Casio fx-115WA Page 27 User Manual Download | Manualshive

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앫

25

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Scientific Constants

(fx-991WA)

• A total of 40 commonly-used scientific constants, such

as the speed of light in a vacuum and Planck's constant
are built-in for quick and easy lookup whenever you need
them.

• Simply input the number that corresponds to the scien-

tific constant you want to look up and it appears instantly
on the display.

• See the Scientific Constant Table shown below for a com-

plete list of available constants.

•

Example:

To determine how much total energy a per-

son weighing 65kg has (E = mc

2

)

65

L

CONST

28

CONST28

28 is the “speed of light in vacuum” constant number.

0.

65 Co

K

0.

65 Co

2

=

65 Co

2

5.841908662

18

• Scientific Constant Table

Based on ISO Standard (1992) data and CODATA Bulletin
63 (1986) data.

Number

Constant Name

Symbol

01

proton mass

mp

02

neutron mass

mn

03

electron mass

me

04

muon mass

m

µ

05

Bohr radius

a

0

06

Planck's constant

h

07

nuclear magneton

µ

N

08

Bohr magneton

µ

B

09

Planck's constant, rationalized (h-bar)

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Summary of Contents for fx-115WA

Page 1: ...E fx 115WA fx 991WA User s Guide ...

Page 2: ...it out from the bottom To Replace the cover Grasp the top of the cover and slide the unit in from the bottom Always slide the unit into the cover with the unit s display end first Never slide the keyboard end of the unit into the cover CASIO ELECTRONICS CO LTD Unit 6 1000 North Circular Road London NW2 7JD U K ...

Page 3: ...ever charge batteries try to take batteries apart or allow batteries to become shorted Never expose bat teries to direct heat or dispose of them by incinera tion Misuse of batteries can cause them to leak acid that can cause damage to nearby items and creates the possibility of fire and personal injury Always make sure that a battery s positive k and negative l sides are facing correctly when you ...

Page 4: ...rmally replace the battery at least once every three years Dead battery can leak causing damage to and malfunc tion of the calculator Never leave the 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 nor mal expected battery life Low battery power can cause memory contents ...

Page 5: ... trou sers or other tight fitting clothing where it might be sub jected to twisting or bending Never try to take the calculator apart Never press the keys of the calculator with a ball point pen or other pointed object Use a soft dry cloth to clean the exterior of the unit If the calculator becomes very dirty wipe it off with a cloth moistened in a weak solution of water and a mild neutral househo...

Page 6: ...11 kFraction Calculations 11 kDecimal to Fraction Conversion 11 kFraction to Decimal Conversion 11 Percentage Calculations 12 Scientific Function Calculations 13 kTrigonometric Inverse Trigonometric Functions 13 kHyperbolic Inverse Hyperbolic Functions 13 kAngle Unit Conversion 14 kCommon and Natural Logarithms Antilogarithms 14 kSquare Roots Cube Roots Roots Squares Cubes Reciprocals Factorials R...

Page 7: ...ions fx 991WA 23 Scientific Constants fx 991WA 25 Base n Calculations 26 Degrees Minutes Seconds Calculations 28 Technical Information 28 kWhen you have a problem 28 kError Messages 29 kOrder of Operations 30 kStacks 31 kPower Supply 31 kInput Ranges 33 Specifications 35 Two line Display You can simultaneously check the calculation formula and its answer The first line displays the calculation for...

Page 8: ... Page Page Page Page Page Page Page Page 11 8 2 15 15 25 14 17 15 14 11 17 28 14 27 14 27 16 11 15 14 14 14 10 28 10 10 10 13 10 13 10 10 28 13 13 13 19 23 23 10 20 23 19 10 10 10 10 10 10 10 10 19 19 20 16 20 16 20 16 8 10 18 8 20 16 20 16 20 16 18 18 18 16 18 16 18 16 20 20 15 15 15 14 12 10 9 17 23 LOGIC 24 15 27 x T C DRG fx 991WA ON CLEAR Rec nCr 18 18 fx 115WA nPr nPr CONV nPr nCr CONV Key L...

Page 9: ...Unit Modes Degrees DEG R Radians RAD T Grads GRA B Display Modes Exponential notation NORM1 Canceling FIX and SCI NORM2 specification Number of decimal FIX Fix place specification Number of significant SCI Sci digit specification Exponential display range ENG ENG specifications Note Mode indicators appear in the lower part of the display except for the Base n indicators which appear in the ex pone...

Page 10: ...lation into two or more parts 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 in serts the input at the insert cursor position Press e r A K or returns to the normal cur sor from the i...

Page 11: ...eger 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 All of the examples in this manual show calculation re sults using the NORM 1 format k Answer Memory Whenever you press after inputting values or an e...

Page 12: ...calculating cumulative totals Independent memory uses the same memory area as variable M To clear independent memory M input 0 j 3 Example 23 9 32 23 9 j 3 53 6 47 53 6 45 2 90 45 2 A Total 11 0 3 k Variables There are nine variables A through F M X andY which can be used to store data constants results and other values Use the following operation to delete data assigned to all nine variables A C ...

Page 13: ... in decimal format whenever the total number of digits of a fractional value integer numerator denominator separator marks exceeds 10 Example 1 1 2 C 3 1 C 4 C 5 Example 2 1 6 1 C 2 1 6 Fraction decimal calculation results are always decimal k Decimal to Fraction Conversion Example 2 75 2 2 75 2 75 C A B k Fraction to Decimal Conversion Example 0 5 Fraction Decimal 1 C 2 2 100 1 2 3 4 2 3 4 00 11 ...

Page 14: ...ple 3 To add 15 onto 2500 2500 15 A v Example 4 To discount 3500 by 25 3500 25 A v Example 5 If 300 grams are added to a test sample originally weighing 500 grams what is the percentage increase in weight 100 160 300 500 A v Example 6 If temperature changes from 40 C to 46 C what percentage did it rise 100 15 46 40 A v 0 500 1 2 00 180 00 75 00 2625 00 160 00 2875 00 300 500 500 15 00 46 40 40 ...

Page 15: ...63 52 41 q q q 1 R S 63 I 52 I 41 I Example 2 cos rad q q q 2 T W R A x 3 T Example 3 cos 1 rad q q q 2 T W A V R L 2 2 T g A x Example 4 tan 10 741 q q q 1 R A g 0 741 k Hyperbolic Inverse Hyperbolic Functions Example 1 sinh 3 6 M S 3 6 Example 2 sinh 1 30 M A j 30 0 89785901200 0 500 R T 0 78539816300 0 2500 36 5384457700 T R π 3 2 2 π 4 4 09462222400 18 2854553600 ...

Page 16: ...5 A v 2 R 243 5070629 4 25r k Common and Natural Logarithms Antilogarithms Example 1 log 1 23 R 1 23 Example 2 In 90 loge 90 T 90 Example 3 e10 A U 10 Example 4 101 5 A Q 1 5 Example 5 24 2 w 4 k Square Roots Cube Roots Roots Squares Cubes Reciprocals Factorials Random Numbers and π Example 1 2 3 5 L 2 L 3 L 5 Example 2 3 5 3 27 D 5 D D 27 1 2 3 D R G F F F 1 R 0 08990511100 4 4998096700 22026 465...

Page 17: ...e 3 7 123 123 7 A H 123 Example 4 123 302 123 30 K Example 5 123 12 N Example 6 R 3 a 4 a T a Example 7 8 8 A f Example 8 To generate a random number between 0 000 and 0 999 A M Example results differ each time Example 9 3π 3 A x k FIX SCI RND Example 1 200 7 14 400 200 7 14 F F F F 1 3 200 7 14 Performing the same calculation using the specified number of decimal places 200 7 Internal rounding A ...

Page 18: ...meters 56088 J Example 2 To convert 0 08125 grams to milligrams 0 08125 J k Inputting ENG Calculation Symbols F F F F F 1 enters the ENG mode in which ENG symbols can be used in calculations To exit the ENG mode press F F F F F 2 The following are the nine ENG symbols that can be used in ENG mode calculations Key Operation Unit Symbol A k 103 k kilo A M 106 M Mega A g 109 G Giga A t 1012 T Tera A ...

Page 19: ...xponen tial value in the Unit column without inputting the ENG symbol Example 9 10 0 9 m milli F F F F F 1 0 ENG 9 10 900 9 1 m In the ENG mode even standard non ENG calculation results are displayed using ENG symbols A P 0 9 J 900 9 1 m k Coordinate Conversion Pol x y Rec r θ Calculation results are automatically assigned to vari ables E and F Example 1 To convert polar coordinates r 2 60 to rect...

Page 20: ...Example To determine how many different 4 member groups can be organized in a group of 10 individuals fx 115WA 10 n 4 fx 991WA 10 A n 4 Statistical Calculations k Standard Deviation SD Mode Press F F 1 to enter the SD Mode for statistical calculations using standard deviation Data input always starts with A m to clear statisti cal memory Input data is used to calculate values for n Σx Σx2 o σn and...

Page 21: ... S S inputs the same data twice You can also input multiple entries of the same data us ing A G To input the data 110 ten times for example press 110 A G 10 S The above results can be obtained in any order and not necessarily that shown above To delete data you have just input press A U k Probability Distribution Calculations Press A D to produce the screen shown below Input a value from 1 to 4 to...

Page 22: ...ower regression r 2 Inverse regression r 3 Quadratic regression Data input always starts with A m to clear statisti cal memory 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 Linear Regression The regression formula for linear regression is y A Bx A N xσn 1 A l p A d yσn A c yσn 1 A q Regressio...

Page 23: ...eric Pressure at 18 C 18 A b Temperature at 1000 hPa 1000 A O Quadratic Regression The regression formula for quadratic regression is y A Bx Cx2 Input data using the following key sequence x data P y data S Example Perform quadratic regression to de termine the regression formula terms and correlation coefficient for the data nearby Next use the regression for mula to estimate the values for y es ...

Page 24: ...ions S S inputs the same data twice You can also input multiple entries of the same data us ing 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 To delete data you have just input press A U Complex Number Calculations CMPLX Mode Press F 2 to enter the CMPLX Mode for calculations that inc...

Page 25: ... which is pre sumed to exist as coordinates on a Gaussian plane Example To obtain the absolute value r and argu ment θ for the complex number 3 4i when DEG is set for the angle unit mode Imaginary number axis Real number axis Determine the absolute value A A R 3 4 i T 5 CMPLX Determine the argument A a R 3 4 i T 53 13010235 Metric Conversions fx 991WA A total of 20 different conversion pairs are b...

Page 26: ...lletin 63 1986 data Number Conversion Pair Number Conversion Pair 01 in cm 21 oz g 02 cm in 22 g oz 03 ft m 23 lb kg 04 m ft 24 kg lb 05 yd m 25 atm Pa 06 m yd 26 Pa atm 07 mile km 27 mmHg Pa 08 km mile 28 Pa mmHg 09 n mile m 29 hp kW 10 m n mile 30 kW hp 11 acre m2 31 kgf cm2 Pa 12 m2 acre 32 Pa kgf cm2 13 gal US r r r r r 33 kgf m J 14 r r r r r gal US 34 J kgf m 15 gal UK r r r r r 35 lbf in2 k...

Page 27: ...Table shown below for a com plete list of available constants Example To determine how much total energy a per son weighing 65kg has E mc2 65 L CONST 28 CONST28 28 is the speed of light in vacuum constant number 0 65Co K 0 65Co2 65Co2 5 841908662 18 Scientific Constant Table Based on ISO Standard 1992 data and CODATA Bulletin 63 1986 data Number Constant Name Symbol 01 proton mass mp 02 neutron ma...

Page 28: ...volume of ideal gas Vm 27 molar gas constant R 28 speed of light in vacuum C0 29 first radiation constant C1 30 second radiation constant C2 31 Stefan Boltzmann constant σ 32 permittivity of vacuum ε0 33 permeability of vacuum µ0 34 magnetic flux quantum φ0 35 standard acceleration of gravity g 36 astronomical unit AU 37 parsec pc 38 Celsius temperature t 39 Newtonian constant of gravitation G 40 ...

Page 29: ...oduct or logical sum xor exclusive logical sum xnor exclu sive logical sum negation Not negation and Neg mi nus The following are the allowable ranges for each of the available number systems Binary 1000000000 x 1111111111 0 x 0111111111 Octal 4000000000 x 7777777777 0 x 3777777777 Decimal 2147483648 x 2147483647 Hexadecimal 80000000 x FFFFFFFF 0 x 7FFFFFFF Example 1 To perform the following calcu...

Page 30: ...gesimal and decimal values Example 1 To convert the decimal value 2 258 to a sexagesimal value 2 258 2 258 A O 2 15 28 8 Example 2 To perform the following calculation 12 34 56 3 45 12 I 34 I 56 I 3 45 0 43 24 31 2 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 F 1 COMP mode 2 F F F 1 DEG mode 3 F F...

Page 31: ...on page 9 for details Ma ERROR Cause Calculation result is outside the allowable calculation range Attempt to perform a function calculation using a value that exceeds the allowable input range 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 a...

Page 32: ...ed and then the function key is pressed x2 x 1 x 3 Powers and roots xy x 4 ab c 5 Abbreviated multiplication format in front of π memory name or variable name 2π 5A πA 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 sin 1 cos 1 tan 1 sinh cosh tanh sinh 1 cosh 1 tanh 1 7 Abbreviated multiplication format in front of ...

Page 33: ...elatively bright light is present The TWO WAY POWER system however lets you con tinue 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 t...

Page 34: ...ss to turn power on Be sure not to skip this step Auto Power Off Calculator power automatically turns off if you do not per form any operation for about six minutes When this hap pens press to turn power back on ...

Page 35: ...0009 1010 tanx DEG Same as sinx except when x 2n 1 90 RAD Same as sinx except when x 2n 1 π 2 GRA Same as sinx except when x 2n 1 100 sin 1x 0 x 1 cos 1x tan 1 x 0 x 9 999999999 1099 sinhx 0 x 230 2585092 coshx sinh 1 x 0 x 4 999999999 1099 cosh 1 x tanhx 0 x 9 999999999 10 1 tanh 1 x logx lnx 0 x 10 x 9 999999999 1099 x 99 99999999 ex 9 999999999 1099 x 230 2585092 x 0 x 1 10100 x2 x 1 1050 1 x x...

Page 36: ...990 590 x 0 1 10100 ylogx 100 xy x 0 y 0 x 0 y n n is an integer However 1 10100 ylog x 100 y 0 x G 0 1 10100 1 x logy 100 x y y 0 x 0 y 0 x 2n 1 n G 0 n is an integer However 1 10100 1 x log y 100 ab c x 1 1050 y 1 1050 SD n 1 10100 REG x n y n o p A B r n G 0 x n 1 y n 1 n G 0 1 Erros are cumulative with such internal continuous cal culations as xy x x x and 3 x so accuracy may be adversely affe...

Page 37: ... and a single G13 Type button battery LR44 Battery Life Approximately 3 years 1 hour use per day Dimensions 10 H 76 W 150 D mm 3 8 H 3 W 57 8 D Weight 85 g 3oz including battery Power Consumption 0 0001W Operating Temperature 0 C 40 C 32 F 104 F ...

Page 38: ...SA9911 A Printed in China HA310537 1 U S Pat 4 410 956 CASIO COMPUTER CO LTD 6 2 Hon machi 1 chome Shibuya ku Tokyo 151 8543 Japan ...

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