SHARP EL-W516T 16 Digit Advanced Scientific Calculator Instruction Manual

SHARP EL-W516T 16 Digit Advanced Scientific Calculator

Specifications

• Model: EL-W516T
• Display: Dot matrix display
• Mantissa: Shown in the display and calculation examples
• Exponent: Shown in the display and calculation examples

Product Usage Instructions

Operational Notes
NOTICE: If service should be required on this calculator, have the calculator serviced in the region (country) where you purchased it.

Hard Case
The calculator comes with a hard case for protection during storage and transportation. Make sure to use the hard case to prevent any damage to the calculator.

Display
The calculator features a dot matrix display that shows the numerical values, functions, and calculation examples.

Function Indicators

The following function indicators may appear on the display:

• 2ndF: Appears when @ is pressed, indicating that the functions shown in the same color as @ are enabled.
• HYP: Indicates that H has been pressed and the hyperbolic functions are enabled. If @ > is pressed, the symbols 2ndF HYP appear, indicating that inverse hyperbolic functions are enabled.
• ALPHA: Appears when ; is pressed, indicating that the functions shown in the same color as ; are enabled.
• M: Indicates that a numerical value is stored in the independent memory (M).
• FIX/SCI/ENG/N1/N2: Indicates the notation used to display a value and can be changed by the SETUP menu. N1 is displayed on-screen as NORM1, and N2 as NORM2.
• DEG/RAD/GRAD: Indicates the angular units.
• BUSY: Appears during the execution of a calculation.
• W-VIEW: Indicates that the WriteView editor is selected.

Before Using the Calculator

To turn on the calculator, press the j key. The data that was on-screen when the power was turned off will appear on the display. To turn off the calculator, press @ o.

Key Notations
The following key notations are used in this manual:

• To specify ex: @
• To specify ln: i
• To specify E: ; E

Clearing the Entry and Memories

1. Press the j key to clear the entry and reset the calculator.
2. Press @ Z to clear the ANS memory.
3. To clear specific memories, use the mode selection key (b) followed by @ P and the memory number (0, 1, or 2).
4. To perform a full reset, use the RESET switch. Note that this will erase all data stored in memory and restore the calculator’s default settings, including the cleared username if stored using the name display function.

Mode Selection

• NORMAL mode (b 0): Used to perform arithmetic operations and function calculations.
• STAT mode (b 1): Used to perform statistical operations.
• TABLE mode (b 2): Used to illustrate the changes in values of one or two functions in table format.
• COMPLEX mode (b 3): Used to perform complex number calculations.
• EQUATION mode (b 4): Used to solve equations.
• MATRIX mode (b 5): Used to perform matrix calculations.
• VECTOR mode (b 6): Used to perform vector calculations.
• DISTRIBUTION mode (b 7): Used to perform distribution calculations.
• DRILL mode (b 8): Used to practice math and multiplication table drills.

Home Key
To return to NORMAL mode from other modes, press the 7 key. Note that equations and values currently being entered will disappear, similar to when changing modes.

SET UP Menu
To access the SETUP menu, press @ J. Press j to exit the SETUP menu. Note that you can press N to return to the previously displayed parent menu.

Selecting the Display Notation and Decimal Places
Use the SETUP menu to select the desired display notation and decimal places.

Setting the Floating Point Number System in Scientific Notation
The calculator offers two options for displaying numbers in scientific notation: NORM1 (the default) and NORM2. A number is automatically displayed in scientific notation outside a preset range.

Frequently Asked Questions

Q: Where should I have the calculator serviced if required?
A: If service is required on the calculator, have it serviced in the region (country) where you purchased it.

Q: How do I clear the entries and memories on the calculator?
A: To clear the entry and reset the calculator, press the j key. To clear specific memories, use the mode selection key (b) followed by @ P and the memory number. To perform a full reset, use the RESET switch.

Q: How do I change the display notation and decimal places?
A: Access the SETUP menu by pressing @ J. Use the menu to select the desired display notation and decimal places.

Performing solver function

1. Pressb 0. 2. Inputanexpressionwithanx variable. 3. Press@ 3. 4. Entera”Start”valueandpresse.Thedefaultvalueis”0″.
5. Enteradxvalue(minuteinterval).
6. Presse.

STATISTICAL CALCULATIONS

Statistical calculations can be performed in STAT mode. There are eight sub- modes within STAT mode. Press b 1, then press the number key that corresponds to your choice:
0 (SD): Single-variable statistics 1 (a+bx): Linear regression 2 (a+bx+cx2): Quadratic regression
3 (ae^bx): Euler exponential regression 4 (a+blnx): Logarithmic regression 5 (ax^b): Power regression
6 (a+b/x): Inverse regression
7 (ab^x): General exponential regression
The statistical data input screen appears.
After entering statistical data from the input screen, press _ or j
and close the input table. You can then check statistical values from the STAT menu (; 8) and specify statistical variables.

Afterenteringthedata,press e. The input is finalized and the cursor moves to the next line. If data was not entered in an x or y, 0 is entered, 1 is entered in FRQ (frequency), and the cursor moves to the next line. · You can use H to enter X and FRQ (or X, Y, and FRQ) at once. in length are displayed in exponent notation.

Up to 100 data items can be entered. With single-variable data, a data item with an assigned frequency of one is counted as one data item, while an item with an assigned frequency of 2 or higher is stored as a set of two data items. With two-variable data, a set of data items with an assigned frequency of one is counted as two data items, while a set of items with an assigned frequency of 2 or higher is stored as a set of three data items. press_ or jand close the i nput table.

Data correction

Use l, r, u, or d to move the cursor and select the desired data. Press @ u or @ d to jump the cursor to the beginning or end of the data.
Data correction Move the cursor to the data that you want to correct, enter the numeric value, and press e.
Data insertion To insert a line in front of the cursor position, press ; T. The initial values entered in the inserted data are 0 in x and y, and 1 in FRQ.
Data deletion To delete the entire line where cursor is positioned, press @ y.

Statistical Calculations and Variables
The following statistics can be obtained for each statistical calculation (refer to the table below):

Single-variable statistical calculation Statistics of 1 , 3 and the value of the normal probability function.

Linear regression calculation
Statistics of 1 , 2 and 4 . In addition, the estimate of y for a given x (estimate y´) and the estimate of x for a given y (estimate x´).

Quadratic regression calculation
Statistics of 1 , 2 and 4 . And coefficients a, b, c in the quadratic regression formula (y = a + bx + cx2). (For quadratic regression calculations, no correlation coefficient (r) can be obtained.) When there are two x´ values, each value will be displayed with “1:” or
“2:”, and stored separately in the X and Y memories.
You can also specify the 1st value (x1′) and the 2nd value (x2′) separately.

Euler exponential regression, logarithmic regression, power regression, inverse regression, and general exponential regression calculations Statistics of 1 , 2 and 4 . In addition, the estimate of y for a given x and the estimate of x for a given y. (Since the calculator converts each formula into a linear regression formula before actual calculation takes place, it obtains all statistics, except coefficients a and b, from
converted data rather than entered data.)

n

Number of samples

­x

Mean of samples (x data)

sx

Sample standard deviation (x data)

s2x

Sample variance (x data)

sx 1 s2x

Population standard deviation (x data) Population variance (x data)

x

Sum of samples (x data)

x2

Sum of squares of samples (x data)

xmin Minimum value of samples (x data)

xmax Maximum value of samples (x data)

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­y

Mean of samples ( y data)

sy

Sample standard deviation ( y data)

s2y

Sample variance ( y data)

sy

Population standard deviation ( y data)

s2y

Population variance ( y data)

y

Sum of samples ( y data)

2 y 2

Sum of squares of samples ( y data)

xy

Sum of products of samples (x, y)

x2y Sum of products of samples (x2, y)

x3

Sum of 3rd powers of samples (x data)

x4 ymin

Sum of 4th powers of samples (x data) Minimum value of samples ( y data)

ymax Maximum value of samples ( y data)

Q1

First quartile of sample (x data)

3 Med Median of sample (x data)

Q3

Third quartile of sample (x data)

r

Correlation coefficient (Except Quadratic regression)

a

Coefficient of regression equation

b 4c

Coefficient of regression equation Coefficient of quadratic regression equation

R2

Coefficient of determination (Quadratic regression)

r2

Coefficient of determination (Except Quadratic regression)

STAT Menu
After closing the input table, you can view statistical values, view regression coefficient values, and specify statistical variables from the STAT menu (; 8).
; 8 0: Display statistical values ; 8 1: Display regression coefficient values ; 8 2: Specify statistical value variables
; 8 3: Specify statistical value ( related) variables
; 8 4: Specify max/min value variables ; 8 5: Specify regression coefficient variables
Notes: · Listdisplayofregressioncoefficientvaluesandspecificationof
regression coefficient variables do not appear in single-variable statistical calculation.
· Estimated values x’ and y’ are specified with the keys (@ V, @ U). If there are two x’ values, you can specify x1′ and x2′ from the STAT
menu (; 8 5) to obtain the values separately. · Inthestatisticalvalueandregressioncoefficientvaluelists,youcannot
return to the menu by pressing N.

Setting a table
1. Press b 2 to enter TABLE mode. 2. Enter a function (Function1), and press e. 3. If needed, enter the 2nd function (Function2) and press e. 4. Enter a starting value (X_Start:), and press e.
The default starting value is 0.
5. Enter a step value (X_Step:). The default step value is 1. · Youcanuseu and d to move the cursor between the starting
value and step value. 6.Presse when you finish entering a step value. A table with a
variable X and the corresponding values (ANS column) appears,
displaying 3 lines below the starting value.
If you entered two functions, the ANS1 and ANS2 columns appear. You can use u and d to change the X value and see its
corresponding values in table format. · Thetableisfordisplayonlyandyoucannoteditthetable. · Thevaluesaredisplayedupto7digits,includingsignsandadecimal
point.

Press l or r to move the cursor to ANS column (ANS1 and ANS2
columns if you entered two functions) or X column. · Full digits of the value on the cursor are displayed on the bottom right.· Irrationalnumberssuchasr and can also be entered into a starting
value or a step value. You cannot enter 0 or a negative number as a
step value. · YoucanuseWriteVieweditorwheninputtingafunction. · ThefollowingfeaturesarenotusedinTABLEmode:coordinate
conversions, conversion between decimal and sexagesimal numbers,
and angular unit conversions. · It may take time to make a table, or “——-” may be displayed, depending on
the function entered or conditions specified for the variable X.  Press @ Z or mode selection to return to the initial screen of the
mode, and return to the default values for the starting value and step value.

COMPLEX NUMBER CALCULATIONS

To carry out addition, subtraction, multiplication, and division using complex numbers, press b 3 to select COMPLEX mode. Results of complex number calculations are expressed using two systems: 1 @ E: Rectangular coordinate system
(The symbol appears.) 2 @ u: Polar coordinate system
(The symbol appears.)

Complex Number Entry
1 Rectangular coordinates x-coordinate + y-coordinate O or x-coordinate + O y-coordinate
2 Polar coordinates
r @ Q r : absolute value : argument
· Onselectinganothermode,theimaginarypartofanycomplexnumber stored in the independent memory (M) and the last answer memory (ANS) will be cleared.
· Acomplexnumberexpressedinrectangularcoordinateswiththe y-value equal to zero, or expressed in polar coordinates with the angle equal to zero, is treated as a real number.
· From the MATH menu, you can obtain the complex conjugate (conj( ), the argument of a complex number (arg( ), the real part of a complex number (real( ), and the imaginary part of a complex number (img( ).

EQUATION SOLVERS

The results obtained by these functions may include a margin of error.

Simultaneous Linear Equations
Simultaneouslinearequationswithtwounknowns(2-VLE)orwiththree unknowns(3-VLE)maybesolvedusingthefollowingfunctions. 1 2-VLE:b 4 0

a1x + b1y = c1 a2x + b2y = c2

D =

a1 b1 a2 b2

2 3-VLE:b 4 1

a1x + b1y + c1z = d1

a1 b1 c1

a2x + b2y + c2z = d2

D =

a2 b2 c2

a3x + b3y + c3z = d3

a3 b3 c3

· IfthedeterminantD=0,anerroroccurs. · Iftheabsolutevalueofanintermediateresultorcalculationresultis1

× 10100 or more, an error occurs.

Solving simultaneous linear equations
1. Press b 4 0 or b 4 1.
2. Enter the value for each coefficient (a1, etc.).
· Coefficientscanbeenteredusingordinaryarithmeticoperations. · Tocleartheenteredcoefficient,pressj. · Pressu or d to move the cursor up or down through the
coefficients. Press @ u or @ d to jump to the first or
last coefficient. 3. When all coefficients have been entered, press e to solve the
equation. · While the solution is displayed, press e or j to return to the
coefficient entry display. To clear all the coefficients, press @ Z .

Quadratic and Cubic Equations
Quadratic (ax2 + bx + c = 0) or cubic (ax3 + bx2 + cx + d = 0)
equations may be solved using the following functions. 1 Quadratic equation solver: b 4 2 2 Cubic equation solver: b 4 3 · If there are two or more solutions, those solutions are also shown. · Ifcalculable,youcanalsoobtaintheminimumvalue(whena>0)and
themaximumvalue(whena<0)ofaquadraticfunction(y = ax2 + bx + c) .
Solving quadratic and cubic equations · Pressb 4 2 or b 4 3. · Coefficientsfortheseequationscanbeenteredinthesamemanneras
those for simultaneous linear equations. · WhenusingtheQUADRATICequationsolver,continuebypressing
e (or d) to display the minimum value or maximum value. To return to the solution, press u with the minimum value or maximum
value displayed. · Toreturntothecoefficiententryscreenwhenthesolution(or
minimum/maximum value) is displayed, press e or j. · Toclearallthecoefficients,press@ Z .

MATRIX CALCULATIONS

You can store and calculate up to four matrices.

Entering and Storing Matrices
1. Press b 5 to enter MATRIX mode. 2. Press N 1 to bring up the matrix entry screen.
· Anymatrixdataremaininginthebuffer,alongwithanypreviously entered, loaded, or calculated matrix data, will be displayed.
3. Define the matrix dimensions (up to four rows by four columns) by entering the required dimensions using the number keys and pressing e.

Matrix dimensions (row × column) Element fields

Entry field
Matrix entry screen (example)
4. Enter each element in the matrix by entering a value in the entry field and pressing e. · Eachmatrixelementcandisplayuptosevendigits(thedecimal point counts as one digit). If an element exceeds seven digits in length, it may be displayed in exponent notation within the matrix. · Amaximumofthreerowsbythreecolumnscanbedisplayedat one time. Use u, d, l, and r to move the cursor through the matrix.
5. When you have entered a value for each element, press j to exit the matrix entry screen.
6. PressN 3 and select a memory (matA­matD) to store the newly-created matrix in.

4/9

Modifying a stored matrix
1. To load a stored matrix into the matrix entry screen, press N 2, then select the memory (matA­matD) that you wish to modify. · Loadingnewdataintothescreenwillautomaticallyreplaceany data that may already exist there.
2. Modify the values of elements in the matrix, and press e after each one. · Ifyouwishtomodifythenumberofrowsorcolumns,firstpress j N 1. You can then enter new values for the matrix dimensions.
3. When you have finished making changes, press j to exit the matrix entry screen.
4. Press N 3 and select a memory (matA­matD) to store the newly-created matrix in.

Using Matrices in Calculations
Matrices stored in memories (matA­matD) can be used in arithmetic calculations (with the exception of division between matrices) and
calculations that use x3, x2, and x-1. You can also use the following
matrix-specific functions that are available in the MATH menu.

det matrix name

Returns the determinant of a square matrix.

trans matrix name

Returns the matrix with the columns transposed to rows and the rows transposed to columns.

identity value

Returns the identity matrix with specified value of rows and columns.

dim (matrix name, row, column) Returns a matrix with dimensions changed as specified.

fill (value, row, column)

Fills each element with a specified value.

rand_mat (row, column)

Returns a random matrix with specified values of rows and columns.

VECTOR CALCULATIONS

Entering and Storing Vectors
Before performing vector calculations, a vector must be created. Follow the steps below to enter and store vectors. 1. Press b 6toenterVECTORmode. 2. Press N 1 to bring up the vector entry screen.
· Any vector data remaining in the buffer, along with any previously entered, loaded, or calculated vector data, will be displayed.
3. Define the vector dimensions (2 dimensions or 3 dimensions) by using the number keys and pressing e.
4. Enter each element in the vector by entering a value in the entry field and pressing e. · Eachvectorelementcandisplayuptosevendigits(thedecimal point counts as one digit). If an element exceeds seven digits in length, it may be displayed in exponent notation within the vector.
5. When you have finished entering a value for each element, press j to exit the vector entry screen.
6. PressN 3 and select a memory (vectA­vectD) to store the newly-created vector in.
Modifying a stored vector
1. To load a stored vector into the vector entry screen, press N 2, then select the memory (vectA­vectD) that you wish to modify. · Loadingnewdataintothescreenwillautomaticallyreplaceany data that may already exist in the vector entry screen.
2. Modify the values of elements in the vector, and press e after each one. · Ifyouwishtomodifythenumberofdimensions,firstpress j N 1. You can then enter new values for the vector dimensions.
3. When you have finished making changes, press j to exit the vector entry screen.
4. Press N 3 and select a memory (vectA­vectD) to store the newly-created vector in.
Using Vectors in Calculations
vectors stored in memories (vectA­vectD) can be used in arithmetic calculations (with the exception of division between vectors). You can also use the following vector-specific functions that are available in the MATH menu.

DISTRIBUTION FUNCTIONS
The calculator has distribution features to find statistical calculations. Press b 7, and select the type (NORMAL, BINOMINAL, POISSON), and then select the desired distribution function. Note: Calculation results are stored in ANS memory.

Normal Distribution
Normal pdf Calculates the probability density of the specified value x for the nor-
maldistribution with the specified mean (µ) and standard deviation ().
Normal cdf Calculates the probability of specified intervals x1-x2 for the normal
distribution with the specified mean (µ) and standard deviation ().
Inverse Normal Calculates the inverse cumulative normal distribution function for a given area (a) under the normal distribution curve specified by mean (µ)
and standard deviation ().

Binomial Distribution
Binomial pdf Calculates a probability density at x for the discrete binomial distribution with the specified trial number (n) and probability of success (p) on each trial.
Binomial cdf Calculates a cumulative probability at x for the discrete binomial distribution with the specified trial number (n) and probability of success (p) on each trial.
Poisson Distribution
Poisson pdf Calculates a probability at x for the Poisson distribution with the specified mean (µ) .
Poisson cdf Calculates a cumulative probability at x for the Poisson distribution with the specified mean (µ).

Math Drill: b 8 0 Math operation questions with positive integers and 0 are displayed randomly. It is possible to select the number of questions and operator type.

Multiplication Table (× Table): b 8 1
Questions from each row of the multiplication table (1 to 12) are displayed serially or randomly.

To exit DRILL mode, press b and select another mode.
Using Math Drill and × Table
1. Press b 8 0 for Math Drill or b 8 1 for × Table.
2. Math Drill: Use u and d to select the number of questions (25,
×50, or 100). Table: Use u and d to select a row in the multiplication
table (1 to 12). 3. Math Drill: Use l and r to select the operator type for
×questions (+, -, ×, ÷, or +-×÷). Table: Use l and r to select the order type (“Serial” or “Random”). 4. Press e to start.

When using Math Drill or × Table (random order only), questions are
randomly selected and will not repeat except by chance. 5. Enter your answer. If you make a mistake, press j or N to clear
any entered numbers, and enter your answer again. 6. Presse.
· Iftheansweriscorrect,” ” appears and the next question is
displayed. · Iftheansweriswrong,” ” appears and the same question is
displayed. This will be counted as an incorrect answer. · Ifyoupresse without entering an answer, the correct answer
is displayed and then the next question is displayed. This will be
counted as an incorrect answer.  and pressing e. 8. After you finish, press e and the number and percentage of
correct answers are displayed. 9. Press e to return to the initial screen for your current drill.

Ranges of Math Drill Questions

The range of questions for each operator type is as follows.

Addition operator: “0 + 0” to “20 + 20”

]

Subtraction operator: “0 – 0” to “20 – 20”; answers are

positive integers and 0.

Multiplication operator: “1 × 0” or “0 × 1” to “12 × 12”

)

Division operator: “0 ÷ 1” to “144 ÷ 12”; answers are positive

integers from 1 to 12 and 0, dividends of up to 144, and

divisors of up to 12.

+]>) Mixed operators: Questions within all the above ranges are

displayed.

ERRORS AND CALCULATION RANGES
Errors
An error will occur if an operation exceeds the calculation ranges, or if a mathematically illegal operation is attempted. When an error occurs, pressing l or r automatically moves the cursor back to the place in the equation where the error occurred. Edit the equation or press j or @ Z to clear the equation.
Error codes and error types

Alert Messages

Cannot delete! · TheselecteditemcannotbedeletedbypressingN or @ y
intheWriteVieweditor. Ex. * 5 r A l N In this example, delete the exponent before attempting to delete the parentheses.
Cannot call! · Thefunctionoroperationstoredindefinablememory(D1toD3)
cannot be called. Ex. An attempt was made to recall a statistical variable from within NORMAL mode.

Buffer full! · Theequation(includinganycalculationendinginstructions)exceeded
itsmaximuminputbuffer(159charactersintheWriteVieweditoror 161charactersintheLineeditor).Anequationmaynotexceedits
maximum input buffer.

Calculation Ranges

Within the ranges specified, this calculator is accurate to ±1

of the 10th digit of the mantissa. However, a calculation error

increases in continuous calculations due to accumulation of each
calculation error. (This is the same for y x, xr, n!, ex, ln, Matrix/
Vector calculations, , etc., where continuous calculations are

performed internally.)

Additionally, a calculation error will accumulate and become

larger in the vicinity of inflection points and singular points of

functions. · Calculationranges
±10-99 to ±9.999999999 × 1099 and 0.

If the absolute value of an entry or a final or intermediate result of a calculation is less than 10-99, the value is considered to be 0 in

calculations and in the display.

Display of results using r (when EXACT is selected)

Calculation results may be displayed using r when all of the following
conditions are met: · Whenintermediateandfinalcalculationresultsaredisplayedinthe

following form:

±a P eb

±

c Pd f

· Wheneachcoefficientfallsintothefollowingranges:

1 a < 100; 1 < b < 1,000; 0 c < 100;

1 d < 1,000; 1 e < 100; 1 f < 100

· Whenthenumberoftermsintheintermediateandfinalcalculation

results is one or two. Note: The result of two fractional terms that include r will be reduced to

a common denominator.

BATTERY REPLACEMENT
Notes on Battery Replacement
Improper handling of batteries can cause electrolyte leakage or explosion. Be sure to observe the following handling rules:
before it reaches the service life stated in the specifications.

Notes on erasure of memory contents
When the battery is replaced, the memory contents are erased. Erasure can also occur if the calculator is defective or when it is repaired. Make a note of all important memory contents in case accidental erasure occurs.

When to Replace the Battery
If the display has poor contrast or nothing appears on the display when j is pressed in dim lighting, even after adjusting the display contrast, it is time to replace the battery.50

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