Re: SIGNIFICANT FIGURES!!!
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Re: SIGNIFICANT FIGURES!!!
> "It isn't perfect." I'll say. The addition and subtraction works okay,
> but the multiplication and division really blows. For instance:
> 0.125 * 0.135 should be .0169, the program gives .01688
> 0.987 * .0321 should be .317, the program gives .3168
> 10.0 * 1.5 should be 15, the program gives 15 then errors, however,
> I wanted to type in 10 meaning one significant figure not three, there
> is no way to do that with your program.
>
> Okay, you do admit that it only works some of the time, and that's true,
> but I would hate to see science students not studying the rules of
> significant figures because they think they can just use your program.
> Call me a purist, but for all this effort I still think it's faster just
> to learn the rules and do the sig fig determination by hand. It's not that
> tough, you can still use a calculator to do the actual math, after all!
> Still, it was a valiant effort, and I congratulate you for making a
> sig fig program that works even half the time.
>
> >I have created a significant figures program for the 86 that does
> >+,-,*,/,logs, and roots. It isn't perfect, but it works most of the time.
> > -Matt
A quick comment on the "I would hate to see science students not studying the
rules of significant figures" part. Learning these rules and applying them
mechanically does not seem (to me) to be superior to actually struggling
with the priciples involved, which is what you need to do to write a program.
It is sometimes not realized that these rules are only "rules of thumb",
approximations for the convenience of quick calculation, and not magic
in themselves. For example, the number 1.014 is stated with only a little
more precision than the number 0.991, and it is a bit of a puzzle, following
the usual rounding rules, to state their product to an appropriate precision.
What is really going on in examples involving multiplication and division
is determining the _relative magnitude_ of the imprecision involved in stating
the numbers involved, and reporting the result accordingly. One way to do this
is to consider the corresponding problem converted to a problem in adding and
subtracting the logarithms of the numbers involved. This is like plotting
the numbers on a logarithmic scale (shades of slide-rule users of the past are
stirring!).
But there remain paradoxes, particularly when it is necessary to divide
nearly-equal numbers (or subtracting their nearly-equal logarithms). This whole
subject is best approached with a light touch, rather than an appeal to heavy
authority.
RWW Taylor
National Technical Institute for the Deaf
Rochester Institute of Technology
Rochester NY 14623
>>>> The plural of mongoose begins with p. <<<<