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HP 6S Scientific Calculator
H
1
Contents
1. Keyboard
5
General keys
5
5
5
5
6
6
Memory keys
Special keys
Base-n keys
Function keys
Statistical keys
2. The display
7
Exponent displays
7
3. Basic functions
8
Entering numbers
Entering negative numbers
Entering exponential numbers
Arithmetic operator
Equals
Making corrections
Clearing errors
Fixing the number of decimal places displayed
Setting the display to scientific notation
8
8
8
8
8
9
9
9
9
4. Calculations
10
Precision
Order of operations
Simple calculations
Specifying the order of calculations
Re-using arithmetic operations
Using memory
10
10
10
10
11
11
11
12
Fraction arithmetic
Percentage calculations
5. Other functions
13
Converting minutes and seconds to decimal format
Conversion between angles, radians and grads
Trigonometric functions
Hyperbolic functions
Logarithmic functions
Powers and roots
Miscellaneous functions
Polar to rectangular coordinates conversions
Rectangular to polar coordinates conversions
13
13
13
14
14
14
15
15
15
3
6. Binary, octal and hexadecimal values
Binary/octal/decimal/hexadecimal conversions
Binary/octal/decimal/hexadecimal calculations
Logical operations
16
16
16
17
18
Radix complement
7 . Using statistics
19
19
19
Entering a list of data items to analyse
Using statistical functions on your data
8 . Specifications
20
21
9 . Changing the battery
4
1. Keyboard
General keys
Key
Functions
Page
Key
Functions
Page
0 to9:. Data entry
8
ØÅ
Sexagesimal/decimal
notation conversion
13
+-*
d=
Basic calculation
8
¯
Ù
Mode of angle
DEG→RAD→GRAD→DEG
13
13
¡
Reset the calculator
and clear the memory
9
Angular conversion of data
DEG→RAD→GRAD→DEG
Ô
Ó
Clear/clear error
Change sign
9
8
²
Õ
Register exchange
11
9
Clearing the last
entered digit
Memory keys
¼
Fix the number of digits
after the decimal point
9
Key
Functions
Page
»
½
¾
Floating notation
9
9
r
Retrieve data from the
independent memory
11
Scientific notation
Engineering notation
´
³
m
Store display data in
memory
11
11
11
15
Base-n keys
Exchange of display data
and contents of memory
Key
Functions
Page
Add displayed data to
memory
¤
Decimal
16
¥
Binary
16
16
16
Special keys
¦
Hexadecimal
Octal
Key
Functions
Page
§
I
Inverse
7
A to F
Hexadecimal numbers only 16–18
M
()
¹
P
Mode
7
10
8
&
o
And
17
17
17
17
17
18
Brackets (parentheses)
Or
Exponent
Pi
x
X
Ì
N
Exclusive Or
Exclusive Nor
Not
13
Negative
Keyboard
5
Function keys
K e y
Functions
Page
K e y
Functions
Page
s
Sine
13
É
Power
8
c
t
S
¨
T
ª
L
Û
È
Cosine
13
13
13
13
13
14
14
14
14
14
14
14
12
14
12
14
Ê
Ä
Ã
%
Root
14
15
15
12
Rectangle to polar
Polar to rectangular
Percent
Tangent
Arc sine
Arc cosine
Arc tangent
Hyperbolic
Common logarithm
Common antilogarithm
Natural logarithm
Natural antilogarithm
Square root
Square
Statistical keys
Key
Functions
Page
¿
Statistical data mode
Data entry
19
À
Á
Ñ
Ò
Ï
19
19
19
Ð
Data delete
Â
º
Sample standard deviation
Population standard deviation 19
ˬ
Ý
Ç
Fraction
Arithmetic mean
Number of data
Sum of value
19
19
19
19
Cube root
n
Reciprocal
Factorial
Í
Î
Æ
Sum of square value
Keyboard
6
2. The display
M
E
1
2 3 4 5
.
INV HYP BIN OCT HEX
Mantissa
LCD Diagram
The display shows input data, interim results and answers to calculations. The mantissa section displays up to 10
digits. The exponent section displays up to ±99.
Display
Meaning
Page
-E-
Indicates an error
9
INV
I has been pressed to enable inverse key functions
Indicates that data is stored in the memory
ª has been pressed for hyperbolic functions
BASE-N mode has been selected
9
M
HYP
11
14
16
19
13
BIN, OCT, HEX
SD
Statistical mode has been selected
DEG, RAD, GRAD
¯ has been pressed to switch between the DEG, RAD and GRAD
angle types
FIX (this does not display) The number of decimal places of a displayed value has been set
9,15
9
SCI (this does not display) Converts a displayed value to exponent display
ENG (this does not display) Converts a displayed value to exponent display of which the exponent
15
is a multiple of 3 and mantissa is between 0 to 999
FLO (this does not display) Convert a SCI or ENG form display to a normal display value
15
11
13
45Ö12×123
4512/123
12.°3'45.6"
Sexagesimal figure 12°3'45.6"
Exponent displays
The display can show calculation results only up to 10 digits long. When an intermediate value or a final result is
longer than 10 digits, the calculator automatically switches over to exponential notation. Values greater than
9,999,999,999 are always displayed exponentially.
The Display
7
3. Basic functions
Entering numbers
123
Press the number keys to enter numbers.
Press . for a decimal point.
etc
.
Entering negative numbers
Ó
Press after a number to make it negative.
5.08Ó
-5.08
Entering exponential numbers
¹
Press to enter an exponential number.
3.08×109
3.08¹9
3.0809
Arithmetic operator
Press to perform an arithmetic operation on the value displayed.
You must enter a number after the arithmetic operator.
If you press more than one arithmetic operator in sequence, the calculator only performs
the last operation (the last key pressed).
+-*
dÉ
4*d+-+5
9.
Equals
=
Press to complete your calculation and display a result. If you press = more than once
without entering a number, the calculator performs the last arithmetic operation on the value
displayed.
4×8
4*8=
32.
4*8==
256.
Basic functions
8
Making corrections
Õ
Press to delete the last number entered.
Ô
Press to remove the displayed value, but retain the calculation being performed.
Press after the arithmetic operator to cancel the entire calculation.
5+5+5+6Ô5=
5+5+5+Ô=
20.
0.
Clearing errors
Ô
¡
Press to clear an error (indicated by “-E-“ in the display)—eg, an overflow error—and retain
data in the memory.
Press to reset the calculator and clear the memory (solar model only).
Fixing the number of decimal places displayed
I¼
2
Press after your arithmetic operation, or after you press ¡, to set the number of decimal
places displayed (the number you press is the number of decimal places you want to
display). The calculator rounds the number in the display but maintains full precision internally.
I
Press to reset the floating decimal point.
¼.
Setting the display to scientific notation
I
½
Press to set the display to scientific notation and express the number as a power of 10—eg,
.0043 is displayed as 4.3.-03 to represent 4.3×10-3.
I
»
Press to reset the display to the floating format.
Basic functions
9
4. Calculations
Precision
The HP 6S scientific calculator calculates answers to 12-digit accuracy, but rounds answers
to 10 digits in the display. When it performs a calculation using the result of a previous
calculation, it uses the stored 12-digit value and not the 10-digit value displayed.
Order of operations
The HP 6S scientific calculator performs operations in the following order:
º, Ê, Ä, Ã
*, d
+, -
&
o, x, X
Simple calculations
Perform calculations in the same way that you write them on paper.
7.2×8.5 – 4.7×3.9
7.2*8.5-4.7*3.9=
42.87
32.
4×8
4*8=
Specifying the order of calculations
( )
Use brackets to specify the order of calculations. You can nest as many as six levels of
brackets.
You do not need to enter the closing brackets. The calculator inserts them for you, although it
does not display them.
-5(4+3)
5Ó*(4+3=
-35.
Calculations
10
Re-using arithmetic operations
Press the arithmetic operator key twice to re-use an arithmetic operation on a new number. The
++
or
calculator stores the operation and applies it when you enter another number and press =.
Store a calculation for re-use by enclosing it in brackets.
**
etc
Clear the stored arithmetic operation by pressing Ô.
3+2.3
6+2.3
9+2.3
4(3×6)
-5(3×6)
3++2.3=
6=
5.3
8.3
9=
11.3
72.
4**(3*6=
5Ó=
-90.
Using memory
´
m
The HP 6S scientific calculator has one independent memory.
M is displayed when there is a value in memory.
r
³
Ô
¡
Press Ô to clear the display or cancel the current calculation without clearing the memory.
Press ´ to store the displayed value in memory.
Press m to add the displayed value to the memory.
Press r to retrieve the contents of memory—to determine its value or include it in your
calculation.
f
e
Press I³ to display the contents of memory and replace it with the value that was
displayed before the keys were pressed.
Press ¡ to clear the display and the memory (solar model).
Press fe to clear the display and the memory (battery model).
Fraction arithmetic
Ë
Press to enter fractions.
Press Ë after = to display the fraction as a decimal.
In the display, a fraction is reduced to its lowest terms when you press a function command
key (×,÷,+,-) or =.
4 5/6 × (3+12/3) ÷ 78/9
4Ë5Ë6*(3+1Ë2Ë3)d7Ë8Ë9=
Ë
2Ö61×71.
2.86
Calculations
11
(1.5×107) – [(2.5×106) × 3/100] =
1.5¹7-2.5¹6*3Ë100= 149250000.
3456/78 = 811/13
3Ë456Ë78
=
3Ö456×78.
8Ö11×13.
I¬
Press these keys to switch between proper and improper fractions.
811/13 = 115/13
8Ö11×13.
115×13.
8Ö11×13.
I¬
I¬
The answer to a calculation involving both fractions and decimals is displayed as a decimal.
41/52 × 78.9
41Ë52*78.9= 62.20961538
Percentage calculations
I%
Press to perform percentage calculations.
12% of 1500
1500*12I%=
660d880I%=
2500+15I%
=
180.
75.
660 as a percentage of 880
2500 plus 15%
375.
2875.
875.
2625.
25% discount on 3500
3500-25I%
=
26% of 2200; 26% of 3300; 26% of 3800;
2200**26I%=
572.
858.
988.
3300=
3800=
$80 last week; $100 this week: what % is the new value of the old value?
100d80I%=
125.
What % is 138gm to 150gm and 129gm to 150gm?
138dd150I%=
129=
92.
86.
Calculations
12
5. Other functions
Converting minutes and seconds to decimal format
Ø
Press to convert minutes and seconds (sexagesimal figure) to decimal format. When you
enter the sexagesimal figure, enter the degrees to the left of the decimal point, and minutes
and seconds to the right—the first and second digits to the left of decimal point are minutes
and the third and subsequent digits seconds.
IÅ
Press to convert decimal format to sexagesimal format.
14°25′36″
14.2536Ø
14.42666667
IÅ
14°25′36″
Conversion between angles, radians and grads
IÙ
45° = 0.785398163 rad = 50 grad
45IÙ RAD 0.785398163
IÙ GRAD
50.
45.
IÙ DEG
Trigonometric functions
Press ¯
sin (π/6 rad) =
to switch
RAD IPd6=s RAD
0.5
between
RAD, DEG
and GRAD
cos 63°52′41″ =
DEG 63.5241Ø DEG 63.87805556
DEG 0.440283084
c
tan (-35 grad) =
GRAD 35Ót GRAD-0.612800788
2 • sin 45° x cos 65° = DEG 2*45s*65c= DEG 0.597672477
cot 30° = 1/tan 30° =
DEG 30tÇ DEG 1.732050808
1
sec (π/3 rad) = cos (π/3 rad)
RAD IPd3=cÇ RAD
30sÇ DEG
2.
2.
1
cosec 30° = sin 30°
-
√2
cos
2
RAD 2IÂÓd2=c RAD 0.760244597
tan –10.6104 =
DEG .6104IT DEG 31.39989118
DEG
IÅ
31°23′59.6″
Other functions
13
Hyperbolic functions
sinh 3.6 =
3.6ªs
2.5ªt
18.28545536
0.986614298
tanh 2.5 =
M
M
cosh 1.5 – sinh 1.5 =
1.5´ªc-
rªs=
2.352409615
0.22313016
sinh –1 30 =
30IªS
4.094622224
0.343941914
solve tanh 4x = 0.88
tan –10.88
x =
=
.88IªTd4=
4
Logarithmic functions
log 1.23 (=log10 1.23) =
1.23L
0.089905111
solve 4x = 64 log 64
x = log4
64Ld4L=
456´LdrÈ=
.4IÛ+5*3ÓIÐ=
5.6É2.3=
3.
0.434294481
2.760821773
52.58143837
1.988647795
1.305111829-21
553467.4658
M
log 456 ÷ In 456 =
100.4 + 5 • e .3
5.62.3
1231/7 (=7√123) =
(78 – 23)-12
=
=
123IÊ7=
=
(78-23)É12Ó=
3É12+10IÐ=
312 + e10
=
Powers and roots
√2 + √3 x √5 =
3√5 + 3√-27 =
123 + 302 =
2IÂ+3IÂ*5IÂ=
5IÝ+27ÓIÝ
123+30º=
5.287196909
-1.290024053
1023.
8! (=1 x 2 x 3 x ꢀ x 7 x 8 ) =
8IÆ
40320
Otherfunctions
14
Miscellaneous functions
1.234 + 1.234 =
I¼21.234+
1.234=
1.23
2.47
I¼.
2.468
1 ÷ 3 + 1 ÷ 3 =
I¼21d3+
I½
0.33
3.33-01
6.67-01
0.67
1d3=
I»
I¼. 0.666666666
123m x 456m = 56088m
= 56.088km
123*456=
56088.
I¾
56.088 03
7.8g ÷ 96 = 0.08125g
= 81.25mg
7.8d96=
I¾
0.08125
81.25 - 03
Polar to rectangular coordinates conversions
Formula: x = r • cosθ
y = r • sinθ
eg, find the value of x and y when the point P is shown
as θ=60 and the length r=2 in the polar coordinates
DEG 2I²60IÃ
1.
(x)
I² 1.732050808
(y)
I²
1.
(x)
Rectangular to polar coordinates conversions
Formula: r = √x2 + y2
y
θ = tan-1 / (-180°<θ ≥ 180°)
x
eg, find the length r and the angle θ in radian when the point
P is shown as x=1 and y=√3 in the rectangular coordinates.
RAD 1I²3IÂÄ=
2.
(r)
I² 1.047197551
(θ in radian)
I²
2.
(r)
Otherfunctions
15
6. Binary, octal and hexadecimal values
Use the M key to set the number base. When you use bases other than 10, you can only
M
enter numbers valid for the base—eg, in binary mode you can only enter 1 and 0.
¦§
¥¤
M¦ sets the mode to hexadecimal. In hexadecimal mode, A to F keys are enabled.
Note that b and d in hexadecimal mode are shown in lower case to distinguish them from
numbers.
M§ sets the mode to octal.
M¥ sets the mode to binary.
M¤ sets the mode to decimal.
Note: When using a number base other than 10, any fractional part is truncated.
Binary/octal/decimal/hexadecimal conversions
Conversion of 2210 to binary.
Conversion of 2210 to octal.
Conversion of 51310 to binary.
22M¥
BIN
10110.
26.
M§
OCT
E BIN
513M¥
0.
Conversion to binary mode generates an error if the result is greater than 10 digits.
Conversion of 7FFFFFFF16 to decimal.
M¦7FFFFFFFM¤
2147483647.
Conversion of 12345610 to octal.
123456M§
OCT
361100.
102.
Conversion of 11001102 to decimal.
M¥1100110M¤
Binary/octal/decimal/hexadecimal calculations
M
101112 + 110102 = 1100012
¦§
¥¤
M¥1011+1101=
BIN
11000.
1238 x ABC16
=37AF416
M§123*M¦ABC=
M¤
HEX
37AF4.
=22808410
228084.
1F2D16 – 10010
=788110
M¦1F2D-M¤100
M¦=
7881.
=1EC916
HEX
1EC9.
Binary, octal and hexadecimal values
16
76548 ÷ 1210
= 334.33ꢀ.10
= 5168
M§7654dM¤12=
334.3333333
M§
OCT
516.
Fractional parts of calculation results are truncated.
1102+4568x7810÷1A16
=39016
M¥110+M§456*
M¤78dM¦1A=
M¤
HEX
390.
912.
=91210
Multiplication and division are given priority over addition and subtraction in mixed calculations.
BC16 x (1410 + 6910
=1560410
=3CF416
M¦BC*(M¤14+69)=
M¦
15604.
3CF4.
HEX
Logical operations
You can use the following logical operations to compare two numbers. When performing
logical operations, keep the following points in mind:
&o
xX
Ì
•
•
You cannot use decimal-base numbers in logical operations.
The calculator compares the binary versions of the numbers you enter. If the number is
less than 10 digits long, the calculator fills values to the left of the number with 0s—eg, if
you compare hexadecimal F1 to octal 4, the calculator compares 0000010001 to
0000000100.
•
If you use one number with a logical operation, the calculator compares it to 0000000000.
The logical operators work in the following way:
1. The operation compares the binary digits in the corresponding positions in each of the
numbers.
2. The operation returns a binary digit corresponding to each position.
3. If you are using a base other than binary, the result is shown in the base of the last
number you entered.
The following logical operators are available:
& returns a 1 for every position where there is a 1 in both numbers.
o returns a 1 for every position where there is a 1 in either number.
x returns a 1 for every position where there is a 1 in either number, but not both numbers.
X returns a 1 for every position where there is the same digit in both numbers.
Ì returns the diminished radix complement.
Press these keys to perform the respective binary, octal, decimal and hexadecimal logical
operations.
Binary, octal and hexadecimal values
17
1916AND 1A16 = 1816
M¦19&1A=
HEX
18.
12016OR 11012 = 12D16
M¦120oM¥1101=
M¦
BIN
100101101.
HEX
12d.
516XOR 316 = 616
M¦5X3=
HEX
6.
2A16XNOR 5D16 = FFFFFFFF8816
M¦2AX5D= HEX FFFFFFFF88.
1A16 AND 2F16 =A16
M¦1A&&2F=
HEX
BIN
A.
NOT of 10102
M¥10110Ì
1111101001.
Radix complement
IN
Press to calculate and display the radix complement of the hexadecimal, octal or binary
number currently displayed—ie, 10000000000-the binary version of the number.
Binary, octal and hexadecimal values
18
7. Using statistics
M¿
Press to use statistics mode. Statistics mode allows you to enter data and apply the statistics
functions to analyse the data.
Entering a list of data items to analyse
À
Press after each data element. When you press À, the calculator displays the number of
data elements entered.
For example, to enter a list of data consisting of 5, 8 and -3, use the following keystrokes:
5 À 8 À3 Ó À
To enter the results of a calculation as a data item, perform the calculation as you would
normally, then press À when the answer is displayed.
You can amend the data entered into the calculator:
To cancel the last entry you made, press Ô before you press À. Note that when you
press Ô, 0 is displayed. Press In to display the number of data elements stored in the
calculator. To delete a data item you entered previously, enter the value again, then press
IÁ.
Using statistical functions on your data
Once you enter a list of data values you can use the following statistical functions:
In The number of data elements entered
IÒ Sample standard deviation
In
ÒÑ
ÏÍ
Î
IÑ
IÏ
Population standard deviation
Arithmetic mean
IÍ
IÎ
The sum of each data element
The sum of the data elements squared
À
Find the sample standard deviation of the data 5, 9 13 and 6.
M¿5À9À13À6ÀIÒ
SD
3.593976442
4, 1, 82, 59, 2, and 103 were entered, but 59 was entered by
mistake. It should have been 58. To fix the mistake, enter the
wrong number, 59, and IÁ, then enter the right number,
58, and À.
Using statistics
19
8. Specifications
Scientific functions/input range
sinx / cosx / tanx
|x|<4.5x1010 degrees
(<25x107πrad,<5x1010grad
|x|≥1
|x|<10100
sin-1x / cos-1x
tan-1x
sinhx / coshx
|x|≥230.2585092
|x|<10100
tanhx
sinh-1x
cosh-1x
tanh-1x
logx / Inx
ex
|x|<5x1099
|x|≥x<5x1099
|x|<1
10-99≥x<10100
-10100<x≥230.2585092
-10100<x<100
10x
yx
y>0→10100<x•logy<100
y=0→x>0
y<0→x : integer or 1/2n +1 (n : integer)
y>0→x≠0 : -10100< 1/x•logy<230.2582092
y=0→x>0
x√y
y<0→x : odd number or 1/n (n : integer)
0≥x<10100
√x
x2
|x|<1050
3√x
1/x
|x|<10100
|x|<10100(x≠o)
n!
0≥x<69 (x: integer)
√x2 + y2<10100
|θ|<4.5x1010 degrees
(<25x107rad, <5x1010grad)
0≥r≥10100
REC→POL
POL→REC
DMS→DEG
DEG→DMS
π
|x|≥10100
|x|≥107
10 digits
Binary
Positive:
Negative: 1000000000≥x≥1111111111
Positive: 0≥x≥3777777777
Negative: 4000000000≥x≥7777777777
Positive: 0≥x≥9999999999
Negative: -9999999999≥x<0
Positive: 0≥x≥2540BE3FF
Negative: FDABF41C01≥x≥FFFFFFFFFF
0≥x≥1111111111
Octal
Decimal
Hexadecimal
Specifications
20
Read-out
•
Liquid crystal display suppressing unnecessary 0s (zeros).
Power source
•
•
Silicon solar cell (solar model only)
Alkaline manganese battery (LR43)—1 battery for the solar model; 2 batteries for the non-solar model.
Ambient Temperature range
•
0°C–40°C (32°F–104°F).
Dimensions
•
127mmH x 72mmW x 8.5mmD (not including the wallet).
Net weight
91g (including wallet).
9. Changing the battery
·
Replace the battery when:
Replace the battery (alkaline manganese battery (LR43)—1 in the solar model and 2 in the non-solar model)
when the display darkens under poor light condition, or disappears, and cannot be restored by pressing ¡.
·
To replace the battery:
1.
2.
3.
4.
5.
6.
Remove the four screws at the back of the calculator. Don’t loose the screws.
Remove the back panel.
Remove the old battery. Lever it out with a sharp object like a pen.
Install the new battery with the + sign at the uppermost.
Replace the back panel and the screws.
Check the display to make sure it is showing 0 in DEG mode.
Changing the battery
21
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