hp 9s
Ex. 7: Change 12385 to 789
1. Key in 12385
Mixed Arithmetic Calculations
Trigonometric and Inverse Trigonometric Functions
Before undertaking a trigonometric or inverse trigonometric
calculation, make sure that the appropriate angular unit is set.
DEG
DEG
789.
123.
Scientific Calculator
DEG
DEG
ENTER
1 [ + ] 2 [ × ] 3 [ ]
1 + 2 × 3 = ?
7.
2. Press [ CE ] 789
DEG
÷
3.5 [ +/– ] [ + ] 8 [
] 2
ENTER
]
3 sin 85° = ?
3 [ × ] 85 [ sin ] [
π
0.5
2.99
0.71
÷
–3.5 + 8 2 = ?
ENTER
[
]
Ex. 8: Change 12385 to 123
1. Key in 12385
π
4
÷
ENTER
] 4 [ ]
[ 2ndF ] [
[ cos ]
] [
RAD
cos (
rad) = ?
General Operations
Parentheses Calculations
Operations inside parentheses are always executed first. You can
specify up to 15 levels of parentheses in a single calculation. When
you enter the first parenthesis, the ( ) indicator appears on the display
and remains until each opening parenthesis has a corresponding
closing parenthesis.
GRAD
DEG
tan 150 grad = ?
150 [ tan ]
–1.00
30.00
Power Supply
On or Off
→
2. Press [ 00 0 ] twice.
sin –1 0.5 = ? deg 0.5 [ 2ndF ] [ sin –1
]
In a series of calculations, you can correct errors in intermediate
results by pressing [ON/C]. This clears the calculation without clearing
memory.
To turn the calculator on, press [ON/C].
1
cos –1
? rad
(
) =
√
[ cos –1
2 [
] [ 2ndF ] [ x –1] [ 2ndF ]
]
RAD
0.79
2
To turn the calculator off, press [2ndF] [OFF].
If you press the wrong arithmetic operation key, just press [ CE ] and
then the correct arithmetic key.
Auto power-off function
tan –1 1 = ? grad
1 [ 2ndF ] [ tan –1
]
GRAD
DEG
50.00
( 5–2 × 1.5 ) × 3
+ 0.8 × (– 4 )
= ?
2.8
[ ( ] 5 [ – ] 2 [ × ] 1.5 [ ) ] [ × ] 3
ENTER
The calculator automatically turns off if it has not been used for
approximately 9 minutes. Power can be restored by pressing the
[ON/C] key again. Memory contents and the current mode setting
(STAT, DEG, CPLX, Base-n,etc) are retained when you turn off the
power and when the calculator automatically turns off.
Exchange key
[ + ] 0.8 [ × ] 4 [ +/– ] [
]
Hyperbolic and Inverse hyperbolic functions
←→
Pressing [ 2ndF ] [ X Y ] changes the currently displayed value to
the previously displayed value.
DEG
cosh1.5+sinh1.5
= ?
1.5 [ HYP ] [ cos ] [ + ] 1.5
ENTER
DEG
2 × ( 7 + 6 × ( 5 2 [ × ] [ ( ] 7 [ + ] 6 [ × ] [ ( ] 5
ENTER
122.
4.48
[ HYP ] [ sin ] [
]
+ 4 )) = ?
[ + ] 4 [
]
sinh –1 7 = ?
tanh 1 =?
7 [ HYP ] [ 2ndF ] [ sin –1
]
DEG
DEG
DEG
ENTER
123 [ + ] 456 [
]
579.00
456.00
579.00
2.64
0.76
ENTER
].
Note: It is not necessary to press [ ) ] before [
Battery replacement
DEG
DEG
123 + 456 = ?
←→
[ 2ndF ] [ X Y ]
1 [ HYP ] [ tan ]
Repeating a Calculation
The calculator is powered by two alkaline button batteries (GP76A or
LR44). If the display becomes dim and difficult to read, the batteries
should be replaced as soon as possible.
←→
[ 2ndF ] [ X Y ]
Rectangular and Polar coordinates
You can repeat the last number entered, or the last operation
ENTER
executed, by pressing [
].
Accuracy and Capacity
Rectangular Coordinates
Polar Coordinates
Accuracy: ±1 in the 10th digit.
To replace the batteries:
Repeating the last number
DEG
DEG
DEG
Capacity: In general, calculations can be displayed as a mantissa of
up to 10 digits, a 10-digit mantissa together with a 2-digit exponent up
to 10 ±99, or as an integer between –9999999999 and 9999999999.
ENTER
]
3 [ × ] [
1. Slide the battery cover off and remove the old batteries.
2. Insert new batteries, with positive polarity facing outward.
3. Replace the battery cover and press [ON/C] to turn on the power.
9.
27.
81.
3 × 3 = ?
3 × 3 × 3 = ?
ENTER
[
[
]
3 × 3 × 3 × 3 = ?
ENTER
]
Numbers used as input to a particular function must be within the
allowable range for that function (as set out in the following table):
Repeating the last arithmetic operation
The keyboard
Most of the keys can perform two functions.
DEG
DEG
ENTER
321 [ + ] 357 [
321 + 357 = ?
654 + 357 = ?
]
678.
ENTER
654 [
]
1011.
Functions
sin x, cos x, tan x
Allowable input range
< 4.5 × 10 10 deg
< 2.5 × 10 8 π rad
< 5 × 10 10 grad
DEG
DEG
2nd function
sin–1
sin
Deg:
Rad:
Grad:
x
x
ENTER
]
579 – 159 = ?
456 – 159 = ?
579 [ – ] 159 [
ENTER
420.
297.
a + b i = r (cosθ + i sinθ)
――――――
456 [
]
Note: Before undertaking a coordinates conversion calculation, make
sure that the appropriate angular unit is set.
―――
1st function
x
DEG
DEG
DEG
ENTER
3 [ × ] 6 [ × ] 45 [
1st functions
]
810.
414.
900.
18 × 45 = ?
18 × 23 = ?
Converting from Rectangular to Polar
Also, for tan x:
ENTER
23 [
]
These are functions that are executed when you press a key without
first pressing [ 2ndF ]. The function performed is indicated by the label
on the key.
DEG
18 × (0.5x102) = ?
7.81
→
5 [ a ] 6 [ b ] [ 2ndF ] [ R P ]
If a = 5 and b = 6,
Deg:
Rad:
x
x
≠ 90 (2n +1)
ENTER
0.5 [ EXP ] 2 [
]
DEG
θ
?
what are r and
π
[ b ]
50.19
DEG
DEG
DEG
≠
(2n +1)
÷
÷
÷
ENTER
]
2
96
75
8 = ?
8 = ?
96 [
75 [
] 8 [
12.
9.375
15.
2nd functions
Converting from Polar to Rectangular
ENTER
]
These are functions that are executed when you press a key after first
pressing [ 2ndF ]. The function performed is indicated by the label
above the key.
Grad:
x
≠ 100 (2n +1)
25 [ a ] 56 [ b ] [ 2ndF ]
→
[ P R ]
θ
If r = 25 and
=
DEG
DEG
(1.2x102)
8 = ?
13.98
20.73
÷
ENTER
1.2 [ EXP ] 2 [
]
56°, what are a
and b?
where n is an integer.
[ b ]
Percentage Calculations
sin –1 x, cos –1
tan –1
x
x
x
x
x
x
≦ 1
When you press [ 2ndF ], the 2ndF indicator appears in the display to
indicate that you will be selecting the second function of the next key
you press. If you press [ 2ndF ] by mistake, simply press [ 2ndF ]
again to remove the 2ndF indicator.
120 [ × ] 30 [ 2ndF ] [ % ]
ENTER
DEG
DEG
DEG
Permutations and Combinations
30% of 120 = ?
70% of 120 = ?
36.
84.
< 1 × 10 100
≦ 230.2585092
< 1 × 10 100
< 5 × 10 99
[
]
x
n!
n!
ENTER
70 [ 2ndF ] [ % ] [
]
nPr =
nCr =
(n− r)!
r !(n − r)!
sinh x, cosh x
tanh x
÷
88 is 55% of what 88 [
] 55 [ 2ndF ] [ % ]
ENTER
]
Note: [ A ], [ B ], [ C ], [ D ], [ E ], [ F ] are 1st functions in HEX mode.
160.
How many
number?
30% mark up of
120 = ?
30% discount of
120 = ?
[
permutations of 4
items can you
select from a set
of 7 items?
120 [ + ] 30 [ 2ndF ] [ % ]
ENTER
Display Symbols
The following symbols, shown on the display, indicate the status of
the calculator.
DEG
DEG
DEG
DEG
ENTER
7 [ 2ndF ] [ nPr ] 4 [
7 [ 2ndF ] [ nCr ] 4 [
]
840.00
35.00
156.
84.
[
]
sinh –1
x
120 [ – ] 30 [ 2ndF ] [ % ]
ENTER
cosh –1
tanh –1
x
1 ≦ x < 5 × 10 99
< 1
[
]
How many
combinations of 4
items can you
select from a set
of 7 items?
Memory Calculations
DEG or RAD or GRAD: degrees, radians or grads angular unit
x
x
ENTER
]
The M indicator appears when a number is stored in memory.
Recalling from memory does not delete the contents of memory.
The memory is not available when you are in statistics mode.
•
•
•
•
M
E
A value is in memory
Overflow or error
Minus
CPLX Complex number mode
STAT Statistical mode
log x, ln x
1 × 10 –99 ≦ x < 1 x 10 100
–1 × 10 100 ＜ x ＜ 100
–1 × 10 100 ＜ x ≦ 230.2585092
0 ≦ x < 1 × 10 100
10 x
e x
–
2ndF
[2ndF] key pressed
Precision capability
Process capability
Deviation
↔
Sexagesimal
You can convert a sexagesimal figure (degree, minute and second) to
a decimal number by pressing [ ] and convert a decimal number
Decimal form Conversions
( )
Parentheses calculation CP
→
To copy the displayed number to memory, press [ X M ].
BIN Binary mode
OCT Octal mode
CPK
σ
→
→
To clear the memory, press [ 0 ] [ X M ], or [ CE ] [ X M ], in
that order.
•
x
to a sexagesimal figure by pressing [ 2ndF ] [
].
x 2
x –1
x
< 1 × 10 50
│x│＜1 × 10 100, X≠0
< 1 × 10 100
HEX Hexadecimal mode
USL
LSL
Setting upper limit
Setting lower limit
Sexagesimal figures are displayed as follows:
ED
Edit mode
DEG
0.
15.
8.
12 ꢀ 45
׀ 30 ׀ ׀ 5
= 12 degrees, 45 minutes, 30.5
seconds
→
[ CE ] [ X M ]
HYP Hyperbolic mode
DEG
3
3 [ × ] 5 [ M+ ]
M
M
M
M
x
x
3 × 5
Note: If the total number of digits in a DD, MM and SS.SS figure
exceeds 8, the figure is truncated.
DEG
DEG
DEG
DEG
÷
56 [
] 7 [ M+ ]
÷
+ 56
7
Display Formats
The calculator can display numbers in four formats: floating point,
fixed point, scientific, and engineering.
≦
≦
0
x
69, where x is an integer.
X !
+ 74 – 8 × 7
Total = ?
74 [ – ] 8 [ × ] 7 [ M+ ]
[ MR ]
→
18.
41.
0.
Converting from Sexagesimal to Decimal
1 × 10 100
→
R
P
2
2
＜
x
+ y
12 deg., 45 min.,
30.5 sec.= ?
12 [
[
] 45 [
] 30.5
DEG
DEG
1 × 10 100
12.76
0 [ X M ]
→
P
≦
＜
r
R
0
Floating point format
]
：│θ│＜
Deg
Rad
Grad
4.5 × 10 10 deg
Converting from Decimal to Sexagesimal
2.12345 = ? 2.12345 [ 2ndF ] [
The floating point format displays numbers in decimal form, using up
to 10 digits. Any trailing zeros are truncated.
Common Math Calculations
8π
2 ꢀ 7
׀ 24 ׀׀ 42 ：│θ│＜
2.5 × 10
rad
]
The following example calculations assume that your display is fixed
at 2 decimal places.
5 × 10 10 grad
If the result of a calculation is too large to be represented by 10 digits,
the display automatically switches to scientific format. If the result of a
later calculation is small enough to be displayed in less than 10 digits,
the calculator returns to floating point format.
：│θ│＜
Base-n Calculations
Converting between bases
Also, for tan x:
Reciprocal, Factorial
：│θ│≠
1
Deg
Rad
Grad
90 (2n+1)
1.25 [ 2ndF ] [ x –1] [
DEG
ENTER
]
You can add, subtract, multiply, and divide binary, octal, and
hexadecimal numbers in addition to decimal numbers. Select the
= ?
0.80
π
1.25
To set the display to floating point display format:
：│θ│≠
(2n+1)
2
DEG
ENTER
]
5! = ?
5 [ 2ndF ] [ x! ] [
120.00
→
→
→
number base you want by pressing [ BIN], [ OCT], [ HEX], or
DEG
•
0.
1. Press [ 2ndF ] [ FIX ] [
]
：│θ│≠
100 (2n+1)
→
DEC]. The BIN, OCT, and HEX indicators show you which base
Square, Square Root, Cube Root, Power, Other Roots
[
2 2 + 3 4 = ?
2 [ x 2 ] [ + ] 3 [ x y ] 4 [
DEG
where n is an integer.
you are using. (If none of these indicators is displayed, you are using
decimal base.)
Fixed point format
ENTER
]
85.00
20.83
1.61
│DD│, MM, SS.SS ＜ 1 × 10 100
,
√
5 [ × ] 27 [ 2ndF ] [ 3 ] [ + ]
ENTER
The fixed point, scientific, and engineering formats use a fixed
number of decimal places to display numbers. If more than the
specified number of decimal places is keyed, the entry will be rounded
to the correct number of decimal places.
DEG
DEG
5 ×3
+
= ?
34
27
The number keys that are active in a particular base are:
Binary base: [ 0 ] and [ 1 ]
√
34 [
] [
]
0 ≦ MM, SS.SS
72 [ 2ndF ] [ X ] 9 [
9
= ?
√
ENTER
]
72
x
< 1 × 10 100
Octal base: [ 0 ] to [ 7 ]
Logarithms and Antilogarithms
Ex. 1: Fix the display at 2 decimal places, then key in 3.256
x y
x > 0 : –1 × 10100 < y log x < 100
DEG
DEG
Decimal base: [ 0 ] to [ 9 ]
ENTER
7 [ ln ] [ + ] 100 [ log ] [
2 [ 2ndF ] [ 10 x ] [
ln7 + log100 = ?
10 2 = ?
]
3.95
DEG
1. Press [ 2ndF ] [ FIX ] 2
ENTER
0.00
3.26
x = 0 : y > 0
Hexadecimal base: [ 0 ] to [ 9 ] and [ A ] to [ F ]
ENTER
]
100.00
DEG
5 [ 2ndF ] [ e x ] [ – ] 2 [+/–]
ENTER
DEG
x < 0 : y = n, 1/(2n+1)
where n is an integer
1
→
[ 2ndF ] [ DEC] 31
2. Key in 3.256 [
]
e 5 – e –2 = ?
31.
11111.
37.
DEG
31 (base 10)
= ? (base 2)
= ? (base 8)
[ 2ndF ] [ e x ] [
]
148.28
DEG BIN
DEG OCT
DEG HEX
→
[ 2ndF ] [ BIN]
→
If fewer than the set number of decimal places is keyed, the entry will
be padded with trailing zeros.
[ 2ndF ] [ OCT]
→
but –1 x 10100
<
log x 100
Fraction calculations
= ? (base 16)
y
[ 2ndF ] [ HEX]
→
Ex. 2: Fix the display at 4 decimal places, then key in 4.23
1F.
Fractions are displayed as follows:
DEG
x Y
[ 2ndF ] [ HEX] 4 [ × ] 1B
ENTER
1
y > 0 : x ≠ 0, –1 x 10100
<
log y < 100
DEG HEX
DEG
1. Press [ 2ndF ] [ FIX ] 4
0.0000
4.2300
6C.
4 × 1B (base 16)
= ? (base 2)
[
]
x
5
DEG
BIN1101100.
108.00
」
」
5
12
ENTER
=
=
2. Key in 4.23 [
]
→
[ 2ndF ] [ BIN]
→
y = 0 : x > 0
12
= ? (base 10)
= ? (base 8)
DEG
[ 2ndF ] [ DEC]
→
Scientific format
y < 0 : x =2n+1, l/n
DEG OCT
In scientific format, the number 891500 is shown as 8.915 × 10 05
where 8.915 is the mantissa and 5 is the exponent of 10.
,
5
[ 2ndF ] [ OCT]
154.
∪
56
5
12
56
where n is an integer other than 0
12
1
but –1 x 10100
<
log y 100
Negative Numbers and Complements
Note :The display is truncated if the integer, numerator, denominator
and fraction symbols together are more than 10 digits.
Ex. 3: To display 7132 × 125 in scientific format:
x
In binary, octal, and hexadecimal bases, negative numbers are
expressed as complements. The complement is the result of
DEG
b
Input：The integer, numerator, denominator
and fraction symbols must in total be no
more than 10 digits.
ENTER
1. Key in 7132 [ × ] 125 [
]
891500.
8.915
a
/c
d
→
Press [ 2ndF ] [
fraction.
/c ] to convert the displayed value to an improper
subtracting that number from 10000000000 in that number’s base.
You do this by pressing [+/–] in a non-decimal base.
DEG
05
←→
2. Press [ F E ]
Result：Displayed as a fraction when the
Calculate the
complement of
binary number
11011
You can convert an entry to scientific notation by pressing [EXP] after
entering the mantissa.
2
3
3
5
integer, numerator and denominator are
b
b
DEG BIN
+ 7
4
2 [ a /c ] 3 [ + ] 7 [ a /c ] 3
DEG
DEG
each less than 1 × 1010
.
∪
」
15
8
4
→
[ 2ndF ] [ BIN ] 11011 [+/–]
b
ENTER
[ a /c ] 5 [
]
1111100101.
Ex. 4: Key the number 4.82296 × 10 5
0 ≦r≦n, n≦9999999999; n, r are integers.
nPr, nCr
STAT
= 8
15
124
DEG
05
x < 1 × 10 50 , Σ x < 1 × 10 100
1. Key in 4.82296 [ EXP ] 5
4.82296
Complex Number Calculations
d
→
[ 2ndF ] [
/c ]
」
124 15
0 ≦│Σx 2│＜1 × 10 100; n, r are integer
=
Engineering format
15
Press [ CPLX ] to enter complex number mode. The CPLX indicator
appears on the display. You can add, subtract, multiply, and divide
complex numbers.
：n≠0, S：n＞1,σ：n＞0
x
Engineering format is similar to scientific format, except that the
mantissa can have up to three digits to the left of the decimal and the
b
ENTER
], or if a fraction was
If you press [ a /c ] after pressing [
combined with a decimal number, the answer is displayed as a
decimal number.
Range = 1 ~ r, 1≦n≦r, 80≦r≦20400
0 ≦ X ≦9999999999 (for zero or positive)
–9999999999 ≦ X ≦ –1 (for negative)
exponent is always a multiple of three. This is useful if you have to
→DEC
→BIN
Complex numbers are generally represented as a + b i, where a is the
real part and bi is the imaginary part.
convert units that are based on multiples of 10 3
Ex. 5: Convert 15V to 15000mV (V = Volts)
.
4
9
3
4
b
b
5 [ a /c ] 4 [ a /c ] 9 [ + ] 3
DEG
5
+ 3
∪
」
[ 2ndF ] [ CPLX ] 7 [ a ] 9
9
7
36
9.19
12.19
≦
≦
b
b
0
X
0111111111 (for zero or
ENTER
[ a /c ] 3 [ a /c ] 4 [
]
DEG CPLX
DEG
DEG
[ +/– ] [ b ] [ + ] 15 [ a ] 10 [ b ]
ENTER
( 7 – 9 i ) +
(15 + 10 i) = ?
22.00
1.00
1. Key in 15
15.
positive)
7
DEG
DEG
[
]
= 9
= 9.19
b
[ a /c ]
– 03
36
DEG CPLX
1000000000 ≦ X ≦ 1111111111
(for negative)
[ b ]
2. Press [ ENG ] twice.
Ex. 6: Convert 15V to 0.015KV (V = Volts)
1. Key in 15
15000.
b
b
4
8
8 [ a /c ] 4 [ a /c ] 9 [ + ]
+ 3.75 = 12.19
Note: Memory calculation is available in complex number mode.
ENTER
3.75 [
]
9
DEG
DEG
→OCT
→HEX
0 ≦ X ≦ 3777777777 (for zero or positive)
4000000000 ≦ X ≦ 7777777777
(for negative)
15.
Where possible, a fraction is reduced to its lowest terms after you
ENTER
Random Numbers
Press [ 2ndF ] [ RND ] to generate a random number between 0.000
and 0.999.
÷
press [ + ], [ – ], [ × ], [
] or [
].
03
←
←
0.015
2. Press [ 2ndF ] [
] [ 2ndF ] [
]
b
b
3 [ a /c ] 119 [ a /c ] 21
ENTER
119
21
2
3
DEG
∪
」
8
2
3
3
= 8
Order of Operations
Unit Conversions
The unit conversion keys are [°F °C ], [ mmHg Kpa ], [ gal I ],
[
]
0 ≦ X ≦2540BE3FF (for zero or positive)
FDABF41C01 ≦ X ≦ FFFFFFFFFF (for
negative)
Each calculation is performed in the following order of precedence:
1. Operations in parentheses.
←→
←→
←→
A result is displayed in decimal format if the integer, numerator,
denominator and fraction symbols are together more than 10 digits.
←→
←→
[ lb kg ] and [ oz g ]. The following example illustrates the general
procedure for converting values from one unit to another.
b
b
b
b
2. Functions that require pressing the function key before entering a
value, for example, [ DATA ] in statistics mode, and [ EXP ].
12345 [ a /c ] 5 [ a /c ] 16
5
12345 +5
16
= 12350.77
6
DEG
Overflow and Error Conditions
The symbol E appears when any of the following conditions occur.
Press [ ON/C ] to remove the overflow or error indicator.
12350.77
[ + ] 5 [ a /c ] 6 [ a /c ] 13
ENTER
13
DEG
→
←→
12 in = ? cm
98 cm = ? in
12 [ A B ] [ 2ndF ] [ in cm]
←
30.48
38.58
[
]
3. Functions that require values to be entered before pressing the
function key, for example, cos, sin, tan, cos –1, sin –1, tan –1, log, ln,
98 [ 2ndF ] [ A B ] [ 2ndF ]
←→
DEG
3
Converting Angular Units
x 2, x –1
,
,
,
, x!, %, RND, ENG,
,
, and the unit
[ in cm ]
√
π
√
When you attempt to perform a function calculation with a number
outside the allowable input range.
•
You can specify an angular unit of degrees (DEG), radians (RAD), or
grads (GRAD). You can also convert a value expressed in one
angular unit to its corresponding value in another angular unit.
conversion functions.
Statistics
4. Fractions.
When you attempt to divide a number by 0.
•
•
Press [ 2ndF ] [ STAT ] to enter statistics mode. The STAT indicator
appears on the display. In statistics mode you can calculate the
following single-variable statistics:
5. +/–
When you have pressed the [ ( ] key more than 15 times in a
single expression.
The relation between the angular units is:
6. x y, X
√
180° = radians = 200 grads
π
n
number of data items
sum of the values of all the data items
sum of the squares
When any result (whether intermediate or final) or the
•
•
7. nPr, nCr
accumulated total in memory is outside ±9.999999999 × 10 99
To change the angular unit setting to another setting, press
[ DRG ] repeatedly until the angular unit you want is indicated in
the display.
•
•
Σx
Σx2
÷
8. ×,
When there are more than six pending operations.
9. +, –
mean value
x
If the calculator becomes locked and pressing keys has no effect,
press [ M+ ] and [ ENG ] at the same time. This unlocks the calculator
and returns all settings to their default values.
→
After entering the value of an angle, press [ 2ndF ] [ DRG
repeatedly until the value is converted to the desired unit.
]
x
2 − ( x)2/n
n −1
Corrections
∑
∑
s
sample standard deviation
DEG
90
If you have made a mistake when entering a number and you have
not yet pressed an arithmetic operator key, just press [ CE ] to clear
the last entry. You can then input the desired number again.
Alternatively,you can delete digits one at a time by pressing the
90.
90° (deg)
= ? (rad)
= ? (grad)
RAD
x
2 − ( x)2/n
→
→
[ 2ndF ] [ DRG
[ 2ndF ] [ DRG
]
]
Basic Calculations
The following examples of basic calculations assume that your
calculator is in decimal base and with floating point display.
1.57
∑
∑
σ
population standard deviation
GRAD
n
100.00
→
backspace key: [ 00 0 ].
Continued on other side
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