HP HP 9s Manual

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HP 9s Operating Modes and Display Format
The Operating Modes of the HP 9s
The Angular Mode
Display Format

hp calculators
HP 9s Operating Modes and Display Format
This learning module introduces the different operating modes in which your HP 9s can work. It then describes the
angular mode used by the trigonometric functions and the coordinate conversion functions. You will also find a
description of the various display formats available.
The operating modes of the HP 9s
Besides the main operating mode, the HP 9s has five more modes in which it can work, namely: Complex (~v),
Statistics (~y), Binary (~:), Octal (~×) and Hexadecimal (~Ø). These five modes light
their corresponding annunciator when they are active – the main mode does not have its own annunciator, though. You
can always select the main mode by pressing ~Ù. The main mode is the default mode and the one you will use
most of the time. Use this mode for most calculations (both arithmetic and function calculations).
In Complex mode the four basic arithmetic functions expect complex numbers as their arguments. Except for some
caveats described in the HP 9s learning module Solving Problems Involving Complex Numbers, postfix functions are
available in this mode. Also, the coordinate conversion functions are available too, which are particularly useful in this
mode. The running memory is available, but parentheses are disabled. Note that the HP 9s will stay in this mode until
another mode is selected or until power is turned off.
In STAT mode the running memory is not available but the contents of M are not lost. Parentheses are not active either,
but chain calculations are possible (e.g. 7321
=
×
+). This mode remains active even if power is turned off in order to
preserve the statistical data entered by the user (up to 80 different items). The data is lost, however, when another
operating mode is selected. There is a special mode in which the data can be edited, the ED mode,. which is described
in the HP 9s learning module Clearing, Editing and Correcting. The modules Statistics – Process Capability and
Statistics – Averages and Standard Deviations deal with statistical calculations.
In Binary, Octal and Hexadecimal modes (often referred to as Base-N mode) the displayed number is not cleared when
these modes are selected (unlike CPLX and STAT mode) but is converted into the corresponding base instead. Also,
pending operations are not cleared so that you can perform mixed calculations, e.g. )Fhd(o 42572 +
×
which can be
calculated by pressing: ~×72*M~Ù25+~Ø4i\. Both parentheses
and the running memory are available, as well as basic arithmetic functions, but most function keys are not active (e.g.
C, ~Ü, unit conversions, etc.) For a more detailed description refer to the HP 9s learning module Base
Conversions and Arithmetic.
The angular mode
The angular mode is shown in the display of your HP 9s with one of these annunciators: DEG, RAD and GRAD. You can
change the angular mode in any operating mode. This setting is kept even if another operating mode is selected or the
power is turned off. To select the desired angular mode, press X; if the displayed setting is not the desired one,
simply press Xagain. Angle values are:
Degrees 360 degrees in a circle
Radians 2πradians in a circle
Grads 400 grads in a circle
The angle measure affect trigonometric calculations and polar/rectangular coordinate conversions.
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hp calculators
HP 9s Operating Modes and Display Format
Display format
The default display format is Floating Point, in which the number of displayed decimal places is not fixed beforehand but
depends on the result. All digits are displayed except trailing zeros. Up to 9 decimal places can be displayed. If the
display format has been changed, the sequence ~p .(decimal point) restores the default setting.
The number of decimal places displayed can be set or fixed to any number from 0 to 9 by pressing ~p and then
the desired number – you need not press the \key. (~p. is disabled in Base-N mode since it works with integers
only). This is called a fixed display format because the number of displayed decimal digits is always the same, trailing
zeros are appended if needed. ~p ndisplays results rounded to ndecimal places, but the actual numbers (that is,
the ones internally stored) are not altered. Note that in the default mode rounding does not always occur. For example:
~p .U~a returns 3.141592654, which is the internal value 3.14159265359 rounded to 9 decimal
places; but, now press: -3\ which results in 0.141592653because for values between –1 and 1, the result
appears truncated instead 1. If you want the results to be always rounded to nine decimal digits use ~p 9.
The FIX setting is retainedso long as it is not changed by theuser. But, the pseudo-random number returned by the
RND function (~Ü) is always displayed in FIX 3 (the display format setting is not actually changed, though, and is
still used in the current calculation); this is convenient because the resulting number is always a number between 0 and
0.999 with three significant digits, that is to say: a result of, say, 0.000 is as though three random digits were generated,
all of them being equal to zero.
It is important to bearin mind the fact that in, say, FIX 3 a 0.000in the display does not necessarily mean that the result
is exactly zero. For example, the number in FIX 3 is displayed as 0.000: U~p 3A=4\
4
10−
Example 1: Calculate 8π2 in the default mode.
Solution: To make sure you are currently in the default mode, press ~p .. Now the calculator is in Floating
Point mode with all digits (except trailing zeros) being displayed. Press:
8*~aO\
Answer: 78.95683521
Example 2: Calculate 8π2 showing only two decimal digits.
Solution: With the previous result still displayed, simply press
~p 2
The result has been rounded (not truncated) to two decimal digits.
Answer: 78.96. When you set FIX · (~p .) again, all digits re-appear because the internal value remains
intact, and is used in chain calculations to full precision.
1The tenth decimal digit can be displayed by pressing P: 1.415926535·10–1, which is also a truncated number. In Engineering
format the number appears rounded: pressing ENG returns 141.5926536·10–3.
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hp calculators
HP 9s Operating Modes and Display Format
It is sometimes necessary to replace a number by its truncated or rounded value. Even though there’s no specific
function to do it on the HP 9s, it can be easily done: to truncate a number to n decimal places, simply add andsubtract
n−13
10 .
Example 3: Truncate πto four decimal digits.
Solution: Let’s select the default mode: ~p .. Now press Uor \to cancel/finish any previous
calculation, and ~a to display thenumber 3.141592654. To truncate it to four decimal places, press:
+A9-A9\
It is important not to use the \key to display the partial result : the sequence ~a+
A9\-A9\ returns 3.14 instead of 3.1415 because the 13-digit precision is only
maintained in chain calculations.
9
10+π
2
Answer: 3.1415
To truncate a number to zero decimal digits, that is to say, to obtain its integer part, the following sequence is shorter:
~Ø~Ù provided the number is between – 9999999999 and 9999999999.
Rounding a number to n decimal digits is a bit more involved, must be added to the number and then the
1
105 −− ⋅n
result must be truncated using the above procedure.
Example 4: Round πto four decimal digits.
Solution: Press ~a again and then:
+A=5+A9-A9\
Answer: 3.1416. Note that this is not the same result as the one obtained by pressing ~a~p 4, even
though they appear to be the same number. Set FIX 6 (~p 6) in both cases to tell the difference.
The HP 9s provides two keys to convert the number that is currently in the display to scientific format (i.e. displayed with
an exponent, and only one digit to the left of the decimal point) and engineering format (i.e. with an exponent that is a
multiple of 3). This conversion affects only the displayed number so that results can be easily interpreted as multiples or
submultiples of a unit, for example, but keying in any new number or continuing the calculation restores the display
setting (i.e. either fixed or floating point). The number of decimal digits in scientific and engineering format is the one
previously set by FIX. In the following example we’ll try to show all possible cases:
Example 5: Let’s set FIX 4 (~p 4) , press Uand key in 123.45678:
123.45678
2The following example will help you tell the difference: 1234567809 {+ 0.001 -[returns 0.001, but [+ 0.001
\-[returns 0.
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HP 9s Operating Modes and Display Format
To display it in scientific notation press \P(press Pagain if you want to restore FIX 4): the display
now reads . Pressing \is necessary because the Pkey is disabled while keying in a
number, it can only be pressed after \or when the display contains a result. Alternatively, you can press
Pafter the `key, because `is enabled while a number is being keyed in.
2
1023461 ⋅.
Press `to express this number with an exponent that is a multiple of three (including zero):
. To change the exponent in multiples of three press the `and ~! keys as many
times as needed. For example, pressing `` returns (NB: not
) and pressing now ~! ~!~! results in (NB: not
). These numbers reveal that `and ~! actually convert the displayed number
as is displayed, not its internal value, which is not modified in any case, though.
00
104568123 ⋅.06
10123456800 − ⋅
06
10123456780 − ⋅3 1012345680 ⋅.
3
10123456780 ⋅.
Press Pto display the number in scientific format and Ponce again to restore FIX 4.
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