Sharp W Series User Manual

SCIENTIFIC  
SCIENTIFIC  
CALCULATOR  
CALCULATOR  
OPERATION GUIDE  
OPERATION GUIDE  
<W Series>  
C O NTENTS  
HOW TOOPERATE  
Read Before Using  
Key layout/Reset switch  
2
Display pattern  
Display format  
Exponent display  
Angular unit  
3
3
4
5
Function and Key Operation  
O N/O FF, entry correction keys  
6
7
8
9
Data entry keys  
Random key  
Modify key  
Basic arithmetic keys, parentheses  
Percent  
10  
11  
Inverse, square, cube, xth power of y,  
square root, cube root, xth root of y  
12  
13  
14  
15  
16  
17  
18  
19  
20  
21  
22  
23  
24  
10 to the power of x, common logarithm  
e to the power of x, natural logarithm  
Factorials  
Permutations, combinations  
Time calculation  
Fractional calculations  
~
Memory calculations  
Last answer memory  
Trigonometric functions  
Arc trigonometric functions  
Hyperbolic functions  
C oordinate conversion  
Binary, pental, octal, decimal, and  
hexadecimal operations (N-base)  
25  
STATISTICS FUNCTION  
26  
27  
31  
Data input and correction  
“ANS” keys for 1-variable statistics  
“ANS” keys for 2-variable statistics  
1
H ow to O pe ra te  
Read B efore Using≈  
This operation guide has been written based on the EL-531W , EL-509W , and EL-531W H  
models. Some functions described here are not featured on other models. In addition,  
key operations and symbols on the display may differ according to the model.  
1 . K E Y L AY O U T  
2nd function key  
Pressing this key will enable the functions  
written in orange above the calculator  
buttons.  
ON/C, OFF key  
D irect function  
2nd function  
<Power on>  
<Power off>  
W ritten in orange above  
the O N/C key  
Mode key  
This calculator can operate in three different  
modes as follows.  
<Example>  
[Normal mode]  
Mode = 0; normal mode for  
performingnormal arithmetic  
and function calculations.  
[STAT-0 mode]  
Mode = 1; STAT- 0 mode for  
performing1-variable statisti-  
cal calculations.  
[STAT-1–6 mode]  
Mode = 1; STAT-1–6 mode  
for performing 2-variable  
statistical calculations.  
W hen changing to the statistical sub-mode,  
press the corresponding number key after  
performing the operation to select the statistics  
mode (press  
).  
RESET  
2 . R E S E T S W I T C H  
(LINE): Linear regression calculation  
If the calculator fails to operate normally,  
press the reset switch on the back to  
reinitialise the unit. The display format  
and calculation mode will return to their  
initial settings.  
(Q UAD): Q uadratic regression calculation  
(EX P):  
Exponential regression calculation  
N O T E :  
(LO G): Logarithmic regression calculation  
(PW R): Power regression calculation  
Pressing the reset switch  
will erase any data stored  
in memory.  
Reset switch  
RESET  
(INV):  
Inverse regression calculation  
2
3 . DI S P L AY PAT T E R N  
The actual display does not appear like this.  
This illustration is for explanatory purposes only.  
4 . DI S P L AY F O R M AT A N D  
DE C I M A L S E T T I N G F U N C T I O N  
For convenient and easy operation, this model can be used in one of four display modes.  
The selected display status is shown in the upper part of the display (Format Indicator).  
Note: If more 0’s (zeros) than needed are displayed when the O N/C key is pressed, check  
whether or not the calculator is set to a Special Display Format.  
• Floating decimal point format (no symbol is displayed)  
Valid values beyond the maximum range are displayed in the form of a [10-digit  
(mantissa) + 2-digit (exponent)]  
• Fixed decimal point format (FIX is displayed)  
Displays the fractional part of the calculation result according to the specified  
number of decimal places.  
• Scientific notation (SC I is displayed)  
Frequently used in science to handle extremely small or large numbers.  
• Engineering scientific notation (ENG is displayed)  
C onvenient for converting between different units.  
<Example>  
Let’s compare the display result of  
[10000 8. 1 =] in each display format.  
Initial display  
(specifies normal mode)  
DEG  
Note: The calculator has two settings for displaying a  
floating point number: NO RM1 (default setting) and  
NO RM2. In each display setting, a number is  
automatically displayed in scientific notation outside a  
preset range:  
NO RM1: 0.000000001 x 9999999999  
NO RM2: 0.01 x 9999999999  
DEG  
10000  
8.1  
(normal mode)  
FIX  
DEG  
(FIX mode TAB = 3)  
3
SCI  
DEG  
X10  
(SC I mode)  
ENG DEG  
X10  
(ENG mode)  
DEG  
(normal mode)  
5 . E X P O N E N T DI S P L AY  
The distance from the earth to the sun is approx. 150,000,000 (1.5 x 108) km.Values  
such as this with many zeros are often used in scientific calculations, but entering the  
zeros one by one is a great deal of work and it’s easy to make mistakes.  
In such a case, the numerical values are divided into mantissa and exponent portions,  
displayed and calculated.  
<Example>  
W hat is the number of electronics flowing in a conductor when  
the electrical charge across a given cross-section is 0.32 cou-  
lombs. (The charge on a single electron = 1.6 x 10-19 coulombs).  
DEG  
0.32  
1.6  
DEG  
19  
X10  
DEG  
X10  
4
6 . A N G U L A R U N I T  
Angular values are converted from DEG to RAD to GRAD with each push of the DRG  
key.This function is used when doing calculations related to trigonometric functions or  
coordinate geometry conversions.  
D egrees (D E G is shown at the top of the display)  
A commonly used unit of measure for angles.The angular measure of a circle  
is expressed as 360°.  
R adians (R A D is shown at the top of the display)  
Radians are different than degrees and express angles based on the circumfer-  
ence of a circle. 180° is equivalent to π radians.Therefore, the angular mea-  
sure of a circle is 2π radians.  
G rads (G R A D is shown at the top of the display)  
Grads are a unit of angular measure used in Europe, particularly in France. An  
angle of 90 degrees is equivalent to 100 grads.  
The relationships between the three types  
of angular units can be expressed as right:  
π
2
90° (DEG) =  
π/2 (RAD) =  
100 (GRAD) =  
<Example>  
C heck to confirm 90 degrees equaling π/2 radians  
equaling 100 grads. (π=3.14159...)  
Angular indicator  
O peration  
D isplay  
DEG  
••••••••  
(in DEG mode)  
RAD  
90  
( π/2)  
GRAD  
DEG  
5
Function and K ey Operation≈  
ON/OFF, Entry  
Correction Keys  
Turns the calculator on or clears the data. It also clears the contents of the  
calculator display and voids any calculator command; however, coeffi-  
cients in 3-variable linear equations and statistics, as well as values stored  
in the independent memory in normal mode, are not erased.  
Turns the calculator off.  
C lears all internal values, including coefficients in 3-variable linear equations and  
statistics.Values stored in memory in normal mode are not erased.  
These arrow keys are useful for Multi-Line playback, which lets you  
scroll through calculation steps one by one. (refer to page 8)  
These keys are useful for editing equations. The  
key moves the  
cursor to the left, and the key moves the cursor to the right. The  
key deletes the symbol/number at the cursor.  
key inserts the symbol/number at the cursor.  
6
Data Entry Keys  
0 to 9 N umeric keys for entering data values.  
Decimal point key. Enters a decimal point.  
Enters minus symbol or sign change key.  
C hanges positive numbers to negative and negative numbers to positive.  
Pressing π automatically enters the value for π (3.14159...).  
The constant π, used frequently in function calculations, is the ratio of the  
circumference of a circle to its diameter.  
Pressing this key switches to scientific notation data entry.  
<Example>  
Provided the earth is moving around the sun in a circular orbit,  
how many kilometers will it travel in a year?  
* The average distance between the earth and the sun being  
1.496 x 108 km.  
C ircumference equals diameter x π; therefore,  
1.496 x 108 x 2 x π  
O peration  
D isplay  
DEG  
496  
8
1
X10  
DEG  
2
7
Random  
Generates random numbers.  
Random numbers are three-decimal-place values between 0.000 and 0.999. Using this  
function enables the user to obtain unbiased sampling data derived from random  
values generated by the calculator.  
<Example>  
0. * * *  
(A random number has been generated.)  
[ R andom D ice]  
To simulate a die-rolling, a random integer between 1 and 6 can be generated by  
pressing  
. To generate the next random dice number, press  
.
[ R andom C oin]  
To simulate a coin flip, 0 (heads) or 1 (tails) can be randomly generated by pressing  
. To generate the next random coin number, press  
[ R andom Integer]  
An integer between 0 and 99 can be generated randomly by pressing  
.
.
To generate the next random integer, press  
.
A PPL IC AT IO N S:  
Building sample sets for statistics or research.  
8
Modify  
Function to round calculation results.  
Even after setting the number of decimal places on the display, the calculator per-  
forms calculations using a larger number of decimal places than that which appears  
on the display. By using this function, internal calculations will be performed using  
only the displayed value.  
FIX mode TAB = 1 (normal calculation)  
<Example>  
9
9
0.6 (internally, 0.5555...)  
5
5.0  
Rounded calculation (MDF)  
(internally, 0.5555...)  
5
9
9
0.6  
(internally, 0.6)  
5.4  
A PPL IC AT IO N S:  
Frequently used in scientific and technical fields, as well as business,  
when performing chained calculations.  
9
Basic Arithmetic  
Keys, Parentheses  
The four basic operators. Each is used in the same way as a standard  
calculator:  
+ (addition), – (subtraction), x (multiplication), and ÷ (division).  
Finds the result in the same way as a standard calculator.  
Used to specify calculations in which certain operations have precedence.  
You can make addition and subtraction operations have precedence over  
multiplication and division by enclosing them in parentheses.  
10  
Percent  
For calculating percentages. Four methods of calculating percentages  
are presented as follows.  
1) $125 increased by 10%137.5  
DEG  
DEG  
DEG  
125  
10  
2) $125 reduced by 20%100  
125  
20  
3) 15% of $125…18.75  
15  
125  
4) W hen $125 equals 5% of X , X equals…2500  
DEG  
125  
5
11  
Inverse, Square, Cube,  
xth Power of y, Square Root,  
Cube Root, xth Root of y  
C alculates the inverse of the value on the display.  
Squares the value on the display.  
C ubes the value on the display.  
C alculates exponential values.  
C alculates the square root of the value on the display.  
C alculates the cube root of the value on the display.  
C alculates the xth root of y.  
<Example>  
O peration  
D isplay  
DEG  
2
2
2
2
4
DEG  
2
DEG  
16  
4
12  
10 to the Power of x,  
Common Logarithm  
C alculates the value of 10 raised to the xth power.  
C alculates logarithm, the exponent of the power to which 10 must be  
raised to equal the given value.  
<Example>  
D isplay  
O peration  
DEG  
3
DEG  
1000  
13  
e to the Power of x,  
Natural Logarithm  
C alculates powers based on the constant e (2.718281828).  
C omputes the value of the natural logarithm, the exponent of the power  
to which e must be raised to equal the given value.  
<Example>  
O peration  
D isplay  
DEG  
5
DEG  
10  
14  
Factorials  
The product of a given positive integer n multiplied by all the lesser positive  
integers from 1 to n-1 is indicated by n! and called the factorial of n.  
<Example>  
O peration  
D isplay  
DEG  
7
c.f  
n! = 1 x 2 x 3 x …xn  
A PPL IC AT IO N S:  
Used in statistics and mathematics. In statistics, this function is used  
in calculations involving combinations and permutations.  
15  
Permutations, Combinations  
This function finds the number of different possible orderings in selecting  
r objects from a set of n objects. For example, there are six different  
ways of ordering the letters ABC in groups of three letters—ABC , AC B,  
BAC , BC A, C AB, and C BA.  
The calculation equation is P3 = 3 x 2 x 1 = 6 (ways).  
3
This function finds the number of ways of selecting r objects from a set of  
n objects. For example, from the three letters ABC , there are three ways  
we can extract groups of two different letters—AB, AC , and C B.  
T he calculation equation is C 2.  
3
<Example>  
O peration  
D isplay  
DEG  
6
6
4
DEG  
4
A PPL IC AT IO N S:  
Used in statistics (probability calculations) and in simulation hypoth-  
eses in fields such as medicine, pharmaceutics, and physics. Also,  
can be used to determine the chances of winning in lotteries.  
16  
Time Calculation  
C onverts a sexagesimal value displayed in degrees, minutes, seconds to  
decimal notation. Also, converts a decimal value to sexagesimal  
notataion (degrees, minutes, seconds).  
Inputs values in sexagesimal notation (degrees, minutes, seconds).  
C onvert 24° 28’ 35” (24 degrees, 28 minutes, 35 sec-  
onds) to decimal notation. T hen conver t 24.476° to  
sexagesimal notation.  
<Example>  
O peration  
D isplay  
DEG  
24  
28  
35  
DEG  
C onvert to decimal notation  
DEG  
Repeat last key operation to return to the previous display.  
A PPL IC AT IO N S:  
Used in calculations of angles and angular velocity in physics, and  
latitude and longitude in geography.  
17  
Fractional Calculations  
Inputs fractions and converts mutually between fractions and decimals.  
C onverts between mixed numbers and improper fractions.  
1
2
5
Add 3  
and , and convert to decimal notation.  
7
<Example>  
O peration  
D isplay  
DEG  
3
1
5
2
7
DEG  
C onvert to decimal notation  
Press once to return to the previous display  
DEG  
C onvert to an improper fraction  
Press once to return to the previous display  
DEG  
A PPL IC AT IO N S:  
T here is a wide variety of applications for this function because  
fractions are such a basic part of mathematics. T his function is useful  
for calculations involving electrical circuit resistance.  
18  
Memory Calculations  
~
Stores displayed values in memories A~F, X ,Y, M.  
Recalls values stored inA~F, X ,Y, M.  
Adds the displayed value to the value in the independent memory M.  
Subtracts the displayed value from the value in the independent memory M.  
Temporary memories  
~
Independent memory  
y
D ispla  
O peration  
<Example 1>  
DEG  
0
(Enter 0 for M)  
DEG  
DEG  
DEG  
M
25  
7
27  
M
3
M
<Example 2>  
C alculates $/¥ at the designated exchange rate.  
$1 = ¥110  
¥26,510 = $?  
$2,750 = ¥?  
y
D ispla  
O peration  
DEG  
DEG  
DEG  
110 Y  
110  
26510ÖY=  
26510  
2750  
2750xY=  
19  
Last Answer Memory  
Automatically recalls the last answer calculated by pressing  
Solve for x first and then solve for y using x.  
<Example>  
x = 2 + 3 and y = 4 ÷ x  
O peration  
D isplay  
DEG  
2
3
DEG  
4
20  
Trigonometric Functions  
Trigonometric functions determine the ratio of three sides  
of a right triangle. The combinations of the three sides are  
sin, cos, and tan. Their relations are:  
a
c
b
θ
b
C alculates the sine of an angle.  
C alculates the cosine of an angle.  
C alculates the tangent of an angle.  
sinθ  
cosθ  
tanθ  
=
=
=
a
c
a
b
c
<Example>  
The angle from a point 15 meters from  
a building to the highest floor of the  
building is 45°. How tall is the building?  
[DEG mode]  
O peration  
D isplay  
DEG  
45  
1
15  
5
View point  
A PPL IC AT IO N S:  
Trigonometric functions are useful in mathematics and various engineering  
calculations.They are often used in astronomical observations, civil engi-  
neering and in calculations involving electrical circuits, as well as in calcula-  
tions for physics such as parabolic motion and wave motion.  
21  
Arc Trigonometric Functions  
Arc trigonometric functions, the inverse of trigonomet-  
ric functions, are used to determine an angle from ratios  
of a right triangle.The combinations of the three sides  
a
c
b
-1  
are sin , cos-1, and tan-1.Their relations are;  
θ
b
a
θ = sin-1  
(arc sine) Determines an angle based on the ratio  
b/a of two sides of a right triangle.  
c
a
θ = cos-1  
(arc cosine) Determines an angle based on the ratio  
c/a for two sides of a right triangle.  
b
c
θ = tan-1  
(arc tangent) Determines an angle based on the  
ratio a/b for two sides of a right triangle.  
<Example>  
At what angle should an airplane climb in order  
to climb 80 meters in 100 meters?  
[DEG mode]  
O peration  
D isplay  
DEG  
80  
100  
22  
Hyperbolic Functions  
The hyperbolic function is defined by using natural exponents in trigo-  
nometric functions.  
Arc hyperbolic functions are defined by using natural logarithms in trigono-  
metric functions.  
A PPL IC AT IO N S:  
Hyperbolic and arc hyperbolic functions are very useful in electrical  
engineering and physics.  
23  
Coordinate Conversion  
C onverts rectangular coordinates to polar coordinates (x, y r,  
θ)  
C onverts polar coordinates to rectangular coordinates (r, θ x, y)  
Splits data used for dual-variable data input.  
Displays r, θ and x, y. (Cx y or r θ)  
y
y
Polar coordinates  
Rectangular coordinates  
P (r,  
θ)  
P (x,y)  
y
r
θ
x
x
o
o
x
<Example> Determine the polar coordinates (r, θ) when the rectangu-  
lar coordinates of Point P are (x = 7, y = 3).  
[ D E G mode]  
O peration  
D isplay  
DEG  
DEG  
DEG  
7
3
23.2  
7.6  
DEG  
A PPL IC AT IO N S:  
C oordinate conversion is often used in mathematics and engineering, espe-  
cially for impedance calculations in electronics and electrical engineering.  
24  
Binary, Pental, Octal,  
Decimal, and Hexadecimal  
Operations (N-Base)  
This calculator can perform conversions between numbers expressed in binary, pental,  
octal, decimal, and hexadecimal systems. It can also perform the four basic arithmetic  
operations, calculations with parentheses and memory calculations using binary, pental,  
octal, decimal, and hexadecimal numbers. In addition, the calculator can carry out the  
logical operations AND, O R, NO T, NEG, X O R, and X NO R on binary, pental, octal, and  
hexadecimal numbers.  
C onverts to the binary system. "b" appears.  
C onverts to the pental system. "P" appears.  
C onverts to the octal system. "o" appears.  
C onverts to the hexadecimal system. "H" appears.  
C onverts to the decimal system. "b", "P", "o", and "H" disappear from the display.  
C onversion is performed on the displayed value when these keys are pressed.  
HEX(1AC) ©BIN ©PEN ©OCT ©DEC  
<Example 1>  
O peration  
D isplay  
DEG  
1AC  
DEG  
1AC BIN  
110101100 PDEEG  
DEG  
3203 OCT  
DEG  
654 DEC  
1011 AND 101 = (BIN) ©DEC  
O peration  
<Example 2>  
D isplay  
DEG  
DEG  
1011AND_  
1011  
1011AND101=  
101  
DEG  
1 DEC  
25  
Statistics Function  
The statistics function is excellent for analyzing qualities of an event.Though primarily  
used for engineering and mathematics, the function is also applied to nearly all other  
fields including economics and medicine.  
DAT A I N P U T A N D C O R R E C T I O N  
Enters data for statistical calculations.  
C lears data input.  
Splits data used for dual-variable data input.  
(Used for dual-variable statistical calculations.)  
<Example 1>  
Here is a table of examination results. Input this data  
for analysis.  
D ata table 1  
1
2
3
4
5
6
7
8
N o.  
Score  
30 40 50 60 70 80 90 100  
N o. of pupils  
2
4
5
7
12 10  
8
2
O peration  
D isplay  
DEG  
STAT  
Stat 0  
Select single-variable statistics mode  
DEG  
STAT  
DATA SET=  
DATA SET=  
2
30  
.
.
.
DEG  
STAT  
100  
2
Score  
Number of pupils  
26  
“ A N S ” K E Y S F O R 1 -V A R I A B L E S T AT I S T I C S  
C alculates the average value of the data (sample data x).  
C alculates the standard deviation for the data (sample data x).  
C alculates the standard deviation of a data population (sample data x).  
Displays the number of input data (sample data x).  
C alculates the sum of the data (sample data x).  
C alculates the sum of the data (sample data x) raised to the second power.  
N OT E :  
1. Sample data refers to data selected randomly from the population.  
2. Standard deviation of samples is determined by the sample data  
shift from an average value.  
3. Standard deviation for the population is standard deviation when  
the sample data is deemed a population (full data).  
Let’s check the results based on the previous data.  
69 (average value)  
17.75686128 (standard deviation)  
17.57839583 (standard deviation of the population)  
50 (total count of data)  
3450 (total)  
27  
DA T A C O R R E C T I O N  
C orrection prior to pressing  
immediately after a data entry: Delete incorrect  
data with  
, then enter the correct data.  
C orrection after pressing  
:
Use  
to display the data previously entered.  
Press  
to display data items in ascending (oldest first) order. To  
reverse the display order to descending (latest first), press the  
key.  
Each item is displayed with 'X n=', 'Yn=', or 'Nn=' (n is the sequential  
number of the data set).  
Display the data item to modify, input the correct value, then press  
Using , you can correct the values of the data set all at once.  
• W hen or appears, more data items can be browsed by pressing  
.
or  
To delete a data set, display an item of the data set to delete, then  
press . The data set will be deleted.  
.
To add a new data set, press  
and input the values, then press  
.
<Example 2>  
D ata table 2  
X: 30, 40, 40, 50  
X: 30, 45, 45, 45, 60  
O peration  
D isplay  
DEG  
DEG  
DEG  
DEG  
STAT  
Stat 0  
Select single-variable statistics mode  
STAT  
STAT  
STAT  
DATA SET=  
DATA SET=  
DATA SET=  
30  
40  
50  
2
28  
O peration  
D isplay  
DEG  
DEG  
DEG  
DEG  
STAT  
STAT  
STAT  
STAT  
X2=  
X2=  
N2=  
X3=  
45  
3
60  
A PPL IC A T IO N S:  
Single-variable statistical calculations are used in a broad range of fields,  
including engineering, business, and economics. They are most often applied to  
analysis in atmospheric observations and physics experiments, as well as for  
quality control in factories.  
29  
<Example 3>  
The table below summarizes the dates inApril when cherry  
blossoms bloom, and the average temperature for March in  
that same area. Determine basic statistical quantities for  
data X and dataY based on the data table.  
D ata table 3  
Year  
1983 1984 1985 1986 1987 1988 1989 1990  
x
y
Average temperature 6.2 7.0 6.8 8.7 7.9 6.5 6.1 8.2  
D ate blossoms bloom 13  
9
11  
5
7
12  
15  
7
O peration  
D isplay  
DEG  
STAT  
Stat 1  
Select dual-variable statistics mode and linear regression calculation in sub-mode.  
DEG  
STAT  
DATA SET=  
6
2
13  
.
.
.
.
.
.
DEG  
STAT  
DATA SET=  
DATA SET=  
6
8
1
2
15  
DEG  
STAT  
7
Temperature  
Date  
30  
“ A N S ” K E Y S F O R 2 -V A R I A B L E S T AT I S T I C S  
In addition to the 1-variable statistic keys, the following keys have been added for calcu-  
lating 2-variable statistics.  
C alculates the sum of the product for sample data x and sample data y.  
C alculates the sum of the data (sample datay).  
C alculates the sum of the data (sample datay) raised to the second power.  
C alculates the average value of the data (sample datay).  
C alculates the standard deviation for the data (sample datay).  
C alculates the standard deviation of a data population (sample datay).  
N OT E :  
The codes for basic statistical quantities of sample data x and their meanings  
are the same as those for single-variable statistical calculations.  
Let’ s check the results based on the previous data.  
7.175  
(Average for data x)  
0.973579551 (Standard deviation for data x)  
0.91070028  
(Standard deviation of the population for data x)  
(Average for data y)  
9.875  
3.440826313 (Standard deviation for datay)  
3.218598297 (Standard deviation of the population for datay)  
8
(Total count of data)  
57.4  
418.48  
544.1  
79  
(Sum of data x)  
(Sum of data x raised to the second power)  
(Sum of the product of data x and data y)  
(Sum of datay)  
863  
(Sum of data y raised to the second power)  
31  
©SHARP CORP. (MAR. '05)  

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