Casio fx 570MS User Manual

E
fx-570MS  
fx-991MS  
User’s Guide 2  
(Additional Functions)  
CA 310030-001V08  
Contents  
Before getting started............................. 3  
kModes .................................................................... 3  
Mathematical Expression Calculations  
and Editing Functions ............................ 4  
kReplay Copy .......................................................... 4  
kCALC Memory ....................................................... 5  
kSOLVE Function .................................................... 5  
Scientific Function Calculations............ 6  
kInputting Engineering Symbols .............................. 6  
Complex Number Calculations .............. 8  
kAbsolute Value and Argument Calculation............. 9  
kRectangular Form Polar Form Display.............. 9  
kConjugate of a Complex Number ........................ 10  
Base-n Calculations .............................. 10  
Statistical Calculations......................... 12  
Normal Distribution .................................................. 12  
Differential Calculations ....................... 13  
Integration Calculations ....................... 14  
Matrix Calculations ............................... 15  
kCreating a Matrix ................................................. 15  
kEditing the Elements of a Matrix .......................... 16  
kMatrix Addition, Subtraction, and Multiplication ... 16  
kCalculating the Scalar Product of a Matrix........... 16  
kObtaining the Determinant of a Matrix ................. 17  
kTransposing a Matrix ........................................... 17  
kInverting a Matrix ................................................. 18  
kDetermining the Absolute Value of a Matrix ......... 18  
E-1  
Vector Calculations ............................... 18  
kCreating a Vector ................................................. 19  
kEditing Vector Elements....................................... 19  
kAdding and Subtracting Vectors .......................... 19  
kCalculating the Scalar Product of a Vector .......... 20  
kCalculating the Inner Product of Two Vectors ...... 20  
kCalculating the Outer Product of Two Vectors ..... 21  
kDetermining the Absolute Value of a Vector ........ 21  
Metric Conversions............................... 22  
Scientific Constants.............................. 23  
Power Supply ........................................ 25  
Specifications........................................ 27  
See the “fx-95MS/fx-100MS/fx-115MS/fx-570MS/fx-991MS  
User’s Guide” for details about the following items.  
Removing and Replacing the Calculator’s 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-2  
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-570MS and fx-991MS.  
fx-570MS and fx-991MS Modes  
To perform this type of  
Perform this  
To enter  
calculation:  
key operation:  
this mode:  
Basic arithmetic  
calculations  
Complex number  
calculations  
F 1  
F 2  
COMP  
CMPLX  
Standard deviation  
Regression calculations  
Base-n calculations  
Solution of equations  
Matrix calculations  
Vector calculations  
SD  
REG  
BASE  
EQN  
MAT  
VCT  
F F 1  
F F 2  
F F 3  
F F F 1  
F F F 2  
F F F 3  
• Pressing the  
key more than three times displays  
F
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  
CMPLX  
Note!  
To return the calculation mode and setup to the initial  
defaults shown below, press A B 2(Mode) =.  
Calculation Mode:  
Angle Unit:  
COMP  
Deg  
Exponential Display Format:  
Norm 1, Eng OFF  
Complex Number Display Format: a+bi  
Fraction Display Format:  
Decimal Point Character:  
ab/c  
Dot  
E-3  
• 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  
COMP  
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).  
• You can also edit expressions on the display and per-  
form other multi-statement operations. For more details  
E-4  
about using multi-statements, see “Multi-statements” in  
the separate “User’s 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.  
CMPLX  
COMP  
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  
(Store the expression.)  
(Input 7 for X? prompt.)  
(Input 8 for X? prompt.)  
C
7 =  
C 8 =  
• 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.  
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)  
E-5  
1
2
B AC –  
DC2  
p 2 p u p 1 - p k ,  
R 1 \ 2 T - p h - p k K  
A I  
14 =  
]
(B?)  
(A?)  
(C?)  
(D?)  
2 =  
9 l 8 =  
[ [  
A I  
(A?)  
• Since the SOLVE function uses Newton’s Method, cer-  
tain initial values (assumed values) can make it impos-  
sible to obtain solutions. In this case, try inputting an-  
other value that you assume to be near the solution and  
perform the calculation again.  
• The SOLVE function may be unable to obtain a solution,  
even though a solution exists.  
• Due to certain idiosyncrasies of Newton’s method, solu-  
tions for the following types of functions tend to be diffi-  
cult to calculate.  
Periodic functions (i.e. y = sin x)  
Functions whose graph produce sharp slopes (i.e. y =  
ex, y = 1/x)  
Discontinuous functions (i.e. y = x )  
• If an expression does not include an equals sign (=), the  
SOLVE function produces a solution for expression = 0.  
Scientific Function  
Calculations  
COMP  
Use the F key to enter the COMP Mode when you  
want to perform scientific function 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-6  
To turn engineering symbols on and off, press the F  
key a number of times until you reach the setup screen  
shown below.  
Disp  
1
• Press 1. On the engineering symbol setting screen that  
appears, press the number key (1 or 2) that corre-  
sponds 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:  
Unit  
k (kilo)  
M (Mega)  
G (Giga)  
T (Tera)  
m (milli)  
µ (micro)  
n (nano)  
p (pico)  
A k  
A M  
A g  
A t  
A m  
A N  
A n  
A p  
A f  
103  
106  
109  
1012  
10–3  
10–6  
10–9  
10–12  
10–15  
f (femto)  
• For displayed values, the calculator selects the engineer-  
ing symbol that makes the numeric part of the value fall  
within the range of 1 to 1000.  
• Engineering symbols cannot be used when inputting frac-  
tions.  
Example: 9 Ö10 = 0.9 m (milli)  
Eng  
.....  
(Disp)  
1
F
1
0.  
9Ϭ1  
m
900.  
9 \ 10 =  
When engineering symbols are turned on, even standard (non-engineering)  
calculation results are displayed using engineering symbols.  
E-7  
A P  
0.9  
9Ϭ1  
m
900.  
J
Complex Number  
Calculations  
CMPLX  
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 expres-  
sion 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: (2ѿ3i)ѿ(4ѿ5i) 6ѿ8i  
(Real part 6)  
2 + 3 i + 4 + 5 i =  
(Imaginary part 8i)  
A r  
E-8  
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 rЄ.  
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)  
A A R 3 + 4 i T =  
(53.13010235°)  
A a R 3 + 4 i T =  
• The complex number can also be input using the polar  
form rЄ.  
Example 2: 2 Є 45 1 ѿ i  
(Angle unit: Deg)  
L 2 A Q 45 =  
A r  
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 ѿ i 1.414213562 Є 45  
(Angle unit: Deg) 1 + i A Y = A r  
L 2 A Q 45 A Z = A r  
E-9  
You select rectangular form (a+bi) or polar form (rЄ)  
for display of complex number calculation results.  
...  
F
1(Disp) r  
1(a+bi):Rectangular form  
2(rЄ): Polar form (indicated by “rЄ” on the display)  
k Conjugate of a Complex Number  
For any complex number z where z = a+bi, its conjugate  
(z) is z = abi.  
Example: To determine the conjugate of the complex  
number 1.23 + 2.34i (Result: 1.23 – 2.34i)  
A S R 1 l 23 + 2 l 34 i T =  
A r  
BASE  
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 two’s complement.  
E-10  
• 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.  
Binary  
1000000000 Ϲ x Ϲ 1111111111  
0 Ϲ x Ϲ 0111111111  
Octal  
4000000000 Ϲ x Ϲ 7777777777  
0 Ϲ x Ϲ 3777777777  
Decimal  
–2147483648 Ϲ x Ϲ 2147483647  
Hexadecimal  
80000000 Ϲ x Ϲ  
FFFFFFFF  
7FFFFFFF  
0 Ϲ x Ϲ  
Example 1: To perform the following calculation and  
produce a binary result:  
101112 ѿ 110102 1100012  
b
Binary mode:  
t b  
0.  
10111 + 11010 =  
Example 2: To perform the following calculation and  
produce an octal result:  
76548 ÷ 1210 5168  
Octal mode:  
o
t o  
0.  
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 12d16 30110  
H
Hexadecimal mode:  
t h  
0.  
120 l 2(or)  
( )  
b
l l l 3 1101 =  
Decimal mode:  
K
E-11  
Example 4: To convert the value 2210 to its binary, oc-  
tal, and hexadecimal equivalents.  
(101102 , 268 , 1616  
)
b
0.  
10110.  
26.  
Binary mode:  
t b  
b
o
l l l 1(d) 22 =  
Octal mode:  
Hexadecimal mode:  
o
h
H
16.  
Example 5: To convert the value 51310 to its binary  
equivalent.  
b
0.  
Binary mode:  
t b  
Ma t h ERROR  
l l l 1(d) 513 =  
b
You may not be able to convert a value from a number  
system whose calculation range is greater than the cal-  
culation range of the resulting number system.  
• The message “Math ERROR” indicates that the result  
has too many digits (overflow).  
SD  
Statistical  
Calculations  
REG  
SD  
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  
• In the SD Mode and REG Mode, the | key operates as  
the S key.  
• Press A D, which produces the screen shown below.  
(
(
(
P Q R  
t  
1 2 3 4  
E-12  
• 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 = Ҁ0.284747398, 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  
COMP  
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 dif-  
ferential 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 de-  
crease in x is x = 2 × 10–4 (Result: 7 )  
A J 3 p x K , 5 p x + 2 P 2 P  
2 e D 4 T =  
E-13  
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.  
• Select Rad (Radian) for the angle unit setting when  
performing trigonometric function differential calculations.  
Integration  
Calculations  
COMP  
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 Simpson’s rule.  
d expression P a P b P n F  
5
Example: (2x2 + 3x + 8) dx = 150.6666667  
1
(Number of partitions n = 6)  
2
3
p x K + p x +  
d
8 P 1 P 5 P 6 T =  
Note!  
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.  
• Select Rad (Radian) for the angle unit setting when  
performing trigonometric function integration calculations.  
E-14  
MAT  
Matrix Calculations  
The procedures in this section describe how to create  
matrices with up to three rows and three columns, and  
how to add, subtract, multiply, transpose and invert  
matrices, and how to obtain the scalar product,  
determinant, and absolute value of a matrix.  
Use the F key to enter the MAT Mode when you want  
to perform matrix calculations.  
MAT ..................................................... F F F 2  
Note that you must create one or more matrices before  
you can perform matrix calculations.  
You can have up to three matrices, named A, B, and C,  
in memory at one time.  
• The results of matrix calculations are stored automatically  
into MatAns memory. You can use the matrix in MatAns  
memory in subsequent matrix calculations.  
• Matrix calculations can use up to two levels of the matrix  
stack. Squaring a matrix, cubing a matrix, or inverting a  
matrix uses one stack level. See “Stacks” in the separate  
“User’s Guide” for more information.  
k Creating a Matrix  
To create a matrix, press A j 1(Dim), specify a matrix  
name (A, B, or C), and then specify the dimensions  
(number of rows and number of columns) of the matrix.  
Next, follow the prompts that appear to input values that  
make up the elements of the matrix.  
M
atA2 3  
2 rows and 3 columns  
You can use the cursor keys to move about the matrix in  
order to view or edit its elements.  
To exit the matrix screen, press t.  
E-15  
k Editing the Elements of a Matrix  
Press A j 2(Edit) and then specify the name (A, B, or  
C) of the matrix you want to edit to display a screen for  
editing the elements of the matrix.  
k Matrix Addition, Subtraction, and  
Multiplication  
Use the procedures described below to add, subtract,  
and multiply matrices.  
1 2  
4 0  
Example: To multiply Matrix A =  
by  
[
]
]
–2 5  
3
–8  
5
–1  
2 –4  
0
3
1
Matrix B =  
–4 0 12  
1220 –1  
[
(
[
)
]
(Matrix A 3҂2)  
A j 1(Dim) 1(A) 3 = 2 =  
(Element input) 1 = 2 = 4 = 0 = D 2 = 5 = t  
(Matrix B 2҂3)  
A j 1(Dim) 2(B) 2 = 3 =  
(Element input)  
D 1 = 0 = 3 = 2 = D 4 = 1 = t  
(MatA҂MatB)  
A j 3(Mat) 1(A) -  
A j 3(Mat) 2(B) =  
• An error occurs if you try to add, subtract matrices whose  
dimensions are different from each other, or multiply a  
matrix whose number of columns is different from that of  
the matrix by which you are multiplying it.  
k Calculating the Scalar Product of a  
Matrix  
Use the procedure shown below to obtain the scalar  
product (fixed multiple) of a matrix.  
6 –3  
2 –1  
Example: Multiply Matrix C =  
by 3.  
(
[
)
]
–15  
9
[
]
–5  
3
E-16  
(Matrix C 2҂2)  
(Element input)  
(3҂MatC)  
A j 1 (Dim) 3(C) 2 = 2 =  
2 = D 1 = D 5 = 3 = t  
3 - A j 3(Mat) 3(C) =  
k Obtaining the Determinant of a Matrix  
You can use the procedure below to determine the  
determinant of a square matrix.  
Example: To obtain the determinant of  
2
5
3
–1  
0
2
6
1
4
Matrix A =  
(Result: 73)  
[
]
(Matrix A 3҂3)  
A j 1(Dim) 1(A) 3 = 3 =  
(Element input)  
2 = D 1 = 6 = 5 = 0 = 1 =  
3 = 2 = 4 = t  
(DetMatA)  
A j r 1(Det)  
A j 3(Mat) 1(A) =  
• The above procedure results in an error if a non-square  
matrix is specified.  
k Transposing a Matrix  
Use the procedure described below when you want to  
transpose a matrix.  
5
8
7
9
4
3
Example: To transpose Matrix B =  
[
]
5 8  
7 9  
(
[
)
]
4 3  
(Matrix B 2҂3)  
(Element input)  
(TrnMatB)  
A j 1(Dim) 2(B) 2 = 3 =  
5 = 7 = 4 = 8 = 9 = 3 = t  
A j r 2(Trn)  
A j 3(Mat) 2(B) =  
E-17  
k Inverting a Matrix  
You can use the procedure below to invert a square matrix.  
–3 6 –11  
Example: To invert Matrix C =  
3 –4  
6
[
]
4 –8 13  
–0.4 1 –0.8  
–1.5 0.5 –1.5  
–0.8 0 –0.6  
(
)
]
[
(Matrix C 3҂3)  
A j 1(Dim) 3(C) 3 = 3 =  
(Element input) D 3 = 6 = D 11 = 3 = D 4 =  
6 = 4 = D 8 = 13 = t  
(MatC–1  
)
A j 3(Mat) 3(C) a =  
• The above procedure results in an error if a non-square  
matrix or a matrix for which there is no inverse  
(determinant = 0) is specified.  
k Determining the Absolute Value of a  
Matrix  
You can use the procedure described below to determine  
the absolute value of a matrix.  
Example: To determine the absolute value of the matrix  
produced by the inversion in the previous example.  
0.4  
1
0.8  
1.5 0.5 1.5  
(
[
)
]
0.8  
0
0.6  
(AbsMatAns)  
A A A j 3(Mat) 4(Ans) =  
VCT  
Vector Calculations  
The procedures in this section describe how to create a  
vector with a dimension up to three, and how to add, sub-  
tract, and multiply vectors, and how to obtain the scalar  
product, inner product, outer product, and absolute value  
of a vector. You can have up to three vectors in memory at  
one time.  
E-18  
Use the F key to enter the VCT Mode when you want  
to perform vector calculations.  
VCT ..................................................... F F F 3  
Note that you must create one or more vector before you  
can perform vector calculations.  
You can have up to three vectors, named A, B, and C, in  
memory at one time.  
• The results of vector calculations are stored automatically  
into VctAns memory. You can use the matrix in VctAns  
memory in subsequent vector calculations.  
k Creating a Vector  
To create a vector, press A z 1 (Dim), specify a vec-  
tor name (A, B, or C), and then specify the dimensions of  
the vector. Next, follow the prompts that appear input val-  
ues that make up the elements of the vector.  
Vector name  
Dimensions of vector  
Arrow indicates  
direction you should  
scroll to view other  
elements.  
Vc tA1  
0.  
Element value  
You can use the e and r keys to move about the vec-  
tor in order to view or edit its elements.  
To exit the vector screen, press t.  
k Editing Vector Elements  
Press A z 2(Edit) and then specify the name (A, B,  
C) of the vector you want to edit to display a screen for  
editing the elements of the vector.  
k Adding and Subtracting Vectors  
Use the procedures described below to add and subtract  
vectors.  
E-19  
Example: To add Vector A = (1 2 3) to Vector B = (4 5  
6). (Result: (5 3 –3))  
(3-dimensional Vector A)  
(Element input)  
A z 1(Dim) 1(A) 3 =  
1 = D 2 = 3 = t  
A z 1(Dim) 2(B) 3 =  
4 = 5 = D 6 = t  
(3-dimensional Vector B)  
(Element input)  
(VctA + VctB)  
A z 3(Vct) 1(A) +  
A z 3(Vct) 2(B) =  
• An error occurs in the above procedure if you specify  
vectors of different dimensions.  
k Calculating the Scalar Product of  
a Vector  
Use the procedure shown below to obtain the scalar  
product (fixed multiple) of a vector.  
Example: To multiply Vector C = (–7.8 9) by 5.  
(Result: (–39 45))  
(2-dimensional Vector C)  
(Element input)  
(5҂VctC)  
A z 1(Dim) 3(C) 2 =  
D 7 l 8 = 9 = t  
5 - A z 3(Vct) 3(C) =  
k Calculating the Inner Product of  
TwoVectors  
Use the procedure described below to obtain the inner  
product ( ) for two vectors.  
Example: To calculate the inner product of Vector A and  
Vector B  
(Result: 24 )  
(VctA VctB)  
A z 3(Vct) 1(A)  
A z r 1(Dot)  
A z 3(Vct) 2(B) =  
• An error occurs in the above procedure if you specify  
vectors of different dimensions.  
E-20  
k Calculating the Outer Product of  
Two Vectors  
Use the procedure described below to obtain the outer  
product for two vectors.  
Example: To calculate the outer product of VectorA and  
Vector B  
(Result: (–3, 18, 13))  
(VctA҂VctB)  
A z 3(Vct) 1(A) -  
A z 3(Vct) 2(B) =  
• An error occurs in the above procedure if you specify  
vectors of different dimensions.  
k Determining the Absolute Value of  
a Vector  
Use the procedure shown below to obtain the absolute  
value (size) of a vector.  
Example: To determine the absolute value of Vector C  
(Result: 11.90965994 )  
(AbsVctC)  
A A A z 3(Vct) 3(C) =  
Example: To determine the size of the angle (angle unit:  
Deg) formed by vectors A = (–1 0 1) and B = (1 2 0), and  
the size 1 vector perpendicular to both A and B.  
(Result: 108.4349488°)  
(A B)  
A B  
(A B)  
A B  
cos ꢀ  
, which becomes cos–1  
A ҂ B  
A ҂ B  
Size 1 vector perpendicular to both A and B ꢀ  
(3-dimensional Vector A)  
(Element input)  
A z 1(Dim) 1(A) 3 =  
D 1 = 0 = 1 = t  
A z 1(Dim) 2(B) 3 =  
1 = 2 = 0 = t  
(3-dimensional Vector B)  
(Element input)  
(VctA VctB) A z 3(Vct) 1(A) A z r 1(Dot)  
A z 3(Vct) 2(B) =  
E-21  
(AnsÖ(AbsVctA҂AbsVctB))  
\ R A A A z 3(Vct) 1(A)  
- A A A z 3(Vct) 2(B) T =  
(cos–1Ans) (Result: 108.4349488°)  
A V  
=
g
(VctA҂VctB)  
A z 3(Vct) 1(A) -  
A z 3(Vct) 2(B) =  
(AbsVctAns)  
A A A z 3(Vct) 4(Ans) =  
(VctAnsÖAns)  
(Result: (– 0.666666666 0.333333333 – 0.666666666))  
g
A z 3(Vct) 4(Ans) \  
=
COMP  
Metric Conversions  
Use the F key to enter the COMP Mode when you  
want to perform metric conversions.  
COMP ............................................................ F 1  
• A total of 20 different conversion pairs are built-in to  
provide quick and easy conversion to and from metric  
units.  
• See the Conversion Pair Table for a complete list of  
available conversion pairs.  
• When inputting a negative value, enclose it within pa-  
rentheses R, T.  
Example: To convert –31 degrees Celsius to Fahrenheit  
(
)
–31 °C °F  
R D 31 T A c 38 =  
– 23.8  
38 is the Celsius-to-Fahrenheit conversion pair number.  
E-22  
u Conversion Pair Table  
Based on NIST Special Publication 811 (1995).  
To perform  
this conversion:  
To perform  
this conversion:  
Input this  
pair number:  
Input this  
pair number:  
in cm  
cm in  
ft m  
m ft  
yd m  
m yd  
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  
01  
02  
03  
04  
05  
06  
07  
08  
09  
10  
11  
12  
13  
14  
15  
16  
17  
18  
19  
20  
oz g  
g oz  
lb kg  
kg lb  
21  
22  
23  
24  
25  
26  
27  
28  
29  
30  
31  
32  
33  
34  
35  
36  
37  
38  
39  
40  
atm Pa  
Pa atm  
mmHg Pa  
Pa mmHg  
hp kW  
kW hp  
kgf/cm2Pa  
Pa kgf/cm2  
kgf•m J  
J kgf•m  
lbf/in2 kPa  
kPa lbf/in2  
°F → °C  
km pc  
km/h m/s  
m/s km/h  
C → °F  
J cal  
cal J  
COMP  
Scientific Constants  
Use the F key to enter the COMP Mode when you  
want to perform calculations using scientific constants.  
COMP ............................................................ F 1  
• 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.  
E-23  
• Simply input the number that corresponds to the scientific  
constant you want to look up and it appears instantly on  
the display.  
• See the Scientific Constant Table for a complete list of  
available constants.  
Example: To determine how much total energy a person  
weighing 65kg has (E = mc2 = 5.841908662 ×1018  
)
65Co2  
65 L 28 K =  
5.841908662 18  
28 is the “speed of light in vacuum” constant number.  
u Scientific Constant Table  
Based on ISO Standard (1992) data and CODATArecom-  
mended values (1998).  
Input this scientific  
To select this constant:  
constant number:  
proton mass (mp)  
neutron mass (mn)  
electron mass (me)  
muon mass (mµ)  
Bohr radius (a0)  
Planck constant (h)  
nuclear magneton (µN)  
Bohr magneton (µB)  
Planck constant, rationalized ( )  
fine-structure constant (α)  
classical electron radius (re)  
Compton wavelength (λc)  
proton gyromagnetic ratio (γp)  
proton Compton wavelength (λcp)  
neutron Compton wavelength (λcn)  
Rydberg constant (R)  
atomic mass unit (u)  
proton magnetic moment (µp)  
electron magnetic moment (µe)  
neutron magnetic moment (µn)  
muon magnetic moment (µµ)  
Faraday constant (F)  
01  
02  
03  
04  
05  
06  
07  
08  
09  
10  
11  
12  
13  
14  
15  
16  
17  
18  
19  
20  
21  
22  
23  
24  
25  
elementary charge (e)  
Avogadro constant (NA)  
Boltzmann constant (k)  
E-24  
Input this scientific  
constant number:  
To select this constant:  
molar volume of ideal gas (Vm)  
molar gas constant (R)  
26  
27  
28  
29  
30  
31  
32  
33  
34  
35  
36  
37  
38  
39  
40  
speed of light in vacuum (C0)  
first radiation constant (C1)  
second radiation constant (C2)  
Stefan-Boltzmann constant (σ)  
electric constant (ε0)  
magnetic constant (µ0)  
magnetic flux quantum (φ 0)  
standard acceleration of gravity (g)  
conductance quantum (G0)  
characteristic impedance of vacuum (Z0)  
Celsius temperature (t)  
Newtonian constant of gravitation (G)  
standard atmosphere (atm)  
Power Supply  
The type of battery you should use depends on the model  
number of your calculator.  
fx-991MS  
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.  
E-25  
Screw  
Screw  
u To replace the battery  
1 Remove the five 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  
battery with a dry, soft cloth.  
Load it into the unit with the  
positive  
side facing up (so  
k
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-570MS  
This calculator is powered by single G13 Type (LR44)  
button 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.  
Screw  
• To replace the battery  
1 Press A i to turn off power.  
2 Remove the screw that holds  
the battery cover in place and  
then remove the battery cover.  
3 Remove the old battery.  
4 Wipe off the sides of new  
battery with a dry, soft cloth.  
Load it into the unit with the  
positive  
side facing up (so  
k
you can see it).  
E-26  
5 Replace the battery cover and secure it in place with  
the screw.  
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-570MS: Single G13 Type button battery (LR44)  
fx-991MS: Solar cell and a single G13 Type button  
battery (LR44)  
Battery Life:  
fx-570MS: Approximately 9,000 hours continuous  
display of flashing cursor.  
Approximately 3 years when left with power  
turned off.  
fx-991MS: Approximately 3 years (1 hour use per day).  
Dimensions: 12.7 (H) ҂ 78 (W) ҂ 154.5 (D) mm  
1/2Љ (H) ҂ 31/16Љ (W) ҂ 61/16Љ (D)  
Weight:  
105 g (3.7 oz) including battery  
Power Consumption: 0.0002 W  
Operating Temperature: 0°C to 40°C (32°F to 104°F)  
E-27  
CASIO COMPUTER CO., LTD.  
6-2, Hon-machi 1-chome  
Shibuya-ku, Tokyo 151-8543, Japan  
SA0403-F Printed in China  

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