screen that appears, input up to 10 digits for
each of the required values (A, B, C, D).
• To solve 3 : 8 = X : 12 for X, for example, press in step 1, and
then input the following for the coefficients (A = 3, B = 8, D = 12):
3812.
• Pressing will reset all of the coefficients to one.
4. After all the values are the way you want, press .
• This displays the solution (value of X). Pressing again will return
to the Coefficient Editor.
Important: A Math ERROR will occur if you perform a calculation while 0 is
input for a coefficient.
To calculate X in the ratio 1 : 2 = X : 10
(Select Type)(A:B=X:D)
1210
5
(X=)
Changing the Ratio Expression Type
Press (Select Type) and then select the ratio expression type you
want from the menu that appears.
30
Distribution Calculations
You can use the procedures below to perform seven different types of
distribution calculations.
1. Press , select the Distribution Mode icon, and then press .
2. On the menu that appears, select a distribution calculation type.
To select this calculation type:
Press this key:
Normal probability density
(Normal PD)
Normal cumulative distribution
(Normal CD)
Inverse normal cumulative distribution
(Inverse Normal)
Binomial probability
(Binomial PD)
Binomial cumulative distribution
(Binomial CD)
Poisson probability
(Poisson PD)
Poisson cumulative distribution
(Poisson CD)
• If you selected Normal PD, Normal CD, or Inverse Normal as the
calculation type, go to step 4 of this procedure. For any other
calculation type, go to step 3.
3. On the dialog box that appears, select a data (x) input method.
• To input multiple x data items at the same time, press (List). To
input a single data item, press (Variable).
• If you selected (List) above, a list screen will appear at this time so
you can input the x data items.
4. Input values for the variables.
• The variables that require data input depend on the calculation type
you selected in step 2 of this procedure.
5. After inputting values for all of the variables, press .
• This displays the calculation results.
• Pressing while a calculation result is displayed will return to the
variable input screen.
Note
• If you selected something other than “List” in step 3 of this procedure the
calculation result will be stored in Ans memory.
• Distribution calculation accuracy is up to six significant digits.
To change the distribution calculation type: Press (Select Type)
and then select the distribution type you want.
Variables that Accept Input
Distribution calculation variables that accept input values are those below.
Normal PD: x, σ, μ
Normal CD: Lower, Upper, σ, μ
Inverse Normal: Area, σ, μ (Tail setting always left.)
Binomial PD, Binomial CD: x, N, p
Poisson PD, Poisson CD: x, λ
x: data, σ: standard deviation (σ > 0), μ, λ: mean, Lower: lower boundary,
Upper: upper boundary, Area: probability value (0 ≦ Area ≦ 1), N: number
of trials, p: success probability (0 ≦ p ≦ 1)
31
List Screen
You can input up to 45 data samples for each variable. Calculation results
are also displayed on the List Screen.
(1) Distribution calculation type
(2) Value at current cursor position
(3) Data (x)
(4) Calculation results (P)
To edit data: Move the cursor to the cell that contains the data you want to
edit, input the new data, and then press .
To delete data: Move the cursor to the data you want to delete and then
press .
To insert data: Move the cursor to the position where you want to insert the
data, press (Editor)(Insert Row), and then input the data.
To delete all data: Press (Editor)(Delete All).
Distribution Mode Calculation Examples
To calculate the normal probability density when x = 36, σ = 2, μ = 35
1. Perform the key operation below to select Normal PD.
(Select Type)(Normal PD)
• This displays the variable input
screen.
2. Input values for x, σ, and μ. 36235
3. Press .
• This displays the calculation results.
(p=)
0.1760326634
• Pressing again or pressing returns to the variable input
screen in step 1 of this procedure.
Note: You can assign the currently displayed solution to a variable. While
the solution is displayed, press and then the key that corresponds to
the name of the variable to which you want to assign it.
To calculate binomial probability for the data {10, 11, 12, 13} when N = 15
and p = 0.6
1. Perform the key operation below to select Binomial PD.
(Select Type)(Binomial PD)
2. Because you want to input four data (x) values, press (List) here.
• This displays the List Screen.
3. Input a value for x. 10111213
4. After inputting all of the values, press .
• This displays the variable input screen.
5. Input values for N and p. 150.6
6. Press .
• This returns to the List Screen, with
the calculation result for each x value
shown in the P column.
Pressing returns to the variable input screen in step 4 of this procedure.
Note
• Changing any x value in step 6 of the above procedure will clear all
calculation results and return to step 2. In this case, all of the other x
values (except for the one you changed), and the values assigned to
32
variables N and p remain the same. This means you can repeat a
calculation changing only one specific value.
• On the List Screen, you can assign the value in a cell to a variable. Move
the cell cursor to cell that contains the value you want to assign, press
, and then press the key that corresponds to the desired variable
name.
• An error message appears if the input value is outside the allowable
range. “ERROR” will appear in the P column of the Result Screen when
the value input for the corresponding data is outside the allowable range.
Using Spreadsheet
To perform the operations in this section, first enter the Spreadsheet Mode.
The Spreadsheet Mode makes it possible to
perform calculations using a 45-row × 5column (cell A1 to E45) spreadsheet.
(1) Row numbers (1 to 45)
(2) Column letters (A to E)
(3) Cell cursor: Indicates the currently
selected cell.
(4) Edit box: Shows the contents of the cell
where the cell cursor is currently located.
Important: Any time you exit the Spreadsheet Mode, turn off the calculator
or press the key, every input into the spreadsheet is cleared.
Inputting and Editing Cell Contents
You can input a constant or a formula into each cell.
Constants: A constant is something whose value is fixed as soon as you
finalize its input. A constant can be either a numeric value, or a calculation
formula (such as 7+3, sin30, A1×2, etc.) that does not have an equal sign
(=) in front of it.
Formula: A formula that starts out with an equal sign (=), such as =A1×2, is
executed as it is written.
Note: Up to 10 bytes can be input into each cell in the case of a constant.
In the case of a formula, you can input up to 49 bytes into each cell.
Inputting a formula into a cell requires 11 bytes in addition to the number of
bytes for the actual formula data.
To display the remaining input capacity: Press (Free Space).
To input a constant and/or formula into a cell
Ex 1: Into cells A1, A2, and A3, input constants 7×5, 7×6, and A2+7
respectively. And then, input the following formula into cell B1: =A1+7.
1. Move the cell cursor to cell A1.
2. Perform the key operation below.
7576(A)7
3. Move the cell cursor to cell B1, and then perform the key operation
below.
(=)(A)7
Note: You can specify whether a formula in the edit box should be
displayed as it is or as its calculation result value.
33
To edit existing cell data
1. Move the cell cursor to the cell whose contents you want to edit, and
then press (Edit Cell).
• Cell contents in the edit box will change from align right to align left. A
text cursor will appear in the edit box so you can edit its contents.
2. Use and to move the cursor around the contents of the cell, and
edit them as required.
3. To finalize and apply your edits, press .
To input a cell reference name using the Grab command
The Grab command can be used in place of manual reference name (such
as A1) input using a key operation to select and input a cell you want to
reference.
Ex 2: Continuing from Ex 1, input the following formula into cell B2: =A2+7.
1. Move the cell cursor to cell B2.
2. Perform the key operation below.
(=)(Grab)
7
Cell Relative and Absolute References
There are two types of cell reference: relative and absolute.
Relative cell reference: The cell reference (A1) in a formula like =A1+7 is a
relative reference, which means that it changes depending on the cell
where the formula is located. If the formula =A1+7 is originally located in
cell B1, for example, copying and then pasting to cell C3 will result in
=B3+7 being input into cell C3. Since the copy and paste operation moves
the formula one column (B to C) and two rows (1 to 3) causes the A1
relative cell reference in the formula to change to B3. If the result of a copy
and paste operation causes a relative cell reference name to change to
something that is outside the range of the spreadsheet cells, the applicable
column letter and/or row number will be replaced by a question mark (?),
and “ERROR” will be displayed as the cell’s data.
Absolute cell reference: If you want the row or the column, or both the row
and the column parts of a cell reference name to remain the same no matter
where you paste them, you need to create an absolute cell reference name.
To create an absolute cell reference put a dollar sign () in front of the
column name and/or row number. You can use one of three different
absolute cell references: absolute column with relative row (A1), relative
column with absolute row (A1), or absolute row and column (A1).
To input the absolute cell reference symbol ()
While inputting a formula into a cell, press ().
To cut and paste spreadsheet data
1. Move the cursor to the cell whose data you want to cut and then press
(Cut & Paste).
• This enters paste standby. To cancel paste standby, press .
2. Move the cursor to the cell into which you want to paste the data you
just cut, and then press .
34
• Pasting data simultaneously deletes the data from the cell where you
performed the cut operation, and automatically cancels paste
standby.
Note: In the case of a cut and paste operation, cell references do not
change when pasted, regardless of whether they are relative or absolute.
To copy and paste spreadsheet data
1. Move the cursor to the cell whose data you want to copy and then press
(Copy & Paste).
• This enters paste standby. To cancel paste standby, press .
2. Move the cursor to the cell into which you want to paste the data you
just copied, and then press .
• Paste standby remains enabled until you press , so you can paste
the copied data to other cells, if you want.
Note: When you copy the contents of a cell that contains a formula with a
relative reference, the relative reference will change in accordance with the
location of the cell where the contents are pasted.
To delete input data from a specific cell
Move the cell cursor to the cell whose contents you want to delete and then
press .
To delete the contents of all the cells in a spreadsheet
Press (Delete All).
Using Variables (A, B, C, D, E, F, M, x, y)
You can use to assign the value of a cell to a variable. You can also use
(RECALL) to input the value assigned to a variable into a cell.
Using Spreadsheet Mode Special Commands
In the Spreadsheet Mode, the commands below can be used inside
formulas or constants. These command are on the menu that appears when
you press .
Min(
Returns the minimum of the values in a specified range of cells.
Syntax: Min(start cell:end cell)
Max(
Returns the maximum of the values in a specified range of cells.
Syntax: Max(start cell:end cell)
Mean(
Returns the mean of the values in a specified range of cells.
Syntax: Mean(start cell:end cell)
Sum(
Returns the sum of the values in a specified range of cells.
Syntax: Sum(start cell:end cell)
Ex 3: Continuing from Ex 1, input the formula =Sum(A1:A3), which
calculates the sum of cells A1, A2, and A3, into cell A4.
1. Move the cell cursor to cell A4.
2. Input =Sum(A1:A3).
(=)(Sum)
(A)(:)(A)
3. Press .
35
Batch Inputting the Same Formula or Constant into
Multiple Cells
You can use the procedures in this section to input the same formula or
constant into a specific series of cells. Use the Fill Formula command to
batch input a formula, or Fill Value to batch input a constant.
Note: If the input formula or constant includes a relative reference, the
relative reference will be input in accordance with the upper left cell of the
specified range. If the input formula or constant includes an absolute
reference, the absolute reference will be input into all of the cells in the
specified range.
To batch input the same formula into a series of cells
Ex 4: Continuing from Ex 1, batch input into cells B1, B2, and B3 a formula
that doubles the value of the cell to the left and then subtracts 3.
1. Move the cell cursor to cell B1.
2. Press (Fill Formula).
• This displays a Fill Formula dialog box.
3. In the “Form” row, input the formula “=2A1–3”: 2(A)3.
• Input of the equals symbol (=) at the beginning is not required.
4. Move the highlighting to the “Range” line and specify B1:B3 as the
range of the batch input.
5. To apply the input, press .
• This inputs =2A1–3 into cell B1,
=2A2–3 into cell B2, and =2A3–3
into cell B3.
To batch input the same constant into a series of cells
Ex 5: Continuing from Ex 4, batch input into cells C1, C2, and C3 the values
that are triple those of the cells to the left.
1. Move the cell cursor to cell C1.
2. Press (Fill Value).
• This displays a Fill Value dialog box.
3. In the “Value” line, input the constant B1×3: (B)3.
4. Move the highlighting to the “Range” line and specify C1:C3 as the
range of the batch input.
5. To apply the input, press .
• This inputs the values of each
calculation result into cells C1, C2,
and C3.
Recalculation
Auto Calc is a setup item. Depending on the content of the spreadsheet,
auto recalculation can take a long time to complete. When Auto Calc is
disabled (Off), you need to execute recalculation manually as required.
To perform recalculation manually: Press (Recalculate).
36
Scientific Constants
Your calculator comes with 47 built-in scientific constants.
Example: To input the scientific constant c0 (speed of light in a vacuum),
and display its value
1. Press (CONST) to display a
menu of scientific constant categories.
2. Press (Universal) to display a menu
of scientific constants in the Universal
category.
3. Press (c0).
299792458
• The values are based on CODATA (2010) recommended values.
Metric Conversion
You can use the metric conversion commands to convert from one unit of
measurement to another.
Example: To convert 5 cm into inches (LineI/LineO)
1. Input the value to be converted and display the metric conversion
menu.
5(CONV)
2. On the conversion category menu that appears, select “Length”.
(Length)
3. Select the centimeters-to-inches conversion command and then
perform the conversion.
(cmin)
Note
• Conversion formula data is based on the “NIST Special Publication 811
(2008)”.
• The Jcal command performs conversion for values at a temperature of
15°C.
Errors
The calculator will display an error message whenever an error occurs for
any reason during a calculation. 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.
To clear the error message: While an error message is displayed, press
to return to the calculation screen. Note that this also clears the
calculation that contained the error.
37
Error Messages
Math ERROR
• 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).
→ 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
• 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.
→ 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
• There is a problem with the format of the calculation you are performing.
Argument ERROR
• There is a problem with the argument of the calculation you are
performing.
Dimension ERROR (Matrix and Vector Modes only)
• The matrix or vector you are trying to use in a calculation was input
without specifying its dimension.
• You are trying to perform a calculation with matrices or vectors whose
dimensions do not allow that type of calculation.
→ 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)
• An attempt to execute SOLVE for an expression input without any
variable included.
→ Input an expression that includes a variable.
Cannot Solve (SOLVE feature only)
• The calculator could not obtain a solution.
→ Check for errors in the equation that you input.
→ Input a value for the solution variable that is close to the expected
solution and try again.
Range ERROR
• An attempt to generate a number table in the Table Mode whose
conditions cause it to exceed the maximum number of allowable rows.
• During batch input in the Spreadsheet Mode, input for Range is outside
the allowable range or is a cell name that does not exist.
→ Narrow the table calculation range by changing the Start, End, and
Step values, and try again.
→ For Range, input a cell name within the range of A1 through E45, using
the syntax: “A1:A1”.
Time Out
38
• The current differential or integration calculation ends without the ending
condition being fulfilled.
→ Try increasing the tol value. Note that this also decreases solution
precision.
Circular ERROR (Spreadsheet Mode only)
• There is a circular reference (such as “=A1” in cell A1) in the
spreadsheet.
→ Change cell contents to remove the circular references.
Memory ERROR (Spreadsheet Mode only)
• You are attempting to input data that exceeds the allowable input
capacity (1,700 bytes).
• You are attempting to input data that results in a chain of consecutive cell
references (such as cell A2 referenced from cell A1, cell A3 referenced
from cell A2…, etc.) This type of input always causes this error to be
generated, even if memory capacity (1,700 bytes) is not exceeded.
• Memory capacity was exceeded because a formula that includes a
relative cell reference was copied, or because of batch input of formulas
that use relative cell references.
→ Delete unneeded data and input data again.
→ Minimize input that results in a chain of consecutive cell references.
→ Shorten the formula being copied or the formulas being batch input.
Before Assuming Malfunction of the
Calculator...
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 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.
4. Return the calculation mode and setup (except for the Contrast setting)
to their initial default settings by performing the following operation:
(RESET)(Setup Data)(Yes).
Replacing the Battery
A low battery is indicated by a dim display, even if contrast is adjusted, or
by failure of figures to appear on the display immediately after you turn 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.
39
1. Press (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. As shown in the illustration,
remove the cover, remove the
battery, and then load a new
battery with its plus (+) and
minus (−) ends facing
correctly.
3. Replace the cover.
4. Initialize the calculator: (RESET)(Initialize All)(Yes).
• Do not skip the above step!
Technical Information
Calculation Range and Precision
Calculation Range
±1 × 10-99 to ±9.999999999 × 1099 or 0
Number of Digits for
Internal Calculation
15 digits
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
sinx
cosx
Input Range
Degree
0 ≦ |x| < 9 × 109
Radian
0 ≦ |x| < 157079632.7
Gradian 0 ≦ |x| < 1 × 1010
tanx
Degree
Same as sinx, except when |x| = (2n−1) × 90.
Radian
Same as sinx, except when |x| = (2n−1) × π/2.
Gradian Same as sinx, except when |x| = (2n−1) × 100.
sin-1x, cos-1x
0 ≦ |x| ≦ 1
tan-1x
0 ≦ |x| ≦ 9.999999999 × 1099
sinhx, coshx
0 ≦ |x| ≦ 230.2585092
sinh-1x
0 ≦ |x| ≦ 4.999999999 × 1099
cosh-1x
1 ≦ x ≦ 4.999999999 × 1099
40
tanhx
0 ≦ |x| ≦ 9.999999999 × 1099
tanh-1x
0 ≦ |x| ≦ 9.999999999 × 10-1
logx, lnx
0 < x ≦ 9.999999999 × 1099
10x
-9.999999999 × 1099 ≦ x ≦ 99.99999999
ex
-9.999999999 × 1099 ≦ x ≦ 230.2585092
𝑥
0 ≦ x < 1 × 10100
x2
|x| < 1 × 1050
x-1
|x| < 1 × 10100 ; x ≠ 0
3
𝑥
|x| < 1 × 10100
x!
0 ≦ x ≦ 69 (x is an integer)
nPr
0 ≦ n < 1 × 1010, 0 ≦ r ≦ n (n, r are integers)
1 ≦ {n!/(n−r)!} < 1 × 10100
nCr
0 ≦ n < 1 × 1010, 0 ≦ r ≦ n (n, r are integers)
1 ≦ n!/r! < 1 × 10100 or 1 ≦ n!/(n−r)! < 1 × 10100
Pol(x, y)
|x|, |y| ≦ 9.999999999 × 1099
𝑥2 + 𝑦2 ≦ 9.999999999 × 1099
Rec(r, θ)
0 ≦ r ≦ 9.999999999 × 1099
θ: Same as sinx
°’ ”
|a|, b, c < 1 × 10100 ; 0 ≦ b, c
The display seconds value is subject to an error of ±1 at
the second decimal place.
°’ ”
|x| < 1 × 10100
Decimal ↔ Sexagesimal Conversions
0°0’0” ≦ |x| ≦ 9999999°59’59”
xy
x > 0: -1 × 10100 < ylogx < 100
x = 0: y > 0
𝑚
(m, n are integers)
x < 0: y = n,
2𝑛 + 1
However: -1 × 10100 < ylog |x| < 100
𝑥
𝑦
y > 0: x ≠ 0, -1 × 10100 < 1/x logy < 100
y = 0: x > 0
2𝑛 + 1
(m ≠ 0; m, n are integers)
y < 0: x = 2n+1,
𝑚
However: -1 × 10100 < 1/x log |y| < 100
a b/c
Total of integer, numerator, and denominator must be 10
digits or less (including separator symbol).
RanInt#(a, b)
a < b; |a|, |b| < 1 × 1010; b − a < 1 × 1010
41
• Precision is basically the same as that described under “Calculation
Range and Precision”, above.
• xy, 𝑥 𝑦, 3 , x!, 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 π form when
MathI/MathO is selected for Input/Output on the setup menu is |x| < 106.
Note, however, that internal calculation error can make it impossible to
display some calculation results in π form. It also can cause calculation
results that should be in decimal form to appear in π form.
Specifications
Power Requirements:
fx-570EX: AAA-size battery R03 (UM-4) × 1
fx-991EX: Built-in solar cell; button battery LR44 × 1
Approximate Battery Life:
2 years (based on one hour of operation per day)
Power Consumption: 0.0006 W (fx-570EX)
Operating Temperature: 0°C to 40°C (32°F to 104°F)
Dimensions:
fx-570EX: 13.8 (H) × 77 (W) × 165.5 (D) mm
1
/2” (H) × 3” (W) × 61/2” (D)
fx-991EX: 11.1 (H) × 77 (W) × 165.5 (D) mm
3
/8” (H) × 3” (W) × 61/2” (D)
Approximate Weight:
fx-570EX: 100 g (3.5 oz) including the battery
fx-991EX: 90 g (3.2 oz) including the battery
■■ Frequently Asked Questions ■■
How can I change a fraction form result produced by a division
operation to decimal form?
→ While a fraction calculation result is displayed, press . To have
calculation results initially appear as decimal values, change the setup
menu Input/Output setting to MathI/DecimalO.
What is the difference between Ans memory, independent memory, and
variable memory?
→ Each of these types of memory acts like “containers” for temporary
storage of a single value.
Ans Memory: Stores the result of the last calculation performed. Use
this memory to carry the result of one calculation on to the next.
Independent Memory: Use this memory to totalize the results of
multiple calculations.
Variables: This memory is helpful when you need to uses the same
value multiple times in one or more calculations.
What is the key operation to take me from the Statistics Mode or Table
Mode to a mode where I can perform arithmetic calculations?
→ Press (Calculate).
How can I return the calculator to its initial default settings?
→ Perform the following operation to initialize calculator settings (except
the Contrast setting): (RESET)(Setup Data)(Yes).
42
When I execute a function calculation, why do I get a calculation result
that is completely different from older CASIO calculator models?
→ With a Natural Textbook Display model, the argument of a function that
uses parentheses must be followed by a closing parenthesis. Failing to
press after the argument to close the parentheses may cause
unwanted values or expressions to be included as part of the
argument.
Example: (sin 30) + 15 (Angle Unit: Degree)
Older (S-V.P.A.M.) Model:
15.5
3015
Natural Textbook Display Model:
(LineI/LineO)
15.5
3015
Failure to press here as shown below will result in calculation of sin
45.
3015 0.7071067812
43
Reference Sheet
Scientific Constants (CONST)
(Universal)
:
: μ0
: lP
: c0
: Z0
: tP
: μB
: G0
: e
: KJ
: me
: mμ
: re
: λCp
: μp
: μμ
: mn
: a0
: λC
: λCn
: μe
: mτ
: u
: k
: c1
: F
: Vm
: c2
(Adopted Values)
: g
: KJ-90
: atm
(Other)
: t
(Electromagnetic)
(Atomic&Nuclear)
(Physico-Chem)
: h
: ε0
: G
: μN
: Φ0
: RK
: mp
: α
: γp
: R∞
: μn
: NA
: R
: σ
: RK-90
Metric Conversion (CONV)
(Length)
(Area)
(Volume)
(Mass)
(Velocity)
(Pressure)
(Energy)
(Power)
(Temperature)
: incm
: ftm
: ydm
: milekm
: n milem
: pckm
: acrem2
: gal(US)L
: gal(UK)L
: ozg
: lbkg
: km/hm/s
: atmPa
: mmHgPa
: kgf/cm2Pa
: lbf/in2kPa
: kgf・mJ
: Jcal
: hpkW
: °F°C
44
: cmin
: mft
: myd
: kmmile
: mn mile
: kmpc
: m2acre
: Lgal(US)
: Lgal(UK)
: goz
: kglb
: m/skm/h
: Paatm
: PammHg
: Pakgf/cm2
: kPalbf/in2
: Jkgf・m
: calJ
: kWhp
: °C°F
Manufacturer:
CASIO COMPUTER CO., LTD.
6-2, Hon-machi 1-chome
Shibuya-ku, Tokyo 151-8543, Japan
Responsible within the European Union:
CASIO EUROPE GmbH
Casio-Platz 1
22848 Norderstedt, Germany
This mark applies in EU countries only.
SA1412-A
Printed in China
© 2015 CASIO COMPUTER CO., LTD.
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