fx-115WA
fx-991WA
User’s Guide
E
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Safety Precautions
Be sure to read the following safety precautions before
using this calculator. Keep this manual handy for later ref-
erence.
Caution
This symbol is used to indicate information that can
result in personal injury or material damage if ignored.
Batteries
• After removing the batteries from the calculator, put
them in a safe place where there is no danger of
them getting into the hands of small children and
accidently swallowed.
• Keep batteries out of the reach of small children. If
accidently swallowed, consult with a physician im-
mediately.
• Never 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
load it into the calculator.
• Remove the batteries if you do not plan to use the
calculator for a long time.
• Use only the type of batteries specified for this cal-
culator 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 danger of fire and personal injury.
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• The displays and illustrations (such as key markings)
shown in this User’s Guide are for illustrative pur-
poses only, and may differ somewhat from the ac-
tual items they represent.
• The contents of this manual are subject to change
without notice.
• In no event shall CASIO Computer Co., Ltd. be li-
able to anyone for special, collateral, incidental, or
consequential damages in connection with or aris-
ing 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
culator for the first time.
key before using the cal-
• Even if the calculator is operating normally, 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 to
become corrupted or lost completely. Always keep
written records of all important data.
• Avoid use and storage in areas subjected to tempera-
ture 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-
come exposed to very high temperatures. Heat can
cause discoloration or deformation of the calculator’s
case, and damage to internal circuitry.
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• 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 elements 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 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 household detergent. Wring out all excess mois-
ture before wiping the calculator.Never use thinner, ben-
zine or other volatile agents to clean the calculator. Do-
ing so can remove printed markings and damage the
case.
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Contents
Safety Precautions ........................................... 1
Handling Precautions ...................................... 2
Two-line Display ............................................... 5
Key Layout ........................................................ 6
Before Starting Calculations... ...................... 7
kModes .................................................................... 7
kInput Capacity ........................................................ 8
kMaking Corrections During Input ........................... 8
kReplay Function ..................................................... 8
kError Locator .......................................................... 9
kExponential Display Formats ................................. 9
kAnswer Memory ..................................................... 9
Basic Calculations ......................................... 10
Memory Calculations ..................................... 10
kIndependent Memory ........................................... 10
kVariables .............................................................. 10
Fraction Calculations .................................... 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,
Random Numbers and π .......................................... 14
kFIX, SCI, RND ..................................................... 15
kENG Calculations ................................................ 16
kInputting ENG Calculation Symbols..................... 16
kCoordinate Conversion (Pol(x, y), Rec (r, θ)) ............ 17
kPermutation ......................................................... 18
kCombination ......................................................... 18
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Statistical Calculations .................................. 18
kStandard Deviation (SD Mode) ............................ 18
kProbability Distribution Calculations ................... 19
kRegression Calculations (REG Mode) ................. 20
Complex Number Calculations
(CMPLX Mode) ................................................ 22
kAbsolute Value/Argument Calculation ................. 23
Metric Conversions (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 formula.
The second line displays the answer.
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Key Layout
Key Layout
<fx-991WA>
RE8PLAY
Page
11
ALPHA
2
SHIFT
MODE
ON/CLEAR
Page 15 27
24
17
(
Rec
15
CONV
x! LOGIC
Page
Page 17 23
15
25
11
17
14
15
14
28
14 27 14 27
DEC
HEX
BIN OCT
10
e
Page
Page
16
11
14
10
15
14
14
10 28 10
10 13 10 13 10
A
B
C
sin-1
D
cos-1
E
tan-1
F
Page
Page
10
19
28
23
13
13
13
20 23 23 10 19 10 10 10
DISTR
Re<->lm
r
arg
Abs
M-
X
Y
M
19 DT CL 19
10
Page
Page
10
10
10
10
20 16 20 16 20 16
8
10 18
A
M
B
G
C
T
INS
McI ScI
Page
Page
8
20 16 20 16 20 16
18
18
y
µ
m
k
nPr
nCr
Page
18 16 18 16 18 16
20
20
y
f
p
n
Page
Page
15
15
15
10
14
12
Rnd
Ran#
DRG
9
18
CONV
nPr
nPr
fx-115WA:
nCr
18
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Before Starting Calculations...
k Modes
Mode
Name
Mode
Application
Indicator
Calculation Modes
Normal calculations
COMP
–
Complex number
calculations
CMPLX
CMPLX
Standard deviation
calculations
SD
SD
Regression calculations
REG
REG
Base-n calculations
BASE-N b (binary)
o (octal)
d (decimal)
H (hexadecimal)
Angle Unit Modes
Degrees
DEG
RAD
GRA
R
Radians
T
B
Grads
Display Modes
Exponential notation
(Canceling FIX and SCI
specification)
NORM1
NORM2
–
–
Number of decimal
place specification
FIX
SCI
Fix
Sci
Number of significant
digit specification
Exponential display range
specifications
ENG
ENG
Note!
• Mode indicators appear in the lower part of the display,
except for the Base-n indicators which appear in the ex-
ponent part of the display.
• The ENG mode cannot be selected while the calculator
is in the CMPLX or BASE-N mode.
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• You cannot set the angle unit or the display mode while
the calculator is in the BASE-N mode.
• The COMP, CMPLX, SD, and REG modes can be used
in combination with the angle unit modes.
• Be sure to check the current calculation mode (SD, REG,
COMP, CMPLX) and angle unit mode (DEG, RAD, GRA)
before beginning a calculation.
k Input Capacity
• The memory area used for calculation input can hold 79
“steps.” Whenever you input the 73rd step of any calcu-
lation, the cursor changes from “_” to “k” to let you know
memory is running low. If you still need to input more,
you should divide your calculation 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 insert cursor.
k Replay Function
• Pressing r or e recalls the last calculation you per-
formed. You can then make any changes you want in
the calculation and re-execute it.
• Pressing t does not clear Replay memory, so you can
recall the last calculation even after you press t.
• Replay memory is cleared whenever you start a new
calculation, change to another mode, or turn off power.
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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.
k Exponential Display Formats
This calculator can display up to 10 digits. Larger values
are automatically displayed using exponential notation. In
the case of decimal values, you can select between two
formats that determine at what point exponential notation
(
)
is used. Press F F F F 3 1 or 2 to select
NORM 1 or NORM 2.
• 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.
• 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 ex-
pression, the calculated result is automatically stored in
Answer Memory. You can recall Answer Memory con-
tents 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 changed if the opera-
tion performed by any of the above key operations re-
sults in an error.
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Basic Calculations
• Use the COMP mode for basic calculations.
• Example 1: 3҂(5҂10–9)
3 - R 5 e D 9 T =
1.5-08
80.00
• Example 2: 5҂(9ѿ7)
5 - R 9 + 7 T =
• You can skip all T operations before =.
Memory Calculations
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 j 3.
• Example:
32.00
23 ѿ 9 ҃ 32 23 + 9 j 3
53 Ҁ 6 ҃ 47
47.00
53 , 6 |
Ҁ) 45 ҂ 2 ҃ 90
(Total) –11 45 - 2 A {
90.00
0 3
–11.00
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 = .
• Use the following operation to delete data assigned to a
particular variable: 0 j 1. This operation deletes the
data assigned to variable A.
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• Example: 193.2 Ö 23 ҃ 8.4
193.2 Ö 28 ҃ 6.9
193.2 j 1 \ 23 =
8.400
6.900
p 1 \ 28 =
Fraction Calculations
k Fraction Calculations
• Use the COMP mode for fraction calculations.
• Values are automatically displayed in decimal format
whenever the total number of digits of a fractional value
(integer ѿ numerator ѿ denominator ѿ separator marks)
exceeds 10.
2
3
4
5
• Example 1:
ѿ 1
2 C 3 + 1 C 4 C 5 =
2 7 15.00
1
2
• Example 2:
ѿ1.6
1 C 2 + 1.6 =
2.100
• Fraction/decimal calculation results are always decimal.
k Decimal-to-Fraction Conversion
3
4
• Example: 2.75 → 2
2.75 =
2.75
2 3 4.00
C
11 4.00
A B
k Fraction-to-Decimal Conversion
1
2
• Example:
↔ 0.5 (Fraction ↔Decimal)
1 2.00
1 C 2 =
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0.500
C
C
1 2.00
Percentage Calculations
• Use the COMP mode for percentage calculations.
• Example 1: To calculate 12% of 1500
1500 - 12 A v
180.00
• Example 2: To calculate what percentage of 880 is 660
660 \ 880 A v
75.00
• Example 3: To add 15% onto 2500
2500 - 15 A v +
2875.00
• Example 4: To discount 3500 by 25%
3500 - 25 A v ,
2625.00
• Example 5: If 300 grams are added to a test sample
originally weighing 500 grams, what is the percentage
increase in weight?
300 ѿ 500
҂ 100 ҃ 160 (%)
500
160.00
300 + 500 A v
• Example 6: If temperature changes from 40°C to 46°C,
what percentage did it rise?
46 Ҁ 40
҂ 100 ҃ 15 (%)
40
46 , 40 A v
15.00
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Scientific Function Calculations
• Use the COMP mode for scientific function calculations.
• ꢀ = 3.14159265359
k Trigonometric/Inverse Trigonometric
Functions
• Example 1: sin63°52o41ǥ
“
”
→
q q q 1
R
0.89785901200
S 63 I 52 I 41 I =
R
π
• Example 2: cos
(
q q q 2
rad)
3
“
”
→
T
0.500
W R A x \ 3 T =
T
2
2
π
4
”
• Example 3: cosҀ1
҃
rad
“
→
q q q 2
T
0.78539816300
W A V R L 2 \ 2 T =
g \ A x =
T
0.2500
• Example 4: tanҀ10.741
“
”
→
q q q 1
R
36.5384457700
A g 0.741 =
R
k Hyperbolic/Inverse Hyperbolic
Functions
• Example 1: sinh 3.6
18.2854553600
M S 3.6 =
• Example 2: sinhҀ1 30
M A j 30 =
4.09462222400
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k Angle Unit Conversion
• Press A v to display the following menu.
D
R
G
1 2 3
• Pressing 1, 2, or 3 converts the displayed value to
the corresponding angle unit.
• Example : To convert 4.25 radians to degrees
“
”
→
F F F 1
R
r
4.25
(
)
4.25 A v 2 R =
243.5070629
k Common and Natural Logarithms/
Antilogarithms
0.08990511100
• Example 1: log 1.23 R 1.23 =
• Example 2: In 90 (҃log 90)
e
4.4998096700
22026.4657900
31.622776600
16.00
T 90 =
• Example 3: e10
• Example 4: 101.5
• Example 5: 24
A U 10 =
A Q 1.5 =
2 w 4 =
k Square Roots, Cube Roots, Roots,
Squares, Cubes, Reciprocals,
Factorials, Random Numbers and π
• Example 1: 2ѿ 3҂
5
5.28719690900
–1.29002405300
L 2 + L 3 - L 5 =
• Example 2: 3 5ѿ 3 ꢀ27
D 5 + D D 27 =
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1
7
• Example 3: 7 123 ( = 123 )
1.98864779500
7 A H 123 =
• Example 4: 123ѿ302
123 + 30 K =
1023.00
1728.00
• Example 5: 123
12 N =
1
• Example 6:
1
3
1
4
ꢀ
12.00
3
4
a , a T a =
R
40320.00
• Example 7: 8!
8 A f =
• Example 8: To generate a random number between
0.000 and 0.999
0.66400
A M =
Example (results differ each time)
9.42477796100
• Example 9: 3π
3 A x =
k FIX, SCI, RND
• Example 1: 200Ö7҂14҃400
400.00
200 \ 7 - 14 =
400.00000
(Specifies three
decimal places.)
F F F F 1 3
Fix
(Calculation continues using 10
display digits)
28.57100
200 \ 7 =
- 14 =
400.00000
Performing the same calculation using the specified
number of decimal places
28.57100
200 \ 7 =
28.57100
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(Internal rounding)
A Q
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399.99400
- 14 =
• Press F F F F 3 1 to clear FIX specification.
• Example 2: 1Ö 3, displaying result with two significant
digits (SCI 2)
3.3–01
F F F F 2 2 1 \ 3 =
Sci
• Press F F F F 3 1 to clear SCI specification.
k ENG Calculations
• Example 1: To convert 56,088 meters to kilometers
56.088003
56088 = J
• Example 2: To convert 0.08125 grams to milligrams
81.25–03
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
A M
A g
A t
A m
A N
A n
A p
A f
103
k (kilo)
M (Mega)
G (Giga)
T (Tera)
m (milli)
µ (micro)
n (nano)
p (pico)
106
109
1012
10–3
10–6
10–9
10–12
10–15
f (femto)
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* For displayed values, the calculator selects the ENG sym-
bol that makes the numeric part of the value fall within
the range of 1 to 1000.
* ENG symbols cannot be used when inputting fractions.
* The ENG mode cannot be used in combination with the
CMPLX, or BASE-N modes.
• Performing any of the key operations in the above table
while you are not in the ENG mode inputs the exponen-
tial value in the “Unit” column (without inputting the ENG
symbol).
• Example: 9Ö10 = 0.9 m (milli)
0.
F F F F F 1
ENG
9Ϭ1
m
900.
9 \ 10 =
In the ENG mode, even standard (non-ENG)
calculation results are displayed using ENG symbols.
A P
0.9
9Ϭ1
m
900.
J
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 (r҃2, ҃60°)
to rectangular coordinates (x, y) (DEG mode)
1.00
x
y
A F 2 P 60 T =
0 o
R
1.73205080800
• 0 n, 0 o swaps displayed value with value in
memory.
• Example 2: To convert rectangular coordinates (1, 3)
to polar coordinates (r, ) (RAD mode)
2.00
r
f 1 P L 3 T =
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1.04719755100
0 o
θ
• 0 n, 0 o swaps displayed value with value in
memory.
k Permutation
• Example: To determine how many different 4-digit val-
ues 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).
7 A m 4 =
840.
k Combination
• Example: To determine how many different 4-member
groups can be organized in a group of 10 individuals
fx-115WA ................ 10 n 4 =
210.
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.
0 1 Σx2
0 2 Σx
• Input data is used to calculate values for
n, Σx, Σx , o, σn and σn-1 which you can
recall using the key operations noted
nearby.
2
0 k
A M
n
o
A A σn
A N σn-1
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• Example: To calculate σnҀ1, σn, o, n, Σx, and Σx2 for the
following data : 55, 54, 51, 55, 53, 53, 54, 52
Enter SD Mode F F 1
A m = (Memory Clear)
55 S 54 S 51 S 55 S
52.00
53 S S 54 S 52 S
SD
1.40788595300
(Sample Standard Deviation σnҀ1) A N =
1.31695671900
(Population Standard Deviation σn) A A =
53.37500
8.00
(Arithmetic Mean o)
(Number of Data n)
(Sum of Values Σx)
A M =
0 k
427.00
0 H
(Sum of Squares ofValues Σx 2
)
0 G
22805.00
Data Input Precautions
• 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.
(
(
(
P
Q
R
→t
1 2 3
4
• Input a value from 1 to 4 to select the probability
distribution calculation you want to perform.
P(t)
Q(t)
R(t)
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• Example : Using the x-data values input in the example
on page 20, determine the normalized variate (→t) for
x = 53 and normal probability distribution P(t).
53 A D 4 (→t) =
-0.284747398
A D 1 (P() -0.28 F =
0.38974
k Regression Calculations (REG Mode)
• Press F F 2 to enter the REG mode and then se-
lect one of the following regression types.
1: Linear regression
2: Logarithmic regression
3: Exponential regression
r 1: Power 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.
0 G Σx2 A N
0 H Σx A l
xσn-1
p
yσn
yσn-1
0 k
0 h Σy2 A c
n
A d
0 n Σy A q Regression coefficient A
0 o Σxy A w Regression coefficient B
0 M Σx3 A e Regression coefficient C
0 x Σx2y A J Correlation coefficient r
0 y Σx4 A O
m
n
A M
o
A b
xσn
A A
• Linear Regression
The regression formula for linear regression is: y ҃ A ѿ Bx.
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• Example: Atmospheric Pressure vs. Temperature
Perform linear regression to de-
termine the regression formula
Atmospheric
Temperature
Pressure
10°C
15°C
20°C
25°C
30°C
1003 hPa
1005 hPa
1010 hPa
1011 hPa
1014 hPa
terms and correlation coefficient
for the data nearby. Next, use the
regression formula to estimate at-
mospheric pressure at 18°C and
temperature at 1000 hPa.
Enter REG Mode (Linear Regression)
q q 2 1
A m = (Memory Clear)
10 P1003 S 15 P1005 S
20 P1010 S 25 P 1011 S
30 P1014 S
30.00
REG
997.400
0.5600
(Regression Coefficient A)
(Regression Coefficient B)
(Correlation Coefficient r)
(Atmospheric Pressure at 18°C)
(Temperature at 1000 hPa)
A q =
A w =
A J =
18 A b
0.98260736800
1007.4800
4.64285714300
1000 A O
• Quadratic Regression
• The regression formula for quadratic regression is:
2
y = A + Bx +Cx .
• Input data using the following key sequence.
<x-data> P <y-data> S
• Example:
Perform quadratic regression to de-
xi
29
yi
1.6
termine the regression formula terms
and correlation coefficient for the data
nearby. Next, use the regression for-
mula to estimate the values for ˆy (es-
timated value of y) for xi = 16 and ˆx
(estimated value of x) for yi = 20.
50
23.5
38.0
46.4
48.0
74
103
118
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Enter REG mode (Quadratic regression)
F F 2 r 3
A m =
29 P 1.6 S 50 P 23.5 S
74 P 38.0 S103 P 46.4 S
118 P 48.0 S
118.
REG
(Regression Coefficient A)
(Regression Coefficient B)
(Regression Coefficient C)
(ˆy when xi = 16)
A q =
-
35.59856934
A w = 1.495939413
-
-
6.71629667 03
A e =
16 A b
20 A O
A O
-
13.38291067
47.14556728
175.5872105
(ˆx1 when yi = 20)
(ˆx2 when yi = 20)
Data Input Precautions
• 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 include complex numbers.
• You can use variables A, B, C and M only. Variables D,
E, F, X, andY are used for storage of the imaginary parts
of values and so cannot be used by you.
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• Example: (2 + 3i) + (4 + 5i)
Enter CMPLX Mode F 2
R 2 + 3 i T +
R 4 + 5 i T =
6.
Real number part
A r
8.i
Imaginary number part
k Absolute Value/Argument Calculation
• The procedure described below can be used to deter-
mine the absolute value (Abs) and argument (arg) for a
complex number of the format Z = a + bi, 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.
5.
A A R 3 + 4 i T =
Determine the argument.
A a R 3 + 4 i T =
CMPLX
53.13010235
Metric Conversions (fx-991WA)
• A total of 20 different conversion pairs are built-in to pro-
vide quick and easy conversion to and from metric units.
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• See the Conversion Pair Table shown below for a com-
plete list of available conversion pairs.
• Example: To convert 31 inches to centimeters
CONV
31 A c
CONV
1
01
01 is the inches-to-centimeters conversion pair number.
31in cm
0.
31in cm
=
78.74
• Conversion Pair Table
Based on ISO Standard (1992) data and CODATA Bulletin
63 (1986) data.
Number
01
02
03
04
05
06
07
08
09
10
11
12
13
14
15
16
17
18
19
20
Conversion Pair
in → cm
cm → in
ft → m
m → ft
Number
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
Conversion Pair
oz → g
g → oz
lb → kg
kg → lb
yd → m
m → yd
atm → Pa
Pa → atm
mmHg → Pa
Pa → mmHg
hp → kW
kW → hp
kgf/cm2→ Pa
Pa → kgf/cm2
kgf•m → J
J → kgf•m
lbf/in2 → kPa
kPa → lbf/in2
°F → °C
mile → km
km → mile
n mile → m
m → n mile
acre → m2
m2 → acre
gal (US) →r
r → gal (US)
gal (UK) →r
r → gal (UK)
pc → km
km → pc
km/h → m/s
m/s → km/h
°C → °F
J → cal
cal → J
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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 = mc2)
CONST
65 L
CONST28
28
28 is the “speed of light in vacuum” constant number.
65Co
0.
65Co2
K
0.
65Co2
5.841908662 18
=
• Scientific Constant Table
Based on ISO Standard (1992) data and CODATA Bulletin
63 (1986) data.
Number
01
Constant Name
proton mass
Symbol
mp
02
neutron mass
mn
03
electron mass
me
04
05
muon mass
Bohr radius
mµ
a0
06
07
08
Planck's constant
nuclear magneton
Bohr magneton
h
µN
µB
09
Planck's constant, rationalized (h-bar)
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Number
10
11
Constant Name
fine-structure constant
classical electron radius
electron Compton wavelength
proton gyromagnetic ratio
proton Compton wavelength
neutron Compton wavelength
Rydberg constant
Symbol
α
re
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
λc
γp
λcp
λcn
R∞
u
µp
µe
µn
µµ
F
e
NA
k
Vm
R
C0
C1
C2
atomic mass unit
proton magnetic moment
electron magnetic moment
neutron magnetic moment
muon magnetic moment
Faraday constant
elementary charge
Avogadro constant
Boltzmann constant
molar volume of ideal gas
molar gas constant
speed of light in vacuum
first radiation constant
second radiation constant
31
32
33
34
35
36
37
38
39
40
Stefan-Boltzmann constant
permittivity of vacuum
permeability of vacuum
magnetic flux quantum
standard acceleration of gravity
astronomical unit
parsec
Celsius temperature
Newtonian constant of gravitation
standard atmosphere
σ
ε0
µ0
φ0
g
AU
pc
t
G
atm
Base-n Calculations
• In addition to decimal values, calculations can be per-
formed using binary, octal and hexadecimal values.
• You can specify the default number system to be ap-
plied to all input and displayed values, and the number
system for individual values you input.
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• You cannot use scientific functions in binary, octal, deci-
mal, and hexadecimal calculations.You cannot input val-
ues 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 pro-
duced by taking the two's complement.
• You can use the following logical operators between
values in Base-n calculations: and (logical product), 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 Ϲ x Ϲ 1111111111
0 Ϲ x Ϲ 0111111111
Octal
4000000000 Ϲ x Ϲ 7777777777
0 Ϲ x Ϲ 3777777777
Decimal
Hexadecimal
–2147483648 Ϲ x Ϲ 2147483647
80000000 Ϲ x Ϲ FFFFFFFF
0 Ϲ x Ϲ 7FFFFFFF
• Example 1: To perform the following calculation and
produce a binary result:
101112 + 110102
Binary mode
b
F F 3 b
101112 + 110102
=
0.
0.
b
b
110001.
• Example 2: To perform the following calculation and
produce an octal result:
76548 ÷ 1210
Octal mode
o
F F 3 o
0.
( )
o
l l l 4
76548 \
o
o
l l l 1(d)1210
0.
=
516.
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• Example 3: To perform the following calculation and
produce a hexadecimal result:
12016 or 11012
Hexadecimal mode F F 3 h
H
0.
(
)
or
12016 l 2
H
H
(b)
l l l 3 11012
0.
=
12d.
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
2.258 =
A O
2.258
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 F F 3 1 (NORM 1 mode)
4. Check the formula you are working with to confirm it is
correct.
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5. Enter the correct modes to perform the calculation and
try again.
If the above steps do not correct the problem, press the
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
the display. Press t to clear the error, or press e or r
to display the calculation and correct the problem. See
“Error Locator” 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 are using.
Stk ERROR
• Cause
• Capacity of the numeric stack or operator stack is ex-
ceeded.
• 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.
Syn ERROR
• Cause
• Attempt to perform an illegal mathematical operation.
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• Action
• Press e or r to display the calculation with the
cursor located at the location of the error. Make nec-
essary corrections.
Arg ERROR
• Cause
• Improper use of argument
• 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 prec-
edence.
1 Coordinate transformation: Pol (x, y), Rec (r, θ)
2 Type A functions:
With these functions, the value is entered and then the
function key is pressed.
x2, xҀ1, 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, sinҀ1, cosҀ1
,
tanҀ1, sinh, cosh, tanh, sinhҀ1, coshҀ1, tanhҀ1, (Ҁ)
7 Abbreviated multiplication format in front of Type B
functions: 2 3, Alog2 etc.
8 Permutation and combination: nPr, nCr
9 ҂, Ö
0 ѿ, Ҁ
* 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.
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k Stacks
This calculator uses memory areas, called “stacks,” to tem-
porarily store values (numeric stack) and commands (com-
mand stack) according to their precedence during calcu-
lations.The numeric stack has 10 levels and the command
stack has 24 levels. A stack error (Stk ERROR) occurs
whenever you try to perform a calculation that is so com-
plex that the capacity of a stack is exceeded.
k Power Supply
The TWO WAY POWER system actually has two power
supplies: a solar cell and a G13 Type (LR44) button bat-
tery. 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 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 the display when you press the
key.
• To replace the battery
Screw
Screw
1 Remove the six screws that
hold the back cover in place
and then remove the back
cover.
2 Remove the old battery.
3 Wipe off the sides of new bat-
tery with a dry, soft cloth.Load
it into the unit with the posi-
tive
can see it).
side facing up (so you
k
4 Replace the back cover and
secure it in place with the six
screws.
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5 Press
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.
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k Input Ranges
Internal digits: 12
Accuracy: As a rule, accuracy is ±1 at the 10th digit.
Functions
Input Range
sinx
DEG 0Ϲ ꢀxꢀ Ϲ4.499999999҂1010
RAD 0Ϲ ꢀxꢀ Ϲ785398163.3
GRA 0Ϲ ꢀxꢀ Ϲ4.499999999҂1010
cosx DEG 0Ϲ ꢀxꢀ Ϲ4.500000008҂1010
RAD 0Ϲ ꢀxꢀ Ϲ785398164.9
GRA 0Ϲ ꢀxꢀ Ϲ5.000000009҂1010
tanx DEG Same as sinx, except when ꢀxꢀ= (2n-1)҂90.
RAD Same as sinx, except when ꢀxꢀ= (2n-1)҂π/2.
GRA Same as sinx, except when ꢀxꢀ= (2n-1)҂100.
sin–1x
0Ϲ ꢀxꢀ Ϲ1
cos–1x
tan–1x 0Ϲ ꢀxꢀ Ϲ9.999999999҂1099
sinhx
coshx
0Ϲ ꢀxꢀ Ϲ230.2585092
sinh–1x
cosh–1x
0Ϲ ꢀxꢀ Ϲ4.999999999҂1099
tanhx
tanh–1x
0Ϲ ꢀxꢀ Ϲ9.999999999҂10-1
log
x
/lnx 0 x
x
10
–9.999999999҂1099Ϲ x Ϲ 99.99999999
–9.999999999҂1099Ϲ x Ϲ 230.2585092
0Ϲ x 1 ҂ 10100
ex
x
x2
ꢀxꢀ 1҂ 1050
1/x
ꢀxꢀ 1҂ 10100
ꢀxꢀ 1҂ 10100
;
x G
0
3
x
x!
0Ϲ x Ϲ 69 (x is an integer)
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Functions
Input Range
0Ϲ n Ϲ99, r Ϲ n (n, r is an integer)
1Ϲ {n!/(n–r)!} Ϲ 9.999999999҂1099
0Ϲ n Ϲ99, r Ϲ n (n, r is an integer)
ꢀxꢀ, ꢀyꢀ Ϲ9.999999999҂1049
(x2+y2) Ϲ9.999999999҂1099
0Ϲ r Ϲ9.999999999҂1099
Rec(r, ꢀ)
nPr
nCr
Pol(x, y)
θ: Same as sinx, cosx
ꢀaꢀ, b, c 1҂10100
0 Ϲ b, c
ꢀxꢀ1҂10100
°’ ”
Decimal ↔ Sexagesimal Conversions
000000Ϲ ꢀxꢀ Ϲ9999990590
xŒ0: –1҂10100ylogx100
xy
x҃0: yŒ0
x0: y҃n,
However: –1҂10100 ylogꢀxꢀ100
1
(n is an integer)
2n+1
yŒ0: x G 0
–1҂101001/x logy100
x
y
y҃0: xŒ0
1
y0: x҃2nѿ1, (n G 0; n is an integer)
n
However: –1҂10100 1/x logꢀyꢀ100
Total of integer, numerator, and denominator
must be 10 digits or less (including division
marks).
b
a /c
ꢀxꢀ 1҂1050
ꢀyꢀ 1҂1050
ꢀnꢀ 1҂10100
SD
(REG) xn, yn, o, p
A, B, r : n G 0
xn–1,yn–1 : n G 0, 1
* Erros are cumulative with such internal continuous cal-
3
culations as xy, x x , x!, and x , so accuracy may be
adversely affected.
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Specifications
Power Supply: Solar cell and a single G13 Type button
battery (LR44)
Battery Life: Approximately 3 years (1 hour use per day).
Dimensions: 10(H)i76(W)i150(D) mm
3/8Љ(H)i3Љ(W)i57/8Љ(D)
Weight: 85 g (3oz) including battery
Power Consumption: 0.0001W
Operating Temperature: 0°C ~ 40°C (32°F ~ 104°F)
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CASIO COMPUTER CO., LTD.
6-2, Hon-machi 1-chome
Shibuya-ku, Tokyo 151-8543, Japan
U.S. Pat. 4,410,956
SA9911-A Printed in China
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HA310537-1
|