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HP 48GII Algebraic and RPN Operating Modes
Figure 9
The calculator has figured out what to do and in what order, and has given the result. The calculator knows the "rules of operator
precedence" when it calculates a result, for example that addition and subtraction should be done after multiplication and division, so
it has simplified the expression, taking out the unnecessary brackets in (3.2*SQ(5)). Whenever you type an expression with any
possible ambiguity in it, the HP48GII applies the rules of operator precedence in evaluating the expression.
One important consequence of the rules of precedence can cause confusion. This is that an expression such as –5^2 works out as
–25.00, not 25.00. Raising a number to a power has higher precedence than changing a sign, so it is done first, and the expression
is worked out as –(5^2).
Switch to RPN mode and try doing the same example calculation.
5„º3.2*3~...2+R
As you went through the calculation, you saw intermediate results at each step, so you could notice any obvious errors, but when
you are finished you only see the final result.
Figure 10
The RPN calculation takes 6 fewer keys, and you see what is happening step by step, but you have to work out for yourself what to
do and in what order. Even if you did not put in the extra brackets in the Algebraic example above, RPN would take 3 less
keystrokes. If you are willing to work out how to do the calculation, RPN saves you any confusion about brackets, and works with
fewer keystrokes.
If you are new to HP calculators, try using both modes and see if you prefer one or the other, or if you want to switch between them
as you use the HP48GII.
Example – which stepladder?
Many people would prefer to type the example above as a formula in Algebraic mode, rather than use RPN mode and do it a step at
a time. Now here is an example to show how RPN mode is useful for solving step-by-step problems.
You need to fix a tile that has fallen off your roof. The roof is 28 feet up, and you have a stepladder that is 29 feet long. You could
also borrow your neighbor's 38 foot ladder. Is either ladder good for the job? You could try leaning each one in turn against the roof
and seeing which one is better, but it's raining, so why not work it out first on your HP48GII by seeing what angle each ladder will
make with the vertical when you lean it against the roof?
First try it for your own ladder. Switch to RPN mode if it is not set. Enter the ladder length. 29`.
Then enter the height and divide so you can get the angle, 28`/. You get 1.04. That cannot be right, sines and
cosines should be smaller than 1. Use ...¯ to get the numbers back, then ™ to swap them, as described in the tip above.
Now press / to divide them again, in the right order, and see 0.97.
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HP 48GII Algebraic and RPN Operating Modes
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