fx-100MS fx-115MS (fx-912MS)

Users Guide 2

(Additional Functions)

kfx-912MS owners

Please be sure to read the important notice of this manual.
http://world.casio.com/edu_e/

Important!

Please keep your manual and all information handy for future reference.
CASIO ELECTRONICS CO., LTD. Unit 6, 1000 North Circular Road, London NW2 7JD, U.K.

Contents

Before getting started.. 2

kModes... 2

Mathematical Expression Calculations and Editing Functions.. 3
kReplay Copy... 3 kCALC Memory.. 4 kSOLVE Function.. 4
Scientific Function Calculations. 5
kInputting Engineering Symbols.. 5
Complex Number Calculations. 7
kAbsolute Value and Argument Calculation. 8 kRectangular Form Polar Form Display. 8 kConjugate of a Complex Number. 9
Base-n Calculations.. 9 Statistical Calculations.. 11

Normal Distribution.. 11

Differential Calculations.. 12 Integration Calculations.. 13 Power Supply... 14 Specifications.. 16
See the fx-95MS/fx-100MS/fx-115MS/fx-570MS/fx991MS Users Guide for details about the following items. Removing and Replacing the Calculators Cover/ Safety Precautions/ Handling Precautions/ Two-line Display/ Before getting started. (except for Modes)/ Basic Calculations/ Memory Calculations/ Scientific Function Calculations/ Equation Calculations/ Statistical Calculations/ Technical Information E-1

Before getting started.

k Modes
Before starting a calculation, you must first enter the correct mode as indicated in the table below. The following table shows the modes and required operations for the fx-100MS and fx-115MS.
fx-100MS and fx-115MS Modes
To perform this type of calculation: Basic arithmetic calculations Complex number calculations Standard deviation Regression calculations Base-n calculations Solution of equations Perform this key operation: To enter this mode: COMP CMPLX SD REG BASE EQN

F1 F2 FF1 FF2 FF3 FFF1

Pressing the F key more than three times displays additional setup screens. Setup screens are described where they are actually used to change the calculator setup. In this manual, the name of the mode you need to enter in order to perform the calculations being described is indicated in the main title of each section.

Example:

Complex Number Calculations
To return the calculation mode and setup to the initial defaults shown below, press A B 2(Mode) =. Calculation Mode: Angle Unit: Exponential Display Format: Complex Number Display Format: Fraction Display Format: Decimal Point Character: COMP Deg Norm 1, Eng OFF a+b i a b/c Dot
Mode indicators appear in the upper part of the display, except for the BASE indicators, which appear in the exponent part of the display. Engineering symbols are automatically turned off while the calculator is the BASE Mode. You cannot make changes to the angle unit or other display format (Disp) settings while the calculator is in the BASE Mode. The COMP, CMPLX, SD, and REG modes can be used in combination with the angle unit settings. Be sure to check the current calculation mode (SD, REG, COMP, CMPLX) and angle unit setting (Deg, Rad, Gra) before beginning a calculation.

Mathematical Expression Calculations and Editing Functions
Use the F key to enter the COMP Mode when you want to perform mathematical expression calculations or edit expressions. COMP.. F 1

k Replay Copy

Replay copy lets you recall multiple expressions from replay so they are connected as a multi-statement on the screen. Example: Replay memory contents: 1+1 2+2 3+3 4+4 5+5 6+6 Multi-statement: 4 + 4:5 + 5:6 + 6 Use [ and ] to display the expression 4 + 4. Press A [(COPY). E-3
You can also edit expressions on the display and perform other multi-statement operations. For more details about using multi-statements, see Multi-statements in the separate Users Guide. Only the expressions in replay memory starting from the currently displayed expression and continuing to the last expression are copied. Anything before the displayed expression is not copied.

k CALC Memory

CALC memory lets you temporarily store a mathematical expression that you need to perform a number of times using different values. Once you store an expression, you can recall it, input values for its variables, and calculate a result quickly and easily. You can store a single mathematical expression, with up to 79 steps. Note that CALC memory can be used in the COMP Mode and CMPLX Mode only. The variable input screen shows the values currently assigned to the variables. Example: Calculate the result for Y = X2 + 3X 12 when X = 7 (Result: 58 ), and when X = 8 (Result: 76 ).

(Input the function.)

p y p u p x K + 3 p x , 12 C (Input 7 for X? prompt.) 7= (Input 8 for X? prompt.) C8=

(Store the expression.)

Note that the expression you store is cleared whenever you start another operation, change to another mode, or turn off the calculator.

k SOLVE Function

The SOLVE function lets you solve an expression using variable values you want, without the need to transform or simply the expression. Example: C is the time it would take for an object thrown straight up with initial velocity A to reach height B. E-4
Use the formula below to calculate initial velocity A for a height of B = 14 meters and a time of C = 2 seconds. Gravitational acceleration is D = 9.8 m/s2. (Result: A = 16.8 ) B AC 1 DC 2 2

(B?) (A?) (C?) (D?) (A?)

p2pup1-pk, R1\2T-ph-pkK AI 14 = ] 2= 9l8= [[ AI
The SOLVE function finds approximations based on Newtons method, which means that error can occur. Certain expressions or initial values may result in error without convergence of results. If an expression does not include an equals sign (=), the SOLVE function produces a solution for expression = 0.
Scientific Function Calculations
Use the F key to enter the COMP Mode when you want to perform basic arithmetic calculations. COMP.. F 1
k Inputting Engineering Symbols

COMP EQN CMPLX

Turning on engineering symbols makes it possible for you to use engineering symbols inside your calculations. E-5
To turn engineering symbols on and off, press the F key a number of times until you reach the setup screen shown below.
Press 1. On the engineering symbol setting screen that appears, press the number key ( 1 or 2) that corresponds to the setting you want to use.
1(Eng ON): Engineering symbols on (indicated by

Eng on the display)

2(Eng OFF): Engineering symbols off (no Eng
indicator) The following are the nine symbols that can be used when engineering symbols are turned on. To input this symbol: Perform this key operation: Ak k (kilo) M (Mega) AM G (Giga) Ag T (Tera) At m (milli) Am (micro) AN n (nano) An p (pico) Ap f (femto) Af Unit 1015
For displayed values, the calculator selects the engineering symbol that makes the numeric part of the value fall within the range of 1 to 1000. Engineering symbols cannot be used when inputting fractions. Example: = 0.9 m (milli)

F.. 1(Disp) 1

9 \ 10 =
When engineering symbols are turned on, even standard (non-engineering) calculation results are displayed using engineering symbols.
Use the F key to enter the CMPLX Mode when you want to perform calculations that include complex numbers. CMPLX... F 2 The current angle unit setting (Deg, Rad, Gra) affects CMPLX Mode calculations. You can store an expression in CALC memory while in the CMPLX Mode. Note that you can use variables A, B, C, and M only in the CMPLX Mode. Variables D, E, F, X, and Y are used by the calculator, which frequently changes their values. You should not use these variables in your expressions. The indicator RI in the upper right corner of a calculation result display indicates a complex number result. Press A r to toggle the display between the real part and imaginary part of the result. You can use the replay function in the CMPLX Mode. Since complex numbers are stored in replay memory in the CMPLX Mode, however, more memory than normal is used up. Example: (23 i)(45 i) 68 i

(Real part 6) (Imaginary part 8 i)

2+3i+4+5i=

k Absolute Value and Argument Calculation
Supposing the imaginary number expressed by the rectangular form z = a + bi is represented as a point in the Gaussian plane, you can determine the absolute value (r) and argument ( ) of the complex number. The polar form is r. Example 1: To determine the absolute value (r) and argument () of 3+4i (Angle unit: Deg) (r = 5, = 53.13010235)

Imaginary axis

Real axis

(r 5 ) ( 53.13010235 )

AAR3+4iT= AaR3+4iT=
The complex number can also be input using the polar form r. Example 2: 1 i (Angle unit: Deg)

L 2 A Q 45 = Ar

k Rectangular Form Polar Form Display
You can use the operation described below to convert a rectangular form complex number to its polar form, and a polar form complex number to its rectangular form. Press A r to toggle the display between the absolute value (r) and argument ( ). Example: 1 i 1.(Angle unit: Deg)
1+iAY=Ar L 2 A Q 45 A Z = A r
You select rectangular form (a+bi) or polar form (r ) for display of complex number calculation results. F. 1(Disp) r
1(a+bi):Rectangular form 2(r): Polar form (indicated by r on the display)
k Conjugate of a Complex Number
For any complex number z where z = a+bi, its conjugate (z) is z = a bi. Example: To determine the conjugate of the complex number 1.23 + 2.34i (Result: 1.23 2.34 i )
A S R 1 l 23 + 2 l 34 i T = Ar

Base-n Calculations

Use the F key to enter the BASE Mode when you want to perform calculations using Base-n values. BASE... F F 3 In addition to decimal values, calculations can be performed using binary, octal and hexadecimal values. You can specify the default number system to be applied to all input and displayed values, and the number system for individual values as you input them. You cannot use scientific functions in binary, octal, decimal, and hexadecimal calculations. You cannot input values that include decimal part and an exponent. If you input a value that includes a decimal part, the unit automatically cuts off the decimal part. Negative binary, octal, and hexadecimal values are produced by taking the twos complement.
You can use the following logical operators between values in Base-n calculations: and (logical product), or (logical sum), xor (exclusive or), xnor (exclusive nor), Not (bitwise complement), and Neg (negation). The following are the allowable ranges for each of the available number systems. 1000000000 x x 0111111111 Octal 4000000000 x x 3777777777 Decimal 2147483648 x 2147483647 Hexadecimal 80000000 x FFFFFFFF 0x 7FFFFFFF Binary Example 1: To perform the following calculation and produce a binary result: 1100012 Binary mode:

10111 + 11010 =

Example 2: To perform the following calculation and produce an octal result: 76548

1210 5168

Octal mode:
l l l 4 (o) 7654 \ l l l 1 (d) 12 =
Example 3: To perform the following calculation and produce a hexadecimal and a decimal result: 12016 or 11012 12dHexadecimal mode:
120 l 2 (or) l l l 3 (b) 1101 = Decimal mode: K
Example 4: To convert the value 2210 to its binary, octal, and hexadecimal equivalents. (101102 , 268 , 1616 ) Binary mode:

tb o h

0. 10110.

l l l 1(d) 22 =

Octal mode: Hexadecimal mode:
Example 5: To convert the value 51310 to its binary equivalent. Binary mode:

Ma t h ERROR

l l l 1(d) 513 =
You may not be able to convert a value from a number system whose calculation range is greater than the calculation range of the resulting number system. The message Math ERROR indicates that the result has too many digits (overflow).

Statistical Calculations

Normal Distribution
Use the F key to enter the SD Mode when you want to perform a calculation involving normal distribution. SD... F F 1 Press A D, which produces the screen shown below.

P ( Q ( R ( t

Input a value from 1 to 4 to select the probability distribution calculation you want to perform.

P(t) Q(t) R(t)

Example: To determine the normalized variate ( t) for x = 53 and normal probability distribution P(t) for the following data: 55, 54, 51, 55, 53, 53, 54, 52 (t = 0.284747398, P(t) = 0.38974 ) 55 S 54 S 51 S 55 S 53 S S 54 S 52 S 53 A D 4(t) = A D 1( P( ) D 0.28 F =
Differential Calculations
The procedure described below obtains the derivative of a function. Use the F key to enter the COMP Mode when you want to perform a calculation involving differentials. COMP.. F 1 Three inputs are required for the differential expression: the function of variable x, the point (a) at which the differential coefficient is calculated, and the change in x (x). A J expression P a P x T Example: To determine the derivative at point x = 2 for the function y = 3x2 5x + 2, when the increase or decrease in x is x = (Result: 7 )

AJ3pxK,5px+2P2P 2eD4T=

You can omit input of x, if you want. The calculator automatically substitutes an appropriate value for x if you do not input one. Discontinuous points and extreme changes in the value of x can cause inaccurate results and errors.

Integration Calculations

The procedure described below obtains the definite integral of a function. Use the F key to enter the COMP Mode when you want to perform integration calculations. COMP.. F 1 The following four inputs are required for integration calculations: a function with the variable x; a and b, which define the integration range of the definite integral; and n, which is the number of partitions (equivalent to N = 2n) for integration using Simpsons rule.
d expression P a P b P n F
Example: (Number of partitions n = 6)
15 (2x2 + 3x + 8) dx = 150.6666667

d2pxK+3px+ 8P1P5P6T=

You can specify an integer in the range of 1 to 9 as the number of partitions, or you can skip input of the number of partitions entirely, if you want. Internal integration calculations may take considerable time to complete. Display contents are cleared while an integration calculation is being performed internally.

Power Supply

The type of battery you should use depends on the model number of your calculator.

fx-115MS

The TWO WAY POWER system actually has two power supplies: a solar cell and a G13 Type (LR44) button battery. 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

Either of the following symptoms indicates battery power is low, and that the battery should be replaced. Display figures are dim and difficult to read in areas where there is little light available. Nothing appears on the display when you press the 5 key.

u To replace the battery

1 Remove the five screws that Screw hold the back cover in place and then remove the back cover. 2 Remove the old battery. 3 Wipe off the sides of new battery with a dry, soft cloth. Load it into the unit with the positive k side facing up (so you can see it). 4 Replace the back cover and secure it in place with the five screws. 5 Press 5 to turn power on. Be sure not to skip this step.

fx-100MS

This calculator is powered by a single AA-size 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 become dim.

To replace the battery

1 Press A i to turn power off. Screw 2 Remove the six screws that hold the back cover in place and then remove the back cover. 3 Remove the old battery. 4 Load a new battery into the unit with its positive k and negative l ends facing correctly. 5 Replace the back cover and secure it in place with the six screws. 6 Press 5 to turn power on.

Auto Power Off

Calculator power automatically turns off if you do not perform any operation for about six minutes. When this happens, press 5 to turn power back on.

Specifications

Power Supply: fx-100MS: Single AA-size battery (R6P(SUM-3)) fx-115MS: Solar cell and a single G13 Type button battery (LR44) Battery Life: fx-100MS: Approximately 17,000 hours continuous display of flashing cursor. Approximately 2 years when left with power turned off. fx-115MS: Approximately 3 years (1 hour use per day). Dimensions: fx-100MS: 20.0 (H) 78 (W) 155 (D) mm 13/16 (H) 31/16 (W) 61/8 (D) fx-115MS: 12.7 (H) 78 (W) 154.5 (D) mm 1/2 (H) 31/16 (W) 61/16 (D) Weight: fx-100MS: 133 g (4.7 oz) including battery fx-115MS: 105 g (3.7 oz) including battery Power Consumption: 0.0002 W Operating Temperature: 0C to 40C (32F to 104F)
Important notice for fx-912MS owners
The names fx-912MS (Japan domestic model name) and fx-115MS (international model name) apply to the same model. Owners of the fx-912MS should refer to the description of fx-115MS. E-16

CASIO COMPUTER CO., LTD.

6-2, Hon-machi 1-chome Shibuya-ku, Tokyo 151-8543, Japan
SA0206-D Printed in China CA 310074C-1

fx-95MS fx-100MS fx-115MS (fx-912MS) fx-570MS fx-991MS

User's Guide

kfx-912MS owners
Please be sure to read the important notice of this manual.
http://world.casio.com/edu_e/
CASIO ELECTRONICS CO., LTD. Unit 6, 1000 North Circular Road, London NW2 7JD, U.K.
Removing and Replacing the Calculators Cover
Before starting..1 Holding the cover as shown in the illustration, slide the unit out of the cover. After you are finished..2 Holding the cover as shown in the illustration, slide the unit out of the cover. Always slide the keyboard end of the unit into the cover first. Never slide the display end of the unit into the cover.

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.

Batteries

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 batteries, try to take batteries apart, or allow batteries to become shorted. Never expose batteries to direct heat or dispose of them by incineration. Misuse of batteries can cause them to leak and damage nearby items, and can create the risk of fire and personal injury. Always make sure that the batterys positive k and negative l ends are facing correctly when you load it into the calculator. Remove the battery if you do not plan to use the calculator for a long time (fx-95MS/100MS/570MS). 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. The displays and illustrations (such as key markings) shown in this Users Guide are for illustrative purposes 2
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 these materials. Moreover, CASIO Computer Co., Ltd. shall not be liable for any claim of any kind whatsoever against the use of these materials by any other party.

Handling Precautions

Be sure to press the 5 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 for the fx115MS/fx-570MS/fx-991MS, or at least once every two years for the fx-95MS/fx-100MS. 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 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 calculators case, and damage to internal circuitry. 3
Avoid use and storage 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 moisture 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.

Contents

Removing and Replacing the Calculators Cover.. 1 Safety Precautions.. 2 Handling Precautions.. 3 Two-line Display.. 7 Before getting started.. 7
kModes... 7 kInput Capacity... 8 kMaking Corrections During Input.. 9 kReplay Function... 9 kError Locator... 9 kMulti-statements.. 10 kExponential Display Formats. 10 kDecimal Point and Separator Symbols. 11 k Initializing the Calculator.. 11

Basic Calculations.. 11

k Arithmetic Calculations.. kFraction Operations.. kPercentage Calculations.. kDegrees, Minutes, Seconds Calculations. kFIX, SCI, RND... kAnswer Memory... kConsecutive Calculations. kIndependent Memory.. k Variables.. 17

Memory Calculations.. 16

Scientific Function Calculations.. 18
kTrigonometric/Inverse Trigonometric Functions. 18 kHyperbolic/Inverse Hyperbolic Functions. 19
kCommon and Natural Logarithms/ Antilogarithms.. 19 kSquare Roots, Cube Roots, Roots, Squares, Cubes, Reciprocals, Factorials, Random Numbers, , and Permutation/Combination. 20 kAngle Unit Conversion... 21 kCoordinate Conversion (Pol (x, y), Rec (r, )).. 21 kEngineering Notation Calculations.. 22
Equation Calculations. 22
kQuadratic and Cubic Equations.. 22 kSimultaneous Equations.. 24
Statistical Calculations.. 26
Standard Deviation.. 26 Regression Calculations.. 28
Technical Information.. 32
kWhen you have a problem.. kError Messages... kOrder of Operations.. kStacks... kInput Ranges.. 36
Power Supply (fx-95MS only).. 38 Specifications (fx-95MS only). 39

Two-line Display

The two-line display makes it possible to view both the calculation formula and its result at the same time.
The upper line shows the calculation formula. The lower line shows the result. A separator symbol is displayed every three digits when the integer part of the mantissa has more than three digits.

Before getting started.

k Modes
Before starting a calculation, you must first enter the correct mode as indicated in the table below. The following table shows the modes and required operations for the fx-95MS only. Users of other models should refer to the Users Guide 2 (Additional Functions) for information about modes and their selection.

fx-95MS Modes

To perform this type of calculation: Basic arithmetic calculations Standard deviation Regression calculations Solution of equations 7 Perform this To enter key operation: this mode:

F1 F2 F3 FF1

COMP SD REG EQN
Pressing the F key more than twice displays additional setup screens. Setup screens are described in the sections of this manual where they are actually used to change the calculator setup. In this manual, the name of the mode you need to enter in order to perform the calculations being described is indicated in the main title of each section.

Example:

Equation Calculations
To return the calculation mode and setup to the initial defaults shown below, press A B 2(Mode) =. Calculation Mode: Angle Unit: Exponential Display Format: Fraction Display Format: Decimal Point Character: COMP Deg Norm 1 a b/c Dot
Mode indicators appear in the upper part of the display. Be sure to check the current calculation mode (SD, REG, COMP) and angle unit setting (Deg, Rad, Gra) before beginning a calculation.

k Input Capacity

The memory area used for calculation input can hold 79 steps. One step is taken up each time you press a number key or arithmetic operator key ( +, ,, -, \ ). A A or p key operation does not take up a step, so inputting A D, for example, takes up only one step. You can input up to 79 steps for a single calculation. Whenever you input the 73rd step of any calculation, the cursor changes from _ to k to let you know memory is running low. If you need to input more than 79 steps, you should divide your calculation into two or more parts. Pressing the g key recalls the last result obtained, which you can use in a subsequent calculation. See Answer Memory for more information about using the g key.
k Making Corrections During Input
Use e and r to move the cursor to the location you want. Press [ to delete the number or function at the current cursor position. Press A K to change to an insert cursor t. Inputting something while the insert cursor is on the display inserts the input at the insert cursor position. Pressing A K, or = returns to the normal cursor from the insert cursor.

k Replay Function

Every time you perform a calculation, the replay function stores the calculation formula and its result in replay memory. Pressing the [ key displays the formula and result of the calculation you last performed. Pressing [ again back steps sequentially (new-to-old) through past calculations. Pressing the e or r key while a replay memory calculation is on the display changes to the editing screen. Pressing the e or r key immediately after you finish a calculation displays the editing screen for that calculation. Pressing t does not clear replay memory, so you can recall the last calculation even after you press t. Replay memory capacity is 128 bytes for storage of both expressions and results. Replay memory is cleared by any of the following actions. When you press the 5 key When you initialize modes and settings by pressing A B 2 (or 3) =. When you change from one calculation mode to another When you turn off the calculator.

k Error Locator

Pressing r or e after an error occurs displays the calculation with the cursor positioned at the location where the error occurred. 9

Values are displayed in decimal format automatically whenever the total number of digits of a fractional value (integer + numerator + denominator + separator marks) exceeds 10. Example 1:

2C3+1C5=

13 15.00

Example 2: 3

3C1C4+ 1C2C3=

2C4= 1 C 2 + 1.6 =

Example 3: Example 4:

1 1.6 2.1 2

Results of calculations that mix fraction and decimal values are always decimal.
uDecimal Fraction Conversion
Use the operation shown below to convert calculation results between decimal values and fraction values. Note that conversion can take as long as two seconds to perform. 12

Example 1: 2.75 2

3 (Decimal Fraction) 4 2.75 = 2.75

Example 2: 11 4

4.4.00
1 0.5 (Fraction Decimal) 2 1C2=

1 2.00 0.2.00

uMixed Fraction Improper Fraction Conversion

Example: 3 1C2C3=

3.3.2 3.00
You can use the display setup (Disp) screen to specify the display format when a fraction calculation result is greater than one. To change the fraction display format, press the q key a number of times until you reach the setup screen shown below.
Display the selection screen. fx-95MS: 1 Other Models: 1 r Press the number key ( 1 or 2) that corresponds to the setting you want to use.
1(a b/c): Mixed fraction 2(d/c): Improper fraction
An error occurs if you try to input a mixed fraction while the d/c display format is selected.
k Percentage Calculations
Example 1 : To calculate 12% of 1500 (180) 1500 - 12 A v Example 2: To calculate what percentage of 880 is 660 (75%) 660 \ 880 A v Example 3 : To add 15% onto 2500 (2875) 2500 - 15 A v + Example 4 : To discount 3500 by 25% (2625) 3500 - 25 A v , Example 5: To discount the sum of 168, 98, and 734 by 20% (800) 168 + 98 + 734 = g A j 1 p 1 - 20 A v , * As shown here, if you want to use the current Answer Memory value in a mark up or discount calculation, you need to assign the Answer Memory value into a variable and then use the variable in the mark up/discount calculation. This is because the calculation performed when v is pressed stores a result to Answer Memory before the , key is pressed. Example 6: If 300 grams are added to a test sample originally weighing 500 grams, what is the percentage increase in weight? (160%) 300 + 500 A v Example 7: What is the percentage change when a value is increased from 40 to 46? How about to 48? (15%, 20%) 46 , 40 A v eeeeee8= 14
k Degrees, Minutes, Seconds Calculations
You can perform sexagesimal calculations using degrees (hours), minutes, and seconds, and convert between sexagesimal and decimal values. Example 1: To convert the decimal value 2.258 to a sexagesimal value and then back to a decimal value 2.258 =

2.258 21528.8 2.258

Example 2: To perform the following calculation: 123456 3.I 34 I 56 I - 3.45 =

432431.2

k FIX, SCI, RND
To change the settings for the number of decimal places, the number of significant digits, or the exponential display format, press the F key a number of times until you reach the setup screen shown below.
Press the number key ( 1, 2, or 3) that corresponds to the setup item you want to change.
1 (Fix): Number of decimal places 2 (Sci): Number of significant digits 3 (Norm): Exponential display format

Example 1: \ 7 - 14 =

(Specifies three decimal places.)

400.00

F.. 1(Fix) 3

400.00000

(Internal calculation continues using 12 digits.)

200 \ 7 =

28.57100 400.00000

- 14 =

The following performs the same calculation using the specified number of decimal places. 200 \ 7 =

(Internal rounding)

28.57100 28.57100 399.99400

AQ - 14 =

Press F.. 3(Norm) 1 to clear the Fix specification. Example 2: 1 3, displaying result with two significant digits (Sci 2)

F.. 2(Sci) \ 3 =

Press F.. 3(Norm) 1 to clear the Sci specification.

Memory Calculations

Use the F key to enter the COMP Mode when you want to perform a calculation using memory. COMP... F 1

k Answer Memory

Whenever you press = after inputting values or an expression, the calculated result automatically updates Answer Memory contents by storing the result. In addition to =, Answer Memory contents are also updated with result whenever you press A v, |, A {, or A j followed by a letter (A through F, or M, X, or Y). 16
You can recall Answer Memory contents by pressing g. Answer Memory can store up to 12 digits for the mantissa and two digits for the exponent. Answer Memory contents are not updated if the operation performed by any of the above key operations results in an error.
k Consecutive Calculations
You can use the calculation result that is currently on the display (and also stored in Answer Memory) as the first value of your next calculation. Note that pressing an operator key while a result is displayed causes the displayed value to change to Ans, indicating it is the value that is currently stored in Answer Memory. The result of a calculation can also be used with a subsequent Type A function (x2, x3, x1, x!, DRG'), +, , ^(xy), x , , , nPr and nCr.

k Independent Memory

Values can be input directly into memory, added to memory, or subtracted from memory. Independent memory is convenient for calculating cumulative totals. Independent memory uses the same memory area as variable M. To clear independent memory (M), input 0 A j 3 (M+). Example: ) 90 (Total) 23 + 9 A j 3 (M+) 53 , 6 | 45 - 2 A {

k Variables

There are nine variables (A through F, M, X and Y), which can be used to store data, constants, results, and other values. Use the following operation to delete data assigned to a 17
particular variable: 0 A j 1. This operation deletes the data assigned to variable A. Perform the following key operation when you want to clear the values assigned to all of the variables.

A B 1(Mcl) =

Example: 193.8.4 193.6.9 193.2 A j 1 \ 23 =

p 1 \ 28 =

Scientific Function Calculations
Use the F key to enter the COMP Mode when you want to perform basic arithmetic calculations. COMP... F 1 Certain types of calculations may take a long time to complete. Wait for the result to appear on the display before starting the next calculation. = 3.14159265359
k Trigonometric/Inverse Trigonometric Functions
To change the default angle unit (degrees, radians, grads), press the F key a number of times until you reach the angle unit setup screen shown below.

Deg Rad G r a

Press the number key ( 1, 2, or 3 ) that corresponds to the angle unit you want to use. (90 =

radians = 100 grads) 18

Example 1: sin 63 52o41 0.897859012
q.. 1(Deg) S 63 I 52 I 41 I =

Example 2: cos

rad 0.5 3

q.. 2(Rad) WRAx\3T=

Example 3 : cos1

2 (rad) 0.25 (rad) 2 4

q.. 2 (Rad) AVRL2\2T=g\Ax=
Example 4: tan1 0.741 36.53844577

q.. 1(Deg) A g 0.741 =

k Hyperbolic/Inverse Hyperbolic Functions
Example 1: sinh 3.6 18.28545536 Example 2: sinh4.094622224

M S 3.6 = M A j 30 =

k Common and Natural Logarithms/ Antilogarithms
Example 1: log 1.23 0.089905111
R 1.23 = T 90 = TpP= A U 10 = A Q 1.5 =
Example 2: In 90 (= loge 90) = 4.49980967 ln e 1 Example 3: e10 22026.46579 Example 4: 10 31.6227766

Example 5: 19

k Square Roots, Cube Roots, Roots, Squares, Cubes, Reciprocals, Factorials, Random Numbers, , and Permutation/Combination

Example 1:

5 5.287196909

L2+L3-L5=

Example 2: 1.290024053

A D 5 + A D R D 27 T =

Example 3:
123 ( = ) 1.A H 123 = 123 + 30 K = 12 N * =
Example 4: 1023 Example 5: 123 1728
* A N in the case of fx-570MS/fx-991MS. 1 Example 6: 4 R3a,4aTa= Example 7: 8! 40320 8Af=
Example 8: To generate a random number between 0.000 and 0.999

Example 9: 3 9.424777961

0.66400
(The above value is a sample only. Results differ each time.)
Example 10: To determine how many different 4-digit values can be produced using the numbers 1 through 7 Numbers cannot be duplicated within the same 4-digit value (1234 is allowed, but 1123 is not). (840) 7Am4= Example 11: To determine how many different 4-member groups can be organized in a group of 10 individuals (210) 10 n* 4 = 20

* A n in the case of fx-100MS/fx-115MS/fx-570MS/ fx-991MS.

k Angle Unit Conversion

Press A v to display the following menu.
Pressing 1, 2, or 3 converts the displayed value to the corresponding angle unit. Example: To convert 4.25 radians to degrees

q.. 1(Deg)

4.25 A v 2(R) =

4. 25 r

243.5070629
k Coordinate Conversion (Pol (x, y), Rec (r, ))
Calculation results are automatically assigned to variables E and F. Example 1: To convert polar coordinates (r2, 60) to rectangular coordinates (x, y) (Deg) x1 y 1.732050808

A F 2 P 60 T = 0o

Press 0 n to display the value of x, or 0 o to display the value of y. Example 2: To convert rectangular coordinates (1, 3) to polar coordinates (r,) (Rad) r2 f* 1 P L 3 T = * A f in the case of fx-100MS/fx-115MS/fx-570MS/ fx-991MS.

1.047197551

Press 0 n to display the value of r, or 0 o to display the value of. 21
k Engineering Notation Calculations
Example 1: To convert 56,088 meters to kilometers 56.3 (km) 81.3 (mg) 56088 = J
Example 2: To convert 0.08125 grams to milligrams 0.08125 = J
The EQN Mode lets you solve equations up to three degrees and simultaneous linear equations with up to three unknowns. Use the F key to enter the EQN Mode when you want to solve an equation. EQN. F F 1 (fx-95MS) F F F 1 (Other Models)
k Quadratic and Cubic Equations
Quadratic Equation: ax2 + bx + c = 0 Cubic Equation: ax3 + bx2 + cx + d = 0 Entering the EQN Mode and pressing r displays the initial quadratic/cubic equation screen.

Deg r ee?

Use this screen to specify 2 (quadratic) or 3 (cubic) as the degree of the equation, and input values for each of the coefficients.
Coefficient name Arrow indicates direction you should scroll to view other elements.

Element value

Any time until you input a value for the final coefficient (c for a quadratic equation, d for a cubic equation), you can use the [ and ] keys to move between coefficients on the screen and make changes, if you want. Note that you cannot input complex numbers for coefficients. Calculation starts and one of the solutions appears as soon as you input a value for the final coefficient.
Variable name Arrow indicates direction you should scroll to view other solutions.

Solution

Press the ] key to view other solutions. Use [ and ] to scroll between all of the solutions for the equation. Pressing the t key at this point returns to the coefficient input screen. Certain coefficients can cause calculation to take more time. Example 1: To solve the equation x3 2x2 x + 2 = 0 ( x = 2, 1, 1) (Degree?) 3 (a?) (b?) (c?) (d?) (x1 = 2) (x2 = 1) (x3 = 1) If a result is a complex number, the real part of the first solution appears first. This is indicated by the RI symbol on the display. Press A r to toggle the display between the real part and imaginary part of a solution. 23 1= D2= D1= 2= ] ]

Sample Standard Deviation (n1) = 1.407885953
Population Standard Deviation (n) = 1.316956719 Arithmetic Mean (o) = 53.375 Number of Data (n) = 8 Sum of Values (x) = 427 Sum of Squares of Values (x 2 ) = 22805

AX2= AX1= AU3= AU2= AU1=

Data Input Precautions S S inputs the same data twice.
You can also input multiple entries of the same data using A G. To input the data 110 ten times, for example, press 110 A G 10 S. You can perform the above key operations in any order, and not necessarily that shown above. While inputting data or after inputting data is complete, you can use the [ and ] keys to scroll through data you have input. If you input multiple entries of the same data using A G to specify the data frequency (number of data items) as described above, scrolling through data shows both the data item and a separate screen for the data frequency (Freq). You can then edit the displayed data, if you want. Input the new value and then press the = key to replace the old value with the new one. This also means that if you want to perform some other operation (calculation, recall of statistical calculation results, etc.), you should always press the t key first to exit data display. Pressing the S key instead of = after changing a value on the display registers the value you input as a new data item, and leaves the old value as it is. You can delete a data value displayed using [ and ] by pressing A U. Deleting a data value causes all values following it to be shifted up. Data values you register are normally stored in calculator memory. The message Data Full appears and you will not be able to input any more data if there is no memory left for data storage. If this happens, press the = key to display the screen shown below.

Ed i t OFF ESC

Press 2 to exit data input without registering the value you just input. Press 1 if you want to register the value you just input, without saving it in memory. If you do this, however, you will not be able to display or edit any of the data you have input. To delete data you have just input, press A U. After inputting statistical data in the SD Mode or REG Mode, you will be unable to display or edit individual data items any longer after perform either the following operations. Changing to another mode Changing the regression type (Lin, Log, Exp, Pwr, Inv, Quad)

Regression Calculations

Use the F key to enter the REG Mode when you want to perform statistical calculations using regression. REG.. F 3 (fx-95MS) F F 2 (Other Models) Entering the REG Mode displays screens like the ones shown below.

L i n Log Ex p

I nv Quad
Press the number key ( 1, 2, or 3) that corresponds to the type of regression you want to use.
1 (Lin) : Linear regression 2 (Log) : Logarithmic regression 3 (Exp) : Exponential regression r 1 (Pwr) : Power regression r 2 (Inv) : Inverse regression r 3 (Quad) : Quadratic regression
Always start data input with A B 1 (Scl) = to clear statistical memory. Input data using the key sequence shown below. <x-data> P <y-data> S The values produced by a regression calculation depend on the values input, and results can be recalled using the key operations shown in the table below.
x2 x n y2 y xy o xn xn-1 p yn yn-1
Regression coefficient A Regression coefficient B Regression calculation other than quadratic regression Correlation coefficient r
AU1 AU2 AU3 AUr1 AUr2 AUr3 AX1 AX2 AX3 AXr1 AXr2 AXr3 AXrr1 AXrr2

AXrr3 AXrrr1 AXrrr2

The following table shows the key operations you should use to recall results in the case of quadratic regression.

x3 x2y x4

Regression coefficient C

m1 m2 n

AUrr1 AUrr2 AUrr3 AXrr3 AXrrr1 AXrrr2 AXrrr3
The values in the above tables can be used inside of expressions the same way you use variables.

u Linear Regression

The regression formula for linear regression is: y = A + Bx. Example: Atmospheric Pressure vs. Temperature
Temperature Atmospheric Pressure

10C 15C 20C 25C 30C

1003 hPa 1005 hPa 1010 hPa 1011 hPa 1014 hPa
Perform linear regression to determine the regression formula terms and correlation coefficient for the data nearby. Next, use the regression formula to estimate atmospheric pressure at 18C and temperature at 1000 hPa. Finally, calculate the coefficient of determination (r 2 ) and sample covariance.

In the REG Mode:

1(Lin) A B 1 (Scl) = (Stat clear)

10 P1003 S

15 P 1005 S 20 P1010 S 25 P 1011 S 30 P 1014 S
Regression Coefficient A = 997.4 Regression Coefficient B = 0.56 Correlation Coefficient r = 0.982607368

AXrr1= AXrr2= AXrr3=

Atmospheric Pressure at 18C = 1007.48

18 A X r r r 2 = 30

Temperature at 1000 hPa = 4.642857143

1000 A X r r r 1 =

Coefficient of Determination = 0.965517241

Sample Covariance = 35

AXrr3K= EAUr3, AU3-AX1AXr1F\ EAU3,1F=
u Logarithmic, Exponential, Power, and Inverse Regression
Use the same key operations as linear regression to recall results for these types of regression. The following shows the regression formulas for each type of regression. Logarithmic Regression Exponential Regression Power Regression Inverse Regression y A B In x y A eBx (In y In A + Bx) y A xB (In y In A + B In x) y A B 1/x

u Quadratic Regression

The regression formula for quadratic regression is: y = A + Bx + Cx2. Example: Perform quadratic regression to determine the regression formula terms for the data nearby. Next, use the regression formula to estimate the values for n (estimated value of y) for xi = 16 and m (estimated value of x) for yi = 20.

1.6 23.5 38.0 46.4 48.0

r 3(Quad) A B 1 (Scl) = (Stat clear) 29 P 1.6 S 50 P 23.5 S 74 P 38.0 S 103 P 46.4 S 118 P 48.0 S
Regression Coefficient A = 35.59856934 Regression Coefficient B = 1.495939413
Regression Coefficient C = 6.71629667 i10 3
n when xi is 16 = 13.38291067 m1 when yi is 20 = 47.14556728 m2 when yi is 20 = 175.5872105
16 A X r r r 3 = 20 A X r r r 1 = 20 A X r r r 2 =

Data Input Precautions

S S inputs the same data twice. You can also input multiple entries of the same data using A G. To input the data 20 and 30 five times, for example, press 20 P 30 A G 5 S. The above results can be obtained in any order, and not necessarily that shown above. Precautions when editing data input for standard deviation also apply for regression calculations.

Technical Information

k When you have a problem.
If calculation results are not what you expect or if an error occurs, perform the following steps. 1. Press A B 2(Mode) = to initialize all modes and settings. 2. Check the formula you are working with to confirm it is correct. 3. Enter the correct mode and try performing the calculation again. If the above steps do not correct the problem, press the 5 key. The calculator performs a self-check operation and deletes all data stored in memory if any abnormality is detected. Make sure you always keep written copies of all important data.

k Error Messages

The calculator is locked up while an error message is on 32
the display. Press t to clear the error, or press e or r to display the calculation and correct the problem. See Error Locator for details.

Math ERROR

Causes Calculation result is outside the allowable calculation range. An attempt to perform a function calculation using a value that exceeds the allowable input range. An attempt to perform an illogical operation (division by zero, etc.) Action Check your input values and make sure they are all within the allowable ranges. Pay special attention to values in any memory areas you are using.

Stack ERROR

Cause The capacity of the numeric stack or operator stack is exceeded. Action Simplify the calculation. The numeric stack has 10 levels and the operator stack has 24 levels. Divide your calculation into two or more separate parts.

Syntax ERROR

Cause An attempt to perform an illegal mathematical operation. Action Press e or r to display the calculation with the cursor located at the location of the error and make required corrections.

Arg ERROR

Cause Improper use of an argument 33
Action Press e or r to display the location of the cause of the error and make required corrections.

k Order of Operations

Calculations are performed in the following order of precedence. 1 Coordinate transformation: Pol (x, y), Rec (r, ) Differentials: d/dx* Integrations: dx* Normal distribution: P(*, Q(*, R(* 2 Type A functions: With these functions, the value is entered and then the function key is pressed. x3, x2, x1, x!, Engineering symbols* Normal distribution: t * m, m1, m2, n Angle unit conversions (DRG') Metric conversions** 3 Powers and roots: ^ (xy), x 4 a b/c 5 Abbreviated multiplication format in front of , e (natural logarithm base), memory name, or variable name: 2, 3e, 5A, A, etc. 6 Type B functions: With these functions, the function key is pressed and then the value is entered. 3 , , log, In, ex, 10x, sin, cos, tan, sin1, cos1, tan1, sinh, cosh, tanh, sinh1, cosh1, tanh1, () d*, h*, b*, o*, Neg*, Not*, Det**, Trn**, arg*, Abs*, Conjg* 7 Abbreviated multiplication format in front of Type B functions: 2 3, Alog2, etc. 8 Permutation and combination: nPr, nCr * 9 Dot ()** 0 , ! , @ and* # xnor*, xor*, or* 34
* fx-100MS/fx-115MS/fx-570MS/fx-991MS only. ** fx-570MS/fx-991MS only. Operations of the same precedence are performed from right to left. exIn 120 ex{In( 120)} Other operations are performed from left to right. Operations enclosed in parentheses are performed first. When a calculation contains an argument that is a negative number, the negative number must be enclosed within parentheses. The negative sign () is treated as a Type B function, so particular care is required when the calculation includes a high-priority Type A function, or power or root operations. Example: ( 2)4 = = 16

k Stacks

This calculator uses memory areas, called stacks, to temporarily store values (numeric stack) and commands (command stack) according to their precedence during calculations. The numeric stack has 10 levels and the command stack has 24 levels. A stack error (Stack ERROR) occurs whenever you try to perform a calculation that is so complex that the capacity of a stack is exceeded. Matrix calculations use up to two levels of the matrix stack. Squaring a matrix, cubing a matrix, or inverting a matrix uses one stack level. (fx-570MS, fx-991MS only) Example:

Power Supply

(fx-95MS only)
Users of other models should refer to the Users Guide 2 (Additional Functions). This calculator is powered by a single AA-size battery.

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 become dim.
To replace the battery 1 Press A i to turn power off. Screw
2 Remove the six screws that hold the back cover in place and then remove the back cover. 3 Remove the old battery. 4 Load a new battery into the unit with its positive k and negative l ends facing correctly. 5 Replace the back cover and secure it in place with the six screws. 6 Press 5 to turn power on. 38

u Auto Power Off

Calculator power automatically turns off if you do not perform any operation for about six minutes. When this happens, press 5 to turn power back on.

Specifications

Users of other models should refer to the Users Guide 2 (Additional Functions). Power Supply: Single AA-size battery (R6P (SUM-3)) Battery Life: Approximately 17,000 hours continuous display of flashing cursor. Approximately 2 years when left with power turned off. 19.5 (H) i 78 (W) i 155 (D) mm 3/4 (H) 31/16 (W) 61/8 (D) 130 g (4.6 oz) including battery

Dimensions: Weight:

Power Consumption: 0.0002 W Operating Temperature: 0C to 40C (32F to 104F)
Important notice for fx-912MS owners
The names fx-912MS (Japan domestic model name) and fx-115MS (international model name) apply to the same model. Owners of the fx-912MS should refer to the description of fx-115MS. 39

CASIO COMPUTER CO., LTD.

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