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Calculations Using Engineering Prefixes
Calculation can be executed in the normal mode (excluding N-
base) using the following 9 types of prefixes.
Prefix
Operation
k
(kilo)
∑10
∑11
M
(Mega)
∑12
G
(Giga)
∑13
T
(Tera)
∑14
m
(milli)
µ
(micro)
∑15
∑16
n
(nano)
∑17
p
(pico)
∑18
f
(femto)
Modify Function
Calculation results are internally obtained in scientific notation
with up to 14 digits for the mantissa. However, since calculation
results are displayed in the form designated by the display nota-
tion and the number of decimal places indicated, the internal
calculation result may differ from that shown in the display. By
using the modify function, the internal value is converted to match
that of the display, so that the displayed value can be used
without change in subsequent operations.
Solver Function
The x value can be found that reduces an entered equation to "0".
• This function uses Newton's method to obtain an approxima-
tion. Depending on the function (e.g. periodic) or start value, an
error may occur (Error 2) due to there being no convergence to
the solution for the equation.
• The value obtained by this function may include a margin of
error. If it is larger than acceptable, recalculate the solution
after changing 'Start' and dx values.
• Change the 'Start' value (e.g. to a negative value) or dx value
(e.g. to a smaller value) if:
• no solution can be found (Error 2).
• more than two solutions appear to be possible (e.g. a cubic
equation).
• to improve the arithmetic precision.
• The calculation result is automatically stored in the X memory.
[Performing Solver function]
Q Press m0.
W Input a formula with an x variable.
E Press ∑0.
R Input 'Start' value and press ®. The default value is "0".
T Input dx value (minute interval).
Y Press ®.
SIMULATION CALCULATION (ALGB)
If you have to find a value consecutively using the same formula,
such as plotting a curve line for 2x
2
+ 1, or finding the variable for
2x + 2y =14, once you enter the equation, all you have to do is to
specify the value for the variable in the formula.
Usable variables: A-F, M, X and Y
Unusable functions: Random function
• Simulation calculations can only be executed in the normal
mode.
• Calculation ending instructions other than = cannot be used.
Performing Calculations
Q Press m0.
W Input a formula with at least one variable.
E Press @≤.
R Variable input screen will appear. Input the value of the flashing
variable, then press ® to confirm. The calculation result will
be displayed after entering the value for all used variables.
• Only numerical values are allowed as variables. Input of
formulas is not permitted.
• Upon completing the calculation, press @≤ to per-
form calculations using the same formula.
• Variables and numerical values stored in the memories will
be displayed in the variable input screen. To change a
numerical value, input the new value and press ®.
• Performing simulation calculation will cause memory loca-
tions to be overwritten with new values.
STATISTICAL CALCULATIONS
Press m1 to select the statistics mode. The seven statisti-
cal calculations listed below can be performed. After selecting the
statistics mode, select the desired sub-mode by pressing the
number key corresponding to your choice.
To change statistical sub-mode, reselect statistics mode (press
m1), then select the required sub-mode.
0 (SD)
: Single-variable statistics
1 (LINE)
: Linear regression calculation
2 (QUAD) : Quadratic regression calculation
3 (EXP)
: Exponential regression calculation
4 (LOG)
: Logarithmic regression calculation
5 (PWR)
: Power regression calculation
6 (INV)
: Inverse regression calculation
The following statistics can be obtained for each statistical calcu-
lation (refer to the table below):
Single-variable statistical calculation
Statistics of Q and value of the normal probability function
Linear regression calculation
Statistics of Q and W and, in addition, estimate of y for a given
x (estimate y´) and estimate of x for a given y (estimate x´)
Exponential regression, Logarithmic regression,
Power regression, and Inverse regression calculation
Statistics of Q and W. In addition, estimate of y for a given x and
estimate of x for a given y. (Since the calculator converts each
Unit
formula into a linear regression formula before actual calculation
10
3
takes place, it obtains all statistics, except coefficients a and b,
10
6
from converted data rather than entered data.)
10
9
12
10
Quadratic regression calculation
–3
10
Statistics of Q and W and coefficients a, b, c in the quadratic
10
–6
regression formula (y = a + bx + cx
10
–9
calculations, no correlation coefficient (r) can be obtained.) When
there are two x´ values, press @≠.
10
–12
–15
When performing calculations using a, b and c, only one numeric
10
value can be held.
Mean of samples (x data)
¯ x
sx
Sample standard deviation (x data)
σ x
Population standard deviation (x data)
Q
n
Number of samples
Σ x
Sum of samples (x data)
Σ x
2
Sum of squares of samples (x data)
¯ y
Mean of samples (y data)
sy
Sample standard deviation (y data)
σ y
Population standard deviation (y data)
Σ y
Sum of samples (y data)
Σ y
W
2
Sum of squares of samples (y data)
Σ xy
Sum of products of samples (x, y)
r
Correlation coefficient
a
Coefficient of regression equation
b
Coefficient of regression equation
c
Coefficient of quadratic regression equation
• Use K and R to perform a STAT variable calculation.
Data Entry and Correction
Entered data are kept in memory until @c or mode selec-
tion. Before entering new data, clear the memory contents.
[Data Entry]
Single-variable data
Data k
Data & frequency k (To enter multiples of the same data)
Two-variable data
Data x & Data y k
Data x & Data y & frequency k (To enter multiples
of the same data x and y.)
• Up to 100 data items can be entered. With the single-variable
data, a data item without frequency assignment is counted as
one data item, while an item assigned with frequency is stored as
a set of two data items. With the two-variable data, a set of data
items without frequency assignment is counted as two data items,
while a set of items assigned with frequency is stored as a set of
three data items.
[Data Correction]
Correction prior to pressing k immediately after a data entry:
Delete incorrect data with ª, then enter the correct data.
Correction after pressing k:
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 'Xn=', 'Yn=', or 'Nn=' (n is the sequen-
tial number of the data set).
Display the data item to modify, input the correct value, then
press k. Using &, you can correct the values of the data
set all at once.
• To delete a data set, display an item of the data set to delete,
then press @J. The data set will be deleted.
• To add a new data set, press ª and input the values, then
press k.
Statistical Calculation Formulas
Type
Linear
y = a + bx
Exponential
y = a • e
bx
Logarithmic
y = a + b • ln x
Power
y = a • x
b
Inverse
y = a + b —
Quadratic
y = a + bx + cx
In the statistical calculation formulas, an error will occur when:
• The absolute value of the intermediate result or calculation result
is equal to or greater than 1 × 10
• The denominator is zero.
• An attempt is made to take the square root of a negative number.
• No solution exists in the quadratic regression calculation.
Normal Probability Calculations
• P(t), Q(t), and R(t) will always take positive values, even when
t<0, because these functions follow the same principle used
when solving for an area.
Values for P(t), Q(t), and R(t) are given to six decimal places.
SIMULTANEOUS LINEAR EQUATIONS
Simultaneous linear equation with two unknowns (2-VLE) or with
three unknowns (3-VLE) may be solved using this function.
Q 2-VLE: m20
W 3-VLE: m21
2
). (For quadratic regression
Regression formula
1
x
2
100
.
• If the determinant D = 0, an error occurs.
• If the absolute value of an intermediate result or calculation result
is 1 × 10
100
or more, an error occurs.
• Coefficients ( a
, etc.) can be entered using ordinary arithmetic
1
operations.
• To clear the entered coefficients, press @c.
• Pressing ® when the determinant D is in the display recalls
the coefficients. Each time ® is pressed, a coefficient is
displayed in the order of input, allowing the entered coefficients
to be verified (by pressing @®, coefficients are displayed
in reverse order.) To correct a particular coefficient being dis-
played, enter the correct value and then press ®.
QUADRATIC AND CUBIC EQUATION SOLVERS
Quadratic (ax
2
+ bx + c = 0) or cubic (ax
3
+ bx
may be solved using this function.
Q Quadratic equation solver: m22
W Cubic equation solver:
m23
• Press ® after entering each coefficient.
• The result will be displayed by pressing ® after entering all
coefficients. When there are more than 2 results, the next solu-
tion will be displayed.
• When the result is an imaginary number, "xy" symbol will appear.
The display can be switched between imaginary and real parts
by pressing @≠.
• The results obtained by this function may include a margin of error.
COMPLEX NUMBER CALCULATIONS
To carry out addition, subtraction, multiplication, and division using
complex numbers, press m3 to select the complex number
mode.
Results of complex number calculations are expressed in two modes:
Q @}: Rectangular coordinate mode (xy appears.)
W @{: Polar coordinate mode ( r θ appears.)
Complex number entry
Q Rectangular coordinates
x-coordinate + y-coordinate Ü
or x-coordinate + Ü y-coordinate
W Polar coordinates
r Ö θ
θ: argument
r: absolute value
• On selecting another mode, the imaginary part of any complex
number stored in the independent memory (M) will be cleared.
• A complex number expressed in rectangular coordinates with the
y-value equal to zero, or expressed in polar coordinates with the
angle equal to zero, is treated as a real number.
• Press ∑0 to return the complex conjugate of the speci-
fied complex number.
MATRIX CALCULATIONS
This function enables the saving of up to 4 matrices (4 rows x 4
columns) for calculations. Press m4 to enter the matrix mode.
• Matrix data must be entered prior to making calculations. Press-
ing [/] will display the matrix edit buffer along with
Enter the value of each item ('ROW', 'COLUMN', and then each
element, e.g. 'MAT1,1') and press k after each. After enter-
ing all items, press ª, then press °2 and specify
matA-D to save the data.
• To edit data saved in matA-D, press °1 and specify
matA-D to recall the data to the matrix edit buffer. After editing,
press ª, then press °2 and specify matA-D to save
the data.
• Before performing calculations, press ª to close the matrix
edit buffer.
• When results of calculations are in the matrix format, the matrix
edit buffer with those results will be displayed. (At this time, you
cannot return to the equation.) To save the result in matA-D,
press ª, then press °2 and specify matA-D.
• Since there is only one matrix edit buffer, the previous data will
be overwritten by the new calculation.
• In addition to the 4 arithmetic functions (excluding divisions be-
tween matrices), x
3
, x
2
, and x
–1
, the following commands are
available:
dim( matrix name,
Returns a matrix with dimensions changed as
row,column )
specified.
fill( value,row,column ) Fills each element with a specified value.
cumul matrix name
Returns the cumulative matrix.
aug( matrix name,
Appends the second matrix to the first matrix as new
matrix name )
columns. The first and second matrices must have
the same number of rows.
identity value
Returns the identity matrix with specified value of
rows and columns.
rnd_mat( row,column ) Returns a random matrix with specified values of
rows and columns.
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.
mat→list
Creates lists with elements from the left column of each
(∑5)
matrix. (matA→L1, matB→L2, matC→L3, matD→L4)
Mode changes from matrix mode to list mode.
Creates lists with elements from each column of the
matA→list
(∑6)
matrix. (matA→L1, L2, L3, L4)
Mode changes from matrix mode to list mode.
LIST CALCULATIONS
This function enables the saving of up to 4 lists of 16 elements for
calculations. Press m5 to enter the list mode.
• List data must be entered prior to making calculations. Pressing
[/] will display the list edit buffer along with
2
+ cx + d = 0) equation
.
. Enter
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