HP 9s Scientific manual

hp 9s

Scientific Calculator

General Operations

Power Supply

On or Off

To turn the calculator on, press [ON/C].

To turn the calculator off, press [2ndF] [OFF].

Auto power-off function

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.

Battery replacement

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.

To replace the batteries:

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.

The keyboard

Most of the keys can perform two functions.

2nd function ――――――	sin–1
1st function ―――	sin

1st functions

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.

2nd functions

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.

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.

Note: [ A ], [ B ], [ C ], [ D ], [ E ], [ F ] are 1st functions in HEX mode.

Display Symbols

The following symbols, shown on the display, indicate the status of the calculator.

DEG or RAD or GRAD: degrees, radians or grads angular unit

M	A value is in memory	CPLX	Complex number mode
E	Overflow or error	STAT	Statistical mode
–	Minus	2ndF	[2ndF] key pressed
( )	Parentheses calculation	CP	Precision capability
BIN	Binary mode	CPK	Process capability
OCT	Octal mode	σ	Deviation
HEX	Hexadecimal mode	USL	Setting upper limit
ED	Edit mode	LSL	Setting lower limit
HYP	Hyperbolic mode

Display Formats

The calculator can display numbers in four formats: floating point, fixed point, scientific, and engineering.

Floating point format

The floating point format displays numbers in decimal form, using up to 10 digits. Any trailing zeros are truncated.

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.

To set the display to floating point display format:

1. Press [ 2ndF ] [ FIX ] [•] DEG 0.

Fixed point format

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.

Ex. 1: Fix the display at 2 decimal places, then key in 3.256

1.	Press [ 2ndF ] [ FIX ] 2	DEG	0.00
2.	Key in 3.256 [ENTER]	DEG	3.26

If fewer than the set number of decimal places is keyed, the entry will be padded with trailing zeros.

Ex. 2: Fix the display at 4 decimal places, then key in 4.23

1.	Press [ 2ndF ] [ FIX ] 4	DEG	0.0000
2.	Key in 4.23 [ENTER]	DEG	4.2300

Scientific format

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.

Ex. 3: To display 7132 × 125 in scientific format:

1.	Key in 7132 [ × ] 125 [ENTER]	DEG	891500.
2.	Press [ F←→E ]	DEG	8.915	05

You can convert an entry to scientific notation by pressing [EXP] after entering the mantissa.

Ex. 4: Key the number 4.82296 × 10 5
1. Key in 4.82296 [ EXP ] 5	DEG	4.82296 05

Engineering format

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 exponent is always a multiple of three. This is useful if you have to convert units that are based on multiples of 10 3.

Ex. 5: Convert 15V to 15000mV (V = Volts)

1.	Key in 15	DEG	15.
2.	Press [ ENG ] twice.	DEG	15000.	– 03
Ex. 6: Convert 15V to 0.015KV (V = Volts)
1.	Key in 15	DEG	15.
2.	Press [ 2ndF ] [ ← ] [ 2ndF ] [ ← ]	DEG	0.015	03

Order of Operations

Each calculation is performed in the following order of precedence:

1.Operations in parentheses.

2.Functions that require pressing the function key before entering a value, for example, [ DATA ] in statistics mode, and [ EXP ].

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,

x 2, x –1, √, π, 3√, x!, %, RND, ENG, , , and the unit

conversion functions.

4.Fractions.

5.+/–

6.x y, X√

7.nPr, nCr

8.×, ÷

9.+, –

Corrections

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 backspace key: [ 00→0 ].

Ex. 7: Change 12385 to 789

1.	Key in 12385	DEG	789.
2.	Press [ CE ] 789
Ex. 8: Change 12385 to 123
1.	Key in 12385	DEG	123.
2.	Press [ 00→0 ] twice.

In a series of calculations, you can correct errors in intermediate results by pressing [ON/C]. This clears the calculation without clearing memory.

If you press the wrong arithmetic operation key, just press [ CE ] and then the correct arithmetic key.

Exchange key

Pressing [ 2ndF ] [ X←→Y ] changes the currently displayed value to the previously displayed value.

	123 [ + ] 456 [	ENTER	DEG	579.00
		]
123 + 456 = ?	[ 2ndF ] [ X←→Y ]		DEG	456.00
	←→	Y ]	DEG	579.00
	[ 2ndF ] [ X

Accuracy and Capacity

Accuracy: ±1 in the 10th digit.

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.

Numbers used as input to a particular function must be within the allowable range for that function (as set out in the following table):

Functions

Allowable input range

sin x, cos x, tan x

Deg:

x

< 4.5 × 10

10

deg

Rad:

x

< 2.5 × 10 8 π rad

Grad:

x

< 5 × 10 10 grad

Also, for tan x:

Deg:

x

≠ 90 (2n +1)

Rad:

x

≠ π2 (2n +1)

Grad:

x

≠ 100 (2n +1)

where n is an integer.

sin –1x, cos –1x

x

≦ 1

tan –1x

x

< 1 × 10 100

sinh x, cosh x

x

≦ 230.2585092

tanh x

x

< 1 × 10 100

sinh –1x

x

< 5 × 10 99

cosh –1x

1 ≦ x < 5 × 10 99

tanh –1x

x

< 1

log x, ln x

1 × 10 –99≦ x < 1 x 10 100

10 x

–1 × 10 100 ＜ x ＜ 100

e x

–1 × 10 100 ＜ x ≦ 230.2585092

x

0 ≦ x < 1 × 10 100

x 2

x

< 1 × 10 50

x –1

│x│＜1 × 10 100, X≠0

3

x

x

< 1 × 10 100

X !

0 ≦ x ≦ 69, where x is an integer.

→

x 2 + y 2 ＜ 1 × 10

100

R P

P

→

0

≦

r

＜

1 × 10

100

R

Deg：│θ│＜4.5 × 10 10 deg

Rad：│θ│＜2.5 × 10 8πrad

Grad：│θ│＜5 × 10 10 grad

Also, for tan x:

Deg：│θ│≠90 (2n+1)

Rad：│θ│≠ π2 (2n+1)

Grad：│θ│≠100 (2n+1)

where n is an integer.

│DD│, MM, SS.SS ＜ 1 × 10 100,

0 ≦ MM, SS.SS

x

< 1 × 10 100

x y

x > 0 : –1 × 10100 < y log x < 100

x = 0 : y > 0

x < 0 : y = n, 1/(2n+1)

where n is an integer

but

–1 x 10100 <

1

log x 100

y

x Y

y > 0 : x ≠

0, –1 x 10

100

<

1

log y < 100

x

y = 0 : x > 0

y < 0 : x =2n+1, l/n

where n is an integer other than 0

but

–1 x 10100 <

1

log  y  100

x

a b/c

Input：The integer, numerator, denominator

and fraction symbols must in total be no

more than 10 digits.

Result：Displayed as a fraction when the

integer, numerator and denominator are

each less than 1 × 1010.

nPr, nCr

0≦r≦n, n≦9999999999; n, r are integers.

STAT

x  < 1 × 10 50 , Σ x  < 1 × 10 100

0 ≦│Σx 2│＜1 × 10 100; n, r are integer

：n≠0, S：n＞1,σ：n＞0

x

Range = 1 ~ r, 1≦n≦r, 80≦r≦20400

→DEC

0 ≦ X ≦9999999999 (for zero or positive)

–9999999999 ≦ X ≦ –1 (for negative)

→BIN

0 ≦ X ≦ 0111111111 (for zero or

positive)

1000000000 ≦ X ≦ 1111111111

(for negative)

→OCT

0 ≦ X ≦ 3777777777 (for zero or positive)

4000000000 ≦ X ≦ 7777777777

(for negative)

→HEX

0 ≦ X ≦2540BE3FF (for zero or positive)

FDABF41C01 ≦ X ≦ FFFFFFFFFF (for

negative)

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.

•When you attempt to perform a function calculation with a number outside the allowable input range.

•When you attempt to divide a number by 0.

•When you have pressed the [ ( ] key more than 15 times in a single expression.

•When any result (whether intermediate or final) or the accumulated total in memory is outside ±9.999999999 × 10 99

•When there are more than six pending operations.

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.

Basic Calculations

The following examples of basic calculations assume that your calculator is in decimal base and with floating point display.

Mixed Arithmetic Calculations

1 + 2 × 3 = ?	ENTER		DEG	7.
	1 [ + ] 2 [ × ] 3 [	]
–3.5 + 8 2 = ?	3.5 [ +/– ] [ + ] 8 [	÷ ] 2	DEG	0.5
	[ENTER]
÷

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.

( 5–2 × 1.5 ) × 3	[ ( ] 5 [ – ] 2 [ × ] 1.5 [ ) ] [ × ] 3	DEG	2.8
+ 0.8 × (– 4 )
	[ + ] 0.8 [ × ] 4 [ +/– ] [ENTER]
= ?
2 × ( 7 + 6 × ( 5	2 [ × ] [ ( ] 7 [ + ] 6 [ × ] [ ( ] 5	DEG	122.
+ 4 )) = ?	[ + ] 4 [ENTER]

Note: It is not necessary to press [ ) ] before [ENTER].

Repeating a Calculation

You can repeat the last number entered, or the last operation executed, by pressing [ENTER].

Repeating the last number

3 × 3 = ?

3 [ × ] [

ENTER

DEG

9.

]

3 × 3 × 3 = ?

[

ENTER

DEG

27.

3 × 3 × 3 × 3 = ?

]

[

ENTER

DEG

81.

]

Repeating the last arithmetic operation

321 + 357 = ?

321

[ + ] 357 [

ENTER

DEG

678.

]

654 + 357 = ?

654

[

ENTER

DEG

1011.

]

579 – 159 = ?

579

[ – ] 159 [

ENTER

DEG

420.

]

456 – 159 = ?

456

[

ENTER

DEG

297.

]

18 × 45 = ?

ENTER

DEG

810.

3 [ × ] 6 [ × ] 45 [

]

18 × 23 = ?

23 [

ENTER

DEG

414.

18 × (0.5x102) = ?

]

0.5 [ EXP ] 2 [

]

DEG

900.

ENTER

96

÷

8 = ?

96 [

÷

] 8 [

ENTER

DEG

12.

]

75 ÷ 8 = ?

75 [

ENTER

DEG

9.375

2

8 = ?

]

÷

ENTER

DEG

(1.2x10 )

1.2 [ EXP ] 2 [

15.

]

Percentage Calculations

30% of 120 = ?

120

[ × ] 30 [ 2ndF ] [ % ]

DEG

36.

[ENTER]

70% of 120 = ?

70 [ 2ndF ] [ % ] [

ENTER

DEG

84.

]

88 is 55% of what

88 [ ÷ ] 55 [ 2ndF ] [ % ]

DEG

160.

number?

[ENTER]

30% mark up of

120

[ + ] 30 [ 2ndF ] [ % ]

DEG

156.

120 = ?

[ENTER]

30% discount of

120

[ – ] 30 [ 2ndF ] [ % ]

DEG

84.

120 = ?

[ENTER]

Memory Calculations

•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.

•To copy the displayed number to memory, press [ X→M ].

•To clear the memory, press [ 0 ] [ X→M ], or [ CE ] [ X→M ], in that order.

	→		DEG	0.
	[ CE ] [ X M ]
3 × 5	3 [ × ] 5 [ M+ ]	M	DEG	15.
+ 56 ÷ 7	56 [ ÷ ] 7 [ M+ ]	M	DEG	8.
+ 74 – 8 × 7	74 [ – ] 8 [ × ] 7 [ M+ ]	M	DEG	18.
Total = ?	[ MR ]	M	DEG	41.
	→		DEG	0.
	0 [ X M ]

Common Math Calculations

The following example calculations assume that your display is fixed at 2 decimal places.

Reciprocal, Factorial

1

1.25 [ 2ndF ] [ x

–1

] [

ENTER

DEG

1.25 = ?

]

0.80

5! = ?

5

[ 2ndF ] [ x! ] [

ENTER

DEG

120.00

]

Square, Square Root, Cube Root, Power, Other Roots

2

2

+ 3

4

= ?

2

[ x

2

] [ + ] 3 [ x

y

] 4 [

ENTER

DEG

85.00

]

5 ×3 27 +

34 = ?

5

[ × ] 27 [ 2ndF ] [

3√

] [ + ]

DEG

20.83

34 [ √ ] [ENTER]

9 72 = ?

72 [ 2ndF ] [ X√ ] 9 [ENTER]

DEG

1.61

Logarithms and Antilogarithms

ln7 + log100 = ?

7

[ ln ] [ + ] 100 [ log ] [

ENTER

DEG

3.95

]

10

2

= ?

2

[ 2ndF ] [ 10

x

] [

ENTER

DEG

100.00

]

e

5

– e

–2

= ?

5

[ 2ndF ] [ e x ] [ – ] 2 [+/–]

DEG

148.28

[ 2ndF ] [ e x ] [ENTER]

Fraction calculations

Fractions are displayed as follows:

		5	」12		=		5
						12
								5
56	∪	5	」	12	= 56
								12

Note : The display is truncated if the integer, numerator, denominator and fraction symbols together are more than 10 digits.

Press [ 2ndF ] [→d/c ] to convert the displayed value to an improper fraction.

	2	+ 7		3	2 [ a b/c ] 3 [ + ] 7 [ a b/c ] 3	DEG
3				5			8∪	4 」15
			4		[ a b/c ] 5 [ENTER]
= 8
			15
=		124			[ 2ndF ] [→d/c ]	DEG	124 」15
			15

If you press [ a b/c ] after pressing [ENTER], or if a fraction was combined with a decimal number, the answer is displayed as a decimal number.

4

3

5 [ a b/c ] 4

[ a b/c ]

9

[ + ] 3

DEG

5

9

+ 3

4

[ a b/c ] 3 [ a b/c ] 4

[ENTER]

9 ∪

7」36

7

DEG

= 9 36 = 9.19

[ a b/c ]

9.19

8

4

+ 3.75 = 12.19

8 [ a b/c ] 4

[ a b/c ]

9

[ + ]

DEG

12.19

9

3.75 [

ENTER

]

Where possible, a fraction is reduced to its lowest terms after you press [ + ], [ – ], [ × ], [ ÷ ] or [ENTER].

119	2			3 [ a b/c ] 119 [ a b/c ] 21	DEG	8	∪	2	」	3
3 21	= 8 3			[ENTER]
A result is displayed in decimal format if the integer, numerator,
denominator and fraction symbols are together more than 10 digits.
		5	6	12345 [ a b/c ] 5 [ a b/c ] 16	DEG
12345 16 +5 13				[ + ] 5 [ a b/c ] 6 [ a b/c ] 13		12350.77
= 12350.77				[ENTER]

Converting Angular Units

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.

The relation between the angular units is:

180° = π radians = 200 grads

•To change the angular unit setting to another setting, press

[ DRG ] repeatedly until the angular unit you want is indicated in the display.

•After entering the value of an angle, press [ 2ndF ] [ DRG→] repeatedly until the value is converted to the desired unit.

90° (deg)	90			DEG	90.
= ? (rad)	[ 2ndF ] [ DRG	→	]	RAD	1.57
= ? (grad)
	[ 2ndF ] [ DRG	→	]	GRAD	100.00

Trigonometric and Inverse Trigonometric Functions

Before undertaking a trigonometric or inverse trigonometric calculation, make sure that the appropriate angular unit is set.

3 sin 85° = ?				3	[ × ] 85 [ sin ] [	ENTER	DEG	2.99
						]
	π			[ 2ndF ] [ π ] [		÷ ] 4 [ENTER]	RAD
cos ( 4			rad) = ?	[ cos ]				0.71
tan 150 grad = ?				150 [ tan ]			GRAD	–1.00
sin –10.5 = ? deg				0.5 [ 2ndF ] [ sin –1]			DEG	30.00
cos	–1	(	1	2	[ √ ] [ 2ndF ] [ x –1] [ 2ndF ]		RAD
			2 ) =	[ cos –1]				0.79
? rad
tan –11 = ? grad				1	[ 2ndF ] [ tan –1]		GRAD	50.00
Hyperbolic and Inverse hyperbolic functions
cosh1.5+sinh1.5				1.5 [ HYP ] [ cos ] [ + ] 1.5			DEG	4.48
= ?				[ HYP ] [ sin ] [ENTER]
sinh –17 = ?				7	[ HYP ] [ 2ndF ] [ sin –1]		DEG	2.64
tanh 1 = ?				1	[ HYP ] [ tan ]		DEG	0.76
Rectangular and Polar coordinates
Rectangular Coordinates						Polar Coordinates

a + b i = r (cosθ + i sinθ)

Note: Before undertaking a coordinates conversion calculation, make sure that the appropriate angular unit is set.

Converting from Rectangular to Polar

If a = 5 and b = 6,				5 [ a ] 6 [ b ] [ 2ndF ] [ R				P ]	DEG	7.81
								→
what are r and			?
				[ b ]					DEG	50.19
		θ
Converting from Polar to Rectangular
If r = 25 and θ=				25 [ a ] 56 [ b ] [ 2ndF ]					DEG	13.98
56°, what are a				→
				[ P	R ]
and b?				[ b ]					DEG	20.73
Permutations and Combinations
nPr =	n!		nCr =		n!
	(n − r)!				r !(n − r)!
How many
permutations of 4									DEG
items can you						ENTER				840.00
				7 [ 2ndF ] [ nPr ] 4 [				]
select from a set
of 7 items?
How many
combinations of 4									DEG
items can you				7 [ 2ndF ] [ nCr ] 4 [			ENTER			35.00
								]
select from a set
of 7 items?

Sexagesimal ↔ Decimal form Conversions

You can convert a sexagesimal figure (degree, minute and second) to

a decimal number by pressing [ ] and convert a decimal number

to a sexagesimal figure by pressing [ 2ndF ] [ ]. Sexagesimal figures are displayed as follows:

12		45	׀	30	׀ ׀	5	= 12 degrees, 45 minutes, 30.5
							seconds
Note: If the total number of digits in a DD, MM and SS.SS figure
exceeds 8, the figure is truncated.
Converting from Sexagesimal to Decimal
12 deg., 45 min.,						12 [	] 45 [	] 30.5	DEG	12.76
30.5 sec.= ?						[	]
Converting from Decimal to Sexagesimal
2.12345 = ?						2.12345 [ 2ndF ] [		]	DEG 2 7 ׀24 ׀׀42

Base-n Calculations

Converting between bases

You can add, subtract, multiply, and divide binary, octal, and hexadecimal numbers in addition to decimal numbers. Select the number base you want by pressing [→BIN], [→OCT], [→HEX], or [→DEC]. The BIN, OCT, and HEX indicators show you which base

you are using. (If none of these indicators is displayed, you are using decimal base.)

The number keys that are active in a particular base are: Binary base: [ 0 ] and [ 1 ]

Octal base: [ 0 ] to [ 7 ]

Decimal base: [ 0 ] to [ 9 ]

Hexadecimal base: [ 0 ] to [ 9 ] and [ A ] to [ F ]

31 (base 10)	[ 2ndF ] [	→	DEC] 31	DEG		31.
= ? (base 2)	[ 2ndF ] [→BIN]			DEG	BIN	11111.
= ? (base 8)
	[ 2ndF ] [→OCT]			DEG	OCT	37.
= ? (base 16)
	[ 2ndF ] [→HEX]			DEG	HEX	1F.
4 × 1B (base 16)	[ 2ndF ] [→HEX] 4 [ × ] 1B			DEG	HEX	6C.
	[ENTER]
= ? (base 2)	[ 2ndF ] [→BIN]			DEG	BIN1101100.
= ? (base 10)	[ 2ndF ] [→DEC]			DEG		108.00
= ? (base 8)
	[ 2ndF ] [→OCT]			DEG	OCT	154.

Negative Numbers and Complements

In binary, octal, and hexadecimal bases, negative numbers are expressed as complements. The complement is the result of subtracting that number from 10000000000 in that number’s base. You do this by pressing [+/–] in a non-decimal base.

Calculate the		DEG	BIN
complement of	[ 2ndF ] [→BIN ] 11011 [+/–]
binary number			1111100101.
11011

Complex Number Calculations

Press [ CPLX ] to enter complex number mode. The CPLX indicator appears on the display. You can add, subtract, multiply, and divide complex numbers.

Complex numbers are generally represented as a + b i, where a is the real part and bi is the imaginary part.

	[ 2ndF ] [ CPLX ] 7 [ a ] 9		DEG	CPLX 22.00
( 7 – 9 i ) +	[ +/– ] [ b ] [ + ] 15 [ a ] 10 [ b ]
(15 + 10 i) = ?	[	ENTER
		]
	[ b ]		DEG	CPLX	1.00

Note: Memory calculation is available in complex number mode.

Random Numbers

Press [ 2ndF ] [ RND ] to generate a random number between 0.000 and 0.999.

Unit Conversions

The unit conversion keys are [°F←→°C ], [ mmHg←→Kpa ], [ gal←→I ],

[ lb←→kg ] and [ oz←→g ]. The following example illustrates the general procedure for converting values from one unit to another.

12 in = ? cm	12	[ A B ] [ 2ndF ] [ in			←→	cm]	DEG	30.48
		→
98 cm = ? in	98	[ 2ndF ] [ A	←	B ] [ 2ndF ]			DEG	38.58
	[ in←→cm ]

Statistics

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:

n		number of data items
Σx		sum of the values of all the data items
Σx2		sum of the squares
		mean value
	x
s		sample standard deviation	∑ x2		− (∑ x)2	/n
					n − 1
σ		population standard deviation		∑ x2 − (∑ x)2			/n
					n
				Continued on other side