Casio fx-82SX User's Guide

• ••••••••••••••••••

fx-82SX/ fx-250HC

• ••••••••••••••••••

NQPOR

CASIO ELECTRONICS CO., LTD. Unit 6, 1000 North Circular Road, London NW2 7JD, U.K.

ENGLISH ESPAÑOL FRANÇAIS

Contents

Handling Precautions … 2 Modes … 3 Basic Calculations … 5 Constant Calculations … 6 Memory Calculations … 7 Fraction Calculations … 8 Percentage Calculations … 10 Scientific Function Calculations … 11 Statistical Calculations (SD Mode) … 16 Technical Information … 18

1

33

66

— 1 —

DEUTSCH ITALIANO

99

134

Handling Precautions

•Your calculator is made up of precision components. Never try to take it apart.

•Avoid dropping your calculator and otherwise subjecting it to strong impact.

• Do not store the calculator or leave it in areas exposed to high temperature or humidity, or large amounts of dust. When exposed to low temperature, the calculator may require more time to display results and may even fail to operate. Correct operation will resume once the calculator is brought back to normal temperature.

• The display will go blank and keys will not operate during calculations. When you are operating the keyboard, be sure to watch the display to make sure that all your key operations are being performed correctly.

• Never leave dead batteries in the battery compartment. They can leak and damage the unit.

•Avoid using volatile liquids such as thinner or benzine to clean the unit. Wipe it with a soft cloth, or with a cloth that has been dipped in a solution of water and a neutral detergent and wring out.

• In no event will the manufacturer and its suppliers be liable to you or any other person for any damages, expenses, lost profits, lost savings, or any other damages arising out of malfunction, repairs, or battery replacement. The user should prepare physical records of data to protect against such data loss.

• Never dispose of batteries, the liquid crystal panel, or other components by burning them.

— 2 —

• Before assuming malfunction of the unit, be sure to carefully reread this manual and ensure that the problem is not due to low battery power or operational error.

• The contents of this manual are subject to change without notice.

• No part of this manual may be reproduced in any form without the express written consent of the manufacturer.

• Keep this manual on hand for future reference.

Modes

Application

Standard deviation calculations

Normal calculations

Calculations using degrees

Calculations using radians

Calculations using grads

Number of decimal place specification

Number of significant digit specification

Cancels FIX and SCI settings

* Display indicators show current mode setting. Absence of

display indicator indicates COMP Mode.

— 3 —

Key

Operation

Fl F0 F4 F5 F6

F7

F8

F9

Mode

Name*

SD

COMP

DEG

RAD

GRA

FIX

SCI

NORM

Note!

•A mode guide is located above the display screen.

• DEG, RAD, and GRA modes can be used in combination

with the COMP and SD modes.

•

does not exit SD mode.

F9

•

exits SD mode.

F0

•

does not clear SCI or FIX specifications.

F0

• Always press t before entering DEG, RAD, and GRA

modes.

• Remember to always set the operating mode and angular

unit (DEG, RAD, GRA) before starting your calculation.

— 4 —

Basic Calculations

• Use the COMP mode for basic calculations.

• Example 1: 23ѿ4.5Ҁ53

23 + 4.5 , 53 =

• Example 2: 56҂(Ҁ12)쐦(Ҁ2.5)

56 -12 E \ 2.5 E =

• Example 3: 2쐦3҂(1҂1020)

2 \ 3 -1 e 20 =

• Example 4: 7҂8Ҁ4҂5=36

7 - 8 , 4 - 5 =

• Example 5: =0.3

• Example 6: 2҂[7ѿ6҂(5ѿ4)]҃122

6

4҂5

4 - 5 \ 6 A N =

2 - O 7 + 6 -

O 5 + 4 P P =

•You can skip all P operations before the = ke y.

— 5 —

6.666666667

–25.5

268.8

19

36.

0.3

122.

Constant Calculations

• Press +, ,, -,or \ twice after inputting a number to

make that number a constant.

• “K” is on the display while a constant is being used.

• Use the COMP mode for constant calculations.

• Example 1: 2.3ѿ3, then 2.3ѿ6

(2.3ѿ3) 2.3 + + 3 =

(2.3ѿ6) 6 =

• Example 2: 12҂2.3, then 12҂(앥9)

(12҂2.3) 12 - - 2.3 =

(12҂(앥9)) 9 E =

• Example 3: 17ѿ17ѿ17ѿ17҃68

(17ѿ17) 17 + + =

(17ѿ17ѿ17) =

(17ѿ17ѿ17ѿ17) =

• Example 4: 1.74҃8.3521

(1.72) 1.7 - - =

(1.73) =

(1.74) =

— 6 —

K

–108.

K

4.913

K

8.3521

5.3

8.3

27.6

34.

51.

68.

2.89

Memory Calculations

• Use the COMP mode for memory calculations.

• Use Y, |, A { and Z for memory calculations.

Y replaces current memory contents.

• “M” appears when there is a value in memory.

•To clear memory, press 0 Y or t Y.

• Example 1: (53ѿ6)ѿ(23Ҁ8)ѿ(56҂2)ѿ(99쐦4)҃210.75

(53ѿ6) 53 + 6 = Y

(23앥8) 23 , 8 |

(56҂2) 56 - 2 |

(99앦4) 99 \ 4 |

(Memory recall) Z

• Example 2: To calculate the following using memory as shown.

— 7 —

M

59.

15.

112.

24.75

210.75

13.

• Example 3: To calculate the following using memory and a constant: (12҂3)앥(45҂3)ѿ(78҂3)҃135.

(12҂3) 3 - - 12 = Y

(45҂3) 45 A {

(78҂3) 78 |

(Memory recall) Z

MK

36.

MK

135.

MK

234.

MK

135.

Fraction Calculations

• Use COMP mode for fraction calculations.

•Total number of digits (including division marks) cannot exceed 10.

• Example 1: ѿ ҃1

234

2

• Example 2: 3 ѿ1 ҃ 4

7

15

5

C 3 + 4 C 5 =

142311

12

3 C 1 C 4 +

1 C 2 C 3 =

1 7 15.

4 11 12.

• Example 3: ҃ 2 C 4

241

2

=

— 8 —

2 4.

1 2.

• Example 4: ѿ1.6҃2.1

Fraction/decimal calculation result is always decimal.

1 2

1 C 2 + 1.6 =

2.1

• Example 5: ↔ 0.5 (Fraction ↔ Decimal)

1 2

1 C 2 =

C

• Example 6: 1 ↔

235

3

1 C 2 C 3

A B

— 9 —

1 2.

0.5

1

1 2 3.

5

1 2 3.

2.

3.

Percentage Calculations

• Use COMP mode for percentage calculations.

• Example 1: To calculate 12% of 1500.

1500 - 12 A v

• Example 2: To calculate what percentage of 880 is 660.

660 \ 880 A v

• Example 3: To add 15% onto 2500.

2500 - 15 A v +

• Example 4: To discount 3500 by 25%.

3500 - 25 A v ,

• Example 5: To calculate the following, using a constant.

12% of 1200 = 144 18% of 1200 = 216 23% of 1200 = 276

180.

75.

2875.

2625.

(12%) 1200 - - 12 A v

(18%) 18 A v

(23%) 23 A v

— 10 —

K

144.

K

216.

K

276.

Scientific Function Calculations

• Use COMP mode for scientific function calculations.

• Some calculations may take a long time to complete.

•Wait for result before starting next calculation.

• ␲ =3.1415926536.

kSexagesimal ↔ Decimal Conversion

• Example: 14°25’36” ↔ 14.42667

14 I 25 I 36 I

A O

kTrigonometric/Inverse Trigonometric Functions

• Example 1: sin ( rad) (RAD mode)

␲

6

A x \ 6 = S

• Example 2: cos 63°52’41” (DEG mode)

63 I 52 I 41 I W

• Example 3: tan (앥35gra)(GRA mode)

35 E h

• Example 4: cos–1 ( rad) (RAD mode)

2

2 L \ 2 = A V

— 11 —

14.42666667

14°25°36

RAD

0.5

DEG

0.440283084

–0.612800788

GRA

RAD

0.785398163

kHyperbolic/Inverse Hyperbolic Functions

• Example 1: sinh 3.6 3.6 M S

18.28545536

• Example 2: sinh앥1 30 30 M A j

4.094622224

kCommon and Natural Logarithms, Exponents

• Example 1: log 1.23 1.23 R

• Example 2: In 90 (҃loge 90) 90 T

• Example 3: 64 R \ 4 R =

• Example 4: 10

Iog 64

Iog 4

0.4

ѿ5 e

앥3

.4 A Q +

5 - 3 E A U =

• Example 5: 2

• Example 6: 2

• Example 7: e

3

앥3

2 A w 3 E =

10

2 A w 3 =

10 A U

— 12 —

0.089905111

4.49980967

3.

2.760821773

8.

0.125

22026.46579

• Example 8: log sin 40° +log cos 35° (DEG mode)

40 S R +35 W R =

To con vert to antilogarithm:

A Q

–0.278567983

0.526540784

DEG

• Example 9: 8

1/3

8 A s 3 =

k Square Roots, Cube Roots, Squares,

Reciprocals and Factorials

• Example 1: 2 ѿ 3 ҂ 5

2 L + 3 L - 5 L =

3

• Example 2: 35 ѿ

앥27

5 A D + 27 E A D =

• Example 3: 123ѿ30

2

123 + 30 A K =

1

• Example 4:

1 앥 1

3 4

3 A X , 4 A X = A X

— 13 —

5.287196909

–1.290024053

2.

1023.

12.

• Example 5: 8! 8 A f

40320.

kFIX, SCI, NORM, RND, RAN#, ENG Calculations

• Example 1: 1.234ѿ1.234, rounding result to two places

(FIX 2).

F 7 2

1.234 +1.234 =

FIX

0.00

FIX

2.47

• Example 2: 1.234ѿ1.234, rounding input to two places.

F 7 21.234 A b +

1.234 A b =

• Press F9 to clear FIX specification.

• Example 3: 1쐦 3 , displaying result with two significant

digits (SCI 2).

F 8 2

1 \ 3 =

• Press F9 to clear SCI specification.

• Example 4: To convert 56,088 meters to kilometers.

56088 J

— 14 —

FIX

2.46

SCI

0.0

SCI

3.3

56.088

–01

00

03

• Example 5: To con vert 0.08125 grams to milligrams.

.08125 J

81.25

–03

• Example 6: To generate a random number between 0.000

and 0.999.

Example (results differ each time)

A c

0.664

kCoordinate Conversion

• Example 1: To convert polar coordinates (r҃2, ␪҃60°) to

rectangular coordinates (x, y). (DEG mode)

x 2 A z 60 =

y A N

DEG

1.732050808

1.

ANswaps displayed value with value in memory.

• Example 2: To convert rectangular coordinates (1, 3) to

polar coordinates (r, ␪). (RAD mode)

r 1 A y 3 L =

θ

A N

RAD

1.047197551

2.

kPermutation

• Example: To determine how many different 4-digit values

can be produced using the numbers 1 through 7.

7 A m 4 =

— 15 —

840.

kCombination

• Example: To determine how many different 4-member

groups can be organized in a group of 10 individuals.

10 A n 4 =

210.

Statisticasl Calculations (SD Mode)

• Press Flto enter the SD Mode for statistical calcula-

tions using standard deviation.

• If FIX or SCI is on the display, press F9 first.

• Data input always starts with Au.

• Example: To calculate ␴nҀ1, ␴n, o, n, ⌺x, and ⌺x2 for the

following data : 55, 54, 51, 55, 53, 53, 54, 52.

Enter SD Mode. F l

Input Data. A u 55 }

54 } 51 }

55 } 53 } }

54 } 52 }

Sample standard deviatio

Population standard deviation

n

A q

A p

— 16 —

52.

1.407885953

1.316956719

SD

0.

SD

Arithmetic mean A `

Number of data A r

Sum of values A o

Sum of squares of values A a

53.375

427.

22805.

SD

8.

SD

• }} inputs the same data twice (as above).

•You can also input multiple entries of the same data using

-. To input the data 110 ten times, for example, press

110 -10 }.

• The above results can be obtained in any order, and not necessarily that shown above.

•To delete data you have just input, press A[.

— 17 —

kMaking Corrections During Data Input

• Example 1: To change data you have just input.

Correct Actual

51 } 50 }A [

130 31 }

• Example 2: To change data you previously input.

Correct

51 }

130 31 }

120 -

120 31

Actual Correction

49 }

120 30 }

Correction

51 }

t130 -

31 }

t130 -

31 }

49 A [ 51 }

120 - 30 A [130 31 }

Technical Information

kKey and Their Functions

• General

Arithmetic calculations .......................... +, ,, -,

............. \, =

— 18 —

Clear (retains memory) ......................... k

Number input ........................................ 0 – 9, l

Power off ............................................... i

Power on; All clear ................................ t

Sign change .......................................... E

• Memory

Memory in ............................................. Y

Memory minus ...................................... A {

Memory plus ......................................... |

Memory recall ....................................... Z

• Special

Decimal-to-sexagesimal ........................ A O

Display/memory swap ........................... A N,

............. A d

Exponent ............................................... e

Internal rounding ................................... A b

Parentheses .......................................... O, P

Pi (3.1415926536) ................................ A x

Select mode .......................................... F

Sexagesimal-to-decimal ........................ I

Shifts key functions ............................... A

— 19 —

• Scientific Functions

Arc cosine ............................................. A V

Arc sine ................................................. A j

Arc tangent ............................................ A g

Common antilogarithm .......................... A Q

Common logarithm ................................ R

Cosine ...................................................W

Cube root .............................................. A D

Engineering ...........................................J, A P

Factorial ................................................ A f

Fraction ................................................. C

Fraction ................................................. A B

Hyperbolic ............................................. M

Natural antilogarithm ............................. A U

Natural logarithm ................................... T

Percent .................................................. A v

Polar-to-rectangular .............................. A z

Power ....................................................A w

Random number ................................... A c

Reciprocal ............................................. A X

Rectangular-to-polar ............................. A y

Root ...................................................... A s

Sine ....................................................... S

— 20 —

Square .................................................. A K

Square root ........................................... L

Tangent ................................................. h

Permutation ........................................... A m

Combination .......................................... A n

• Statistics (SD Mode)

Arithmetic mean .................................... A `

Data delete ............................................ A [

Data input .............................................. }

Number of data ..................................... A r

Population standard deviation ............... A p

Sample standard deviation ................... A q

Statistical register clear ......................... A u

Sum of squares of values ..................... A a

Sum of values ....................................... A o

kExponential Display Formats

This calculator can display up to 10 digits. Larger values are automatically displayed using exponential notation. In the case of decimal value, you can select between two formats that determine at what point exponential notation is used.

— 21 —

• NORM 1

With NORM 1, exponential notation is automatically used for integer values with more than 10 digits and decimal values with more than two decimal places.

• NORM 2

With NORM 2, exponential notation is automatically used for integer values with more than 10 digits and decimal values with more than nine decimal places.

To switch between NORM 1 and NORM 2

Press F9. There is no indication on the display of which for mat is currently in effect, but you can determine the setting by performing the following calculation.

0.005

5.

–03

NORM 1 format

NORM 2 format

1 \ 200 =

• All of the examples in this manual show calculation results

using the NORM 1 format.

kWhen you have a problem...

If calculation results are not what you expect or if an error occurs, perform the following steps.

1. F0 (COMP mode)

2. F4 (DEG mode)

3. F9 (NORM mode)

4. Check the formula you are working with to confirm it is

correct.

5. Enter the correct modes to perform the calculation and

try again.

— 22 —

kMaking Corrections During Calculations

• If you make a mistake when inputting a value (but did not

yet press an arithmetic operator key), press k to clear the value and then input the correct one.

• In a series of calculations, press k while an intermediate

result is displayed to clear only the last calculation performed.

•To change the operator key (+, , , -, \, Aw,

As, etc.) you just pressed, simply press the correct

operator key. In this case, the operator of the last key you press is used, but the operation retains the order of precedence of the operation for the first key you pressed.

kOverflow or Error Check

The following conditions make further calculation impossible. a. When a result (whether intermediate or final) or a

total accumulated in memory is greater than ±9.999999999 ҂ 10 display.)

b. When function calculations are performed using a value

that exceeds the input range. (“–E–” indicator appears on the display.)

c. When an illogical operation (such as an attempt to calcu-

late o and ␴ calculations. (“–E–” indicator appears on the display.)

d. When an illegal mathematical operation (such as division

by zero) is performed. (“–E–” indicator appears on display.)

99

. (“–E–” indicator appears on the

while n ҃ 0) is performed during statistical

n

— 23 —

e. The total number of nested parentheses levels exceeds

six, or when more than 18 pairs of parentheses are used. (“– 1–” indicator appears on the display.)

•To clear any of the above conditions, press t and per-

form the calculation from the beginning.

• In the case of condition e, you could also press k. This

clears the intermediate result just prior to the overflow, so you can continue with the calculation from that point.

• No error occurs when the result is within the range of

ѿ(1҂10

Ҁ99

) to Ҁ(1҂10

Ҁ99

). Instead, the display shows all

zeros.

kPower Supply

This calculator is powered by two AA-size manganese dry batteries (R6P (SUM-3) or UM-3). Replace batteries as soon as possible when display characters become dim and difficult to read.

• Press t to turn power on.

• Press i to turn power off.

•Power automatically turns off (but data in memory is re-

tained) if no key operation is performed for about six minutes.

Important!

Incorrect use of batteries can cause them to burst or leak, possible damaging the calculator.

• Be sure to replace the batteries at least once every two

years, regardless of how much the calculator is used. Old batteries may leak, causing serious damage to the interior of the calculator.

— 24 —

• The batteries that come in the calculator when you pur-

chase it are for testing only. They may not provide full service life.

• All data stored in memory is lost when you replace the

batteries. Be sure to write down important data before replacing the batteries.

• Always be sure to load the batteries so their positive (ѿ)

and negative (Ҁ) ends are facing correctly.

•Never mix batteries of different types.

• Never mix new batteries with old ones.

• Never try to charge batteries, take them apart, or allow

them to become shorted. Keep batteries away from direct flame and heat.

Keep batteries out of the reach of small children. If

•

swallowed, consult with your physician immediately.

To replace the batteries

1. Press i to tur n power off.

2. Remove the screws that hold the

back cover in place, and then remove the cover.

3. Remove the old batteries.

4. Install two new batteries with the

positive (ѿ) and negative (Ҁ ) ends facing correctly.

5. Replace the back cover and

secure it in place with the screws.

tto turn power on.

6. Press

— 25 —

Screws

Batteries

Screws

kOrder of Operations and Levels

Operations are performed in the following order of precedence.

1. Functions

1/y

2. xy, x

, R →P, P →R, nPr, nCr

3. ҂, 앦

4. ѿ, Ҁ

• Operations with the same precedence are performed from

left to right, with operations enclosed in parentheses performed first. If parentheses are nested, the operaitons enclosed in the innermost set of parentheses are performed first.

• Registers L

gisters, so calculations up to six levels can be stored.

• Each level can contain up to three open parentheses, so

parentheses can be nested up to 18 times.

• Example: The following operation uses 4 levels and 5

nested parentheses.

- O O O 3 + 4 - O O 5 + 4

2

The table below shows register contents following the above input.

through L6 store operations. There are six re-

1

— 26 —

Register Contents

x

4

L

(( 5 ѿ

1

L

4 ҂

2

L

((( 3 ѿ

3

L

2 ҂

4

L

5

L

6

kFormulas, Ranges, and Conventions

The following are the formulas, ranges, and conventions that are applied to various calculations that can be performed using this calculator.

Coordinate Transformation

• With polar coordinates, θ can be calculated within a range

of –180°쏝θ 울180°. The calculation range is the same for radians and grads.

Y

P (x, y)

y

X0

x

— 27 —

Pol

Rec

Y

P (r, )

θ

r

θ

X0

Permutation

• Input range: n 욷 r 욷 0 (n, r : natural numbers)

• Formula: nPr ҃

n!

(nҀr)!

Combination

• Input range: n 욷 r 욷 0 (n, r : natural numbers)

• Formula: nCr ҃

n!

n!(nҀr)!

Population Standard Deviation

Sample Standard Deviation

Arithmetic Mean

— 28 —

kSpecifications

Power supply : Tw o AA-size manganese dry batteries

Battery Life: Approximately 9,000 hours continuous

Power Consumption: 0.0004W Input Ranges:

sinx cosx tanx

–1

sin

x

–1

x

cos

tan–1x

sinhx

coshx

tanhx

–1

sinh

x

–1

cosh

–1

tanh

logx/lnx

x

10

(UM-3 or R6P (SUM-3))

operation on type UM-3, 11,000 hours continuous operation on R6P(SUM-3)

Input RangeFunctions

(DEG)앚x앚쏝9҂10 (RAD)앚x앚쏝5҂107␲ rad (GRA)앚x앚쏝1҂10

9

10

grad

앚x앚울 1

100

10

앚x앚쏝 1 ҂

앚x앚울 230.2585092

앚x앚쏝 1҂

앚x앚쏝 5 ҂

1울 x 쏝 5 ҂

x

앚x앚쏝 1

x

1҂

–1҂

–99

10

100

10

99

10

울 x 쏝 1 ҂

100

쏝 x 쏝

For sinh and tanh,errors are cumulative and accuracy is affected at a certain point when x=0.

99

10

100

10

100

— 29 —

However, for tan x:

앚x앚≠ 90(2nѿ1):DEG 앚x앚≠ ␲Ⲑ2·(2nѿ1):RAD 앚x앚≠ 100(2nѿ1):GRA

x

e

x

2

x

1/x

3

x

x!

nPr/nCr

R→P

P→R

°’ ”

y

x

Input RangeFunctions

100

–1҂

10

쏝 x 울 230.2585092

0 울 x 쏝 1 ҂

앚x앚쏝 1҂

0울 x 울

100

10

50

10

100

10

;

x ≠

100

10

69 (

x is an integer)

0

0 울 r 울n

10

n 쏝1҂10

(n and r are integers)

x2 ѿ y2 쏝1҂10

0 울 r 쏝 1҂10 (DEG)앚␪앚쏝9҂10 (RAD)앚␪앚쏝5҂107␲ rad (GRA)앚␪앚쏝1҂10

Sexagesimal: 앚a앚, b, c쏝10

100

However, for tan

9

앚␪앚≠ 90(2nѿ1):DEG 앚␪앚≠ ␲Ⲑ2·(2nѿ1):RAD

10

grad

앚␪앚≠ 100(2nѿ1):GRA

100

0 울 b, c

Decimal: 앚x앚 울2.777777777҂10

x 쏜 0: –1҂10 x ҃ 0: y 쏜 0 x 쏝 0: y ҃ n; (n is an integer)

However: –1҂10

100

쏝 y log x 쏝100

1

2nѿ1

100

쏝 y log 앚x앚쏝100

— 30 —

␪

:

96

Input RangeFunctions

x 쏜0: y ≠ 0

100

–1҂10

쏝1/y log x 쏝100

x ҃ 0: y 쏜 0

1/y

x

x 쏝 0: y ҃ 2nѿ1; (n ≠ 0; n is an integer)

However: –1҂10

Total of integer, numerator, and denominator

a b/c

must be 10 digits or less (including division

1

n

100

쏝1/y log 앚x앚쏝100

marks).

y

, x

50

100

1/y

, x!, and

3

x , so accuracy may be

앚x앚쏝 1҂10 앚n앚쏝 1҂10

SD

␴n , o : n ≠ 0 ␴n –1 : n ≠ 0, 1

• Errors are cumulative with such internal continuous calculations as x adversely affected.

Operating Temperature:

0°C–40°C (32°F–104°F)

Dimensions: 19(H)쎹73(W)쎹147(D) mm

Weight: 104g including batteries

— 31 —

Calculation Capacity:

• Input/ Basic Calculations

10-digit mantissa; or 10-digit mantissa plus 2-digit exponent up to 10

±99

— 32 —

CASIO COMPUTER CO., LTD.

6-2, Hon-machi 1-chome,

Shibuya-ku, Tokyo 151-8543, Japan

SA9707-B Printed in China

Imprimé en Chine

Casio fx-82SX User's Guide

Specifications and Main Features

Frequently Asked Questions

User Manual