ERROR 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 < (or >) automatically moves the cursor
back to the place in the equation where the error occurred. Edit the
equation or press N to clear the equation.
COMPLEX NUMBER CALCULATIONS
To carry out addition, subtraction, multiplication, and division using
complex numbers, press m1 to select the complex number
mode.
There are two modes of expression of the results of complex
number calculations.
Q Rectangular coordinate mode. (xy appears on the display.)
@}
W Polar coordinate mode. (
r
θ
appears on the display.)
@{
Complex number entry
Q Rectangular coordinates
x-coordinate
+
y-coordinate
Ü
or
x-coordinate
+ Ü
y-coordinate
W Polar coordinates
r
Ö
θ
r: absolute value
θ: argument
• Upon changing to another mode, the imaginary portion 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.
(12–6i) + (7+15i) m1 12 - 6 Ü+ 7 + 15 Ü
– (11+4i) = -( 11 + 4 Ü)= [x]
8.
û [y]
5.
ù [x]
8.
6×(7–9i) × 6 *( 7 - 9 Ü)*
(–5+8i) = ( 5 ±+ 8 Ü)= [x]
222.
û [y]
606.
16×(sin30°+ 16 *(s 30 +Üu 30 )
icos30°)÷(sin60°+ /(s 60 +Üu 60
icos60°)= )= [x]
13.85640646
û [y]
8.
@{ 8 Ö 70 + 12 Ö 25
= [r]
18.5408873
û [θ]
42.76427608
r1 = 8, θ1 = 70°
r2 = 12, θ2 = 25°
↓
r = ?, θ = ?°
+
+
i
i
m2
1 ® 1 ® 1 ±® 9 ®
6 ® 6 ® 1 ±® 17 ®
14 ® 7 ±® 2 ® 42
x = ? ® [x]
3.238095238
y = ? ® [y]
–1.638095238
z = ? ® [z]
–7.4
det(D) = ? ® [det(D)]
105.
If the coefficients c1, c2 and c3 as well as a3 – d3 are set to zero, the
problem is treated as a 2-dimensional simultaneous equation. The
x and y values as well as the determinant can be retrieved.
i
∠
+
@c 2 ® 3 ®® 4 ®
5 ® 6 ®® 7 ®
x = ? ®®®® [x]
–1.
y = ? ® [y]
2.
det(D) = ? ® [det(D)]
–3.
STATISTICAL CALCULATIONS
Statistical calculations are performed in the statistics mode.
Press m3 to select the statistics mode.
This calculator performs the seven statistical calculations indicated
below. After selecting the statistics mode, select the desired
submode by pressing the number key corresponding to your choice.
When changing to the statistical submode, press the correspond-
ing number key after performing the operation to select the statis-
tics mode (press m3).
0 (STAT 0) : Single-variable statistics
1 (STAT 1) : Linear regression calculation
2 (STAT 2) : Quadratic regression calculation
3 (STAT 3) : Exponential regression calculation
4 (STAT 4) : Logarithmic regression calculation
5 (STAT 5) : Power regression calculation
6 (STAT 6) : Inverse regression calculation
The following statistics can be obtained for each statistical calcula-
tion (refer to the table below):
Notes: • If the determinant D = 0, an error occurs.
• If the absolute value of an intermediate result or calcu-
lation result is 1 × 10
100
or more, an error occurs.
a1x + b1y + c1z = d1
a2x + b2y + c2z = d2
a3x + b3y + c3z = d3
a1 b1 c1
a2 b2 c2
a3 b3 c3
D =
SIMULTANEOUS LINEAR EQUATIONS
WITH THREE UNKNOWNS
To solve simultaneous linear equations with three unknowns, press
m2 to select the 3-VLE mode.
Simultaneous Linear Equations with Three Unknowns:
Performing Calculations
Q Press m2.
W Enter each coefficient from a
1 to d3 followed by ®, as
prompted on the display.
E Upon pressing ® after entering d3, the solution for x will be
displayed. Subsequent pressing will cycle through the values of
y, z and the determinant D.
• Coefficients can be entered using ordinary arithmetic operations.
• To clear the entered coefficients, press @c.
Note: Pressing ® when the determinant D is in the display
recalls the coefficients. Each time ® is pressed, a coeffi-
cient is displayed in the order of input, allowing the entered
coefficients to be verified. (by pressing @® or
@', coefficients are displayed in reverse order.)
To correct a particular coefficient being displayed, enter the
correct value and then press ®.
x Mean of samples (x data)
sx Sample standard deviation (x data)
Q
σ
x Population standard deviation (x data)
n Number of samples
Σ
x Sum of samples (x data)
Σ
x
2
Sum of squares of samples (x data)
y Means of samples (y data)
sy Sample standard deviation (y data)
σ
y Population standard deviation (y data)
Σ
y Sum of samples (y data)
W
Σ
y
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
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
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.)
Quadratic regression calculation:
Statistics of Q and W and coefficients a, b, c in the quadratic
regression formula (y = a + bx + cx
2
). (For quadratic regression
calculations, no correlation coefficient (r) can be obtained.)
When performing calculations using a, b and c, only one numeric
value can be held.
R~
75.71428571
Rp
12.37179148
Rz
530.
Rw
41200.
R£
13.3630621
L=
178.5714286
x = 60 → P(t) ? @π 60 @ü)=
0.102012
t = –0.5 → R(t) ? @∏ 0.5 ±)=
0.691463
x=
σx=
Σx=
Σx
2
=
sx=
sx
2
=
Score
95
80
80
75
75
75
50
Entered data are kept in memory until @ c or m 3
are pressed. 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.)
[Data Correction]
Correction prior to pressing k:
Delete incorrect data with N.
Correction after pressing k:
If nothing else but k is entered, press @J to delete,
then enter the correct value.
Single variable Statistical Calculations
m30
0.
95 k
1.
80 k
2.
k
3.
75 & 3 k
6.
50 k
7.
Regression Calculations
Given the two variable sample data (x,y), determine the standard
deviation of data sets x and y; the coefficients of the linear regres-
sion equation, and the correlation coefficient between x and y.
(Exponential, logarithmic, power, and inverse regression can also
be calculated in much the same way as linear regression.)
Quadratic Regression Calculation
Given the sample data shown, determine the coefficients a, b, and
c of the quadratic regression equation and estimate the following
values:
xy
12 41
813
52
23 200
15 71
m32
0.
12 & 41 k
1.
8 & 13 k
2.
5 & 2 k
3.
23 & 200 k
4.
15 & 71 k
5.
Ra
5.357506761
Rb
–3.120289663
R©
0.503334057
x=10→y’=? 10 @y
24.4880159
y=22→x’=? 22 @x
9.63201409
û*
–3.432772026
ù
9.63201409
* When there are two x values.
m31
0.
2 & 5 k
1.
k
2.
12 & 24 k
3.
21 & 40 & 3 k
6.
15 & 25 k
7.
Ra
1.050261097
Rb
1.826044386
Rr
0.995176343
R£
8.541216597
R¢
15.67223812
The following values are estimated:
x=3 → y’=? 3 @y
6.528394256
y=46 → x’=? 46 @x
24.61590706
xy
25
25
12 24
21 40
21 40
21 40
15 25
1
x
Σx = x
1
+ x
2
+ ··· + x
n
Σx
2
= x
1
2
+ x
2
2
+ ··· + x
n
2
Σxy = x
1
y
1
+ x
2
y
2
+ ··· + x
n
y
n
Σy = y
1
+ y
2
+ ··· + y
n
Σy
2
= y
1
2
+ y
2
2
+ ··· + y
n
2
Statistical Calculation Formulas
Type Regression formula
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
2
(n: Number of samples)
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
100
.
• 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]
1
x
1
x
1
x
1
x
π
2
Function Dynamic range
DEG: | x | < 4.5 × 10
10
(tan x : | x | ≠ 90 (2n–1))*
sin x, cos x, RAD: | x | < —– × 10
10
tan x (tan x : | x | ≠ – (2n–1))*
GRAD: | x | < 5 × 10
10
(tan x : | x | ≠ 100 (2n–1))*
sin
–1
x
,
cos
–1
x | x | ≤ 1
tan
–1
x,
3
¿x | x | < 10
100
In x
,
log x 10
–99
≤ x < 10
100
• y > 0: –10
100
< x ln y ≤ 230.2585092
y
x
• y = 0: 0 < x < 10
100
• y < 0: x = n (0 < | x | < 1: – = 2n–1, x ≠ 0)*,
–10
100
< x ln | y | ≤ 230.2585092
• y > 0: –10
100
< – ln y ≤ 230.2585092 (x ≠ 0)
x
¿y • y = 0: 0 < x < 10
100
• y < 0: x = 2n–1
(0 < | x | < 1 : – = n, x ≠ 0)*,
–10
100
< – ln | y | ≤ 230.2585092
e
x
–10
100
< x ≤ 230.2585092
10
x
–10
100
< x < 100
sinh x,
cosh x
| x | ≤ 230.2585092
tanh x | x | < 10
100
sinh
–1
x | x | < 5 × 10
99
cosh
–1
x 1 ≤ x < 5 × 10
99
tanh
–1
x | x | < 1
x
2
| x | < 10
50
¿x 0 ≤ x < 10
100
x
–1
| x | < 10
100
(x ≠ 0)
n! 0 ≤ n ≤ 69*
nPr 0 ≤ r ≤ n ≤ 9999999999*
0 ≤ r ≤ n ≤ 9999999999*
nCr n – r < r: n – r ≤ 69
n – r ≥ r: r ≤ 69
↔DEG, D°M’S
0°00’00.01 ≤ | x | < 10000°
π
40
Function Dynamic range
x, y → r, θ
| x |, | y | < 10
50
| – |, x
2
+ y
2
< 10
100
0 ≤ r < 10
100
r, θ → x, y
DEG: | θ | < 4.5 × 10
10
RAD: | θ | <
––
× 10
10
GRAD : | θ | < 5 × 10
10
DEG→RAD,
DRG | GRAD→DEG: | x | < 10
100
RAD→GRAD: | x | < – × 10
98
(A+Bi)+(C+Di)| A ± C | < 10
100
(A+Bi)–(C+Di)| B ± D | < 10
100
(A+Bi)×(C+Di) (AC – BD) < 10
100
(AD + BC) < 10
100
AC + BD
< 10
100
C
2
+ D
2
(A+Bi)÷(C+Di)
BC – AD
< 10
100
C
2
+ D
2
C
2
+ D
2
≠ 0
→DEC DEC : | x | ≤ 9999999999
→BIN BIN : 1000000000 ≤ x ≤ 1111111111
→OCT 0 ≤ x ≤ 111111111
→HEX OCT : 4000000000 ≤ x ≤ 7777777777
AND 0 ≤ x ≤ 3777777777
OR HEX : FDABF41C01 ≤ x ≤ FFFFFFFFFF
XOR 0 ≤ x ≤ 2540BE3FF
XNOR
BIN : 1000000000 ≤ x ≤ 1111111111
0 ≤ x ≤ 111111111
NOT OCT : 4000000000 ≤ x ≤ 7777777777
0 ≤ x ≤ 3777777777
HEX : FDABF41C01 ≤ x ≤ FFFFFFFFFF
0 ≤ x ≤ 2540BE3FE
BIN : 1000000001 ≤ x ≤ 1111111111
0 ≤ x ≤ 111111111
NEG OCT : 4000000001 ≤ x ≤ 7777777777
0 ≤ x ≤ 3777777777
HEX : FDABF41C01 ≤ x ≤ FFFFFFFFFF
0 ≤ x ≤ 2540BE3FF
* (n, r: integer)
y
x
π
40
π
2
BATTERY REPLACEMENT
Notes on Battery Replacement
Improper handling of batteries can cause electrolyte leakage or
explosion. Be sure to observe the following handling rules:
• Replace both batteries at the same time.
• Do not mix new and old batteries.
• Make sure the new batteries are the correct type.
• When installing, orient each battery properly as indicated in the
calculator.
When to Replace the Batteries
If the display has poor contrast or nothing appears on the display
even when N is pressed in dim lighting, it is time to replace the
batteries.
Caution
• Fluid from a leaking battery accidentally entering an eye could
result in serious injury. Should this occur, wash with clean water
and immediately consult a doctor.
• Should fluid from a leaking battery come into contact with your
skin or clothes, immediately wash with clean water.
• If the product is not to be used for some time, to avoid damage to
the unit from leaking batteries, remove them and store in a safe
place.
• Do not leave exhausted batteries inside the product.
• Do not fit partially used batteries, and be sure not to mix batter-
ies of different types.
• Keep batteries out of the reach of children.
• Exhausted batteries left in the calculator may leak and damage
the calculator.
• Explosion risk may be caused by incorrect handling.
• Do not throw batteries into a fire as they may explode.
SPECIFICATIONS
Calculations: Scientific calculations, complex number
calculations, simultaneous linear
equations with three unknowns, statistical
calculations, etc.
Internal calculations: Mantissas of up to 12 digits
Pending operations: 16 calculations 8 numeric values
(4 numeric values in STAT and complex
number mode)
Power source: Built-in solar cells
3V ¶ (DC):
Backup batteries (Alkaline batteries (LR44)
× 2)
Operating temperature: 0°C – 40°C (32°F – 104°F)
External dimensions: 78.6 mm (W) × 152 mm (D) × 10.5 mm
(H)
3-3/32” (W) × 5-31/32” (D) × 13/32” (H)
Weight: Approx. 78 g (0.172 lb)
(Including batteries)
Accessories: Batteries × 2 (installed), operation
manual, quick reference card and hard
case.
Replacement Procedure
1. Turn the power off by pressing @ F.
2. Remove two battery cover screws.
3. Slide the battery cover slightly and lift it to remove.
4. Remove the used batteries by prying them with a ball-point pen
or other similar pointed device.
5. Install two new batteries. Make sure the “+” sides are faced up.
6. Replace the cover and screws.
7. Press the RESET switch (on the back).
• Make sure that the display appears as shown below.
If the display does not appear as shown, remove the batteries,
reinstall them and check the display once again.
Automatic Power Off Function
This calculator will turn itself off to save battery power if no key is
pressed for approximately 10 minutes.
··· Standardization conversion formula
*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.
∠
i
–
i
–
(1 + i) @} 1 +Ü=
1.
↓ @{ [r]
1.414213562
r = ?, θ = ?° û [θ]
45.
@}( 2 - 3 Ü)L
(2 – 3i)
2
= = [x]
–5.
û [y]
12.
1
=
( 1 +Ü)@•= [x]
0.5
1 + i û [y]
0.5
x + y – z =9
6x+6y – z =17
14x–7y+2z =42
2x + 3y = 4
5x + 6y = 7
Calculation Ranges
• Within the ranges specified below, this calculator is accu-
rate to ±1 in the least significant digit of the mantissa.
However, a calculation error increases in continuous calcu-
lations due to accumulation of each calculation error. (This
is the same for y
x
,
x
¿¿
¿¿
¿y, n!, e
x
, In, etc. where continuous
calculations are performed internally.)
Additionally, a calculation error will accumulate and be-
come larger in the vicinity of inflection points and singular
points of functions. (for example, calculating sinh x or tanh
x at x = 0)
• Calculation ranges
±10
-99
~ ±9.999999999×10
99
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.
Error Codes and Error Types
Syntax error (Error 1):
• An attempt was made to perform an invalid operation.
Ex. 2 +- 5 =
Calculation error (Error 2):
• The absolute value of an intermediate or final calculation result equals
or exceeds 10
100
.
• An attempt was made to divide by 0.
• The calculation ranges were exceeded while performing calculations.
Depth error (Error 3):
• The available number of buffers was exceeded. (There are 8 buffers*
for numeric values and 16 buffers for calculation instructions).
*4 buffers in STAT and the complex number mode.
Equation too long (Error 4):
• The equation exceeded its maximum input buffer (159 characters).
An equation must be shorter than 159 characters.
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