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[Phys-L] Re: infinite sig. figs.



As noted yesterday, the many people have been taught to report the
_uncertainty_ of their results using /significant/ digits. That's
crazy, because uncertainty is not the same as insignificance, nor
vice versa. This is a big problem. When I read something, I
never know whether "significant digits" refers to significance or
uncertainty ... and the recent posting by Michael E. is a perfect
example of this. The first time I read it, I assumed "significant
digits" referred to uncertainty, but the passage makes much more
sense if "significant digits" is taken to refer to honest-to-goodness
significance.

Specifically, in the passage quoted below, if M.E. says three digits
are significant _to him_, who am I to argue? IMHO he has absolute
authority to say what is significant _to him_. The point of the
passage, as I understand it, is that the digits do *not* encode
the uncertainty of the measurement.

=======

As a trustworthy rule, in my writing and speaking, whenever I am tempted
to say "significant digits" I find that the sentence is greatly improved
by saying something else instead. The quoted passage is a fine example
of this. Please re-read it; don't you think it would be improved by
crossing out "three significant digits" and saying instead "three-digit
representation" or "three digits of resolution" or preferably just "three
decimal places".


Edmiston, Mike wrote:
<snip>
all calculations, even those involving "real-world" examples, are to be
carried out to three decimal places
<snip>

Well, I admit to doing this. For my case, to answer Joel, I tell the
students to carry out the calculations entirely in the calculator, or
Excel, or if using paper write down intermediate results to 5
significant digits... and then report the final answer rounded to
. ^^^^^^^^^^^^^^^^^^

I have to object there. These digits are almost certainly not significant,
nor do they represent the uncertainty of the measurement or anything else.
IMHO this instance really cries out for something other than "significant
digits" ... perhaps 5 decimal places, or 5-digit resolution, or 2 guard
digits ........

3-significant digits.

Why?

(1) I don't want them to waste time worrying about precision and error
analysis on problem sets and exams for which error analysis is not the
point of the problem. If the goal is to learn the physics (or test the
physics knowledge of the student) why throw extra non-physics hurdles in
front of the student?

I agree that it is better to not deal with uncertainty at all than to
deal with it improperly. At least this way we are not reinforcing bad
habits.

(2) I don't have to worry about how I give my data. I can write 2 m/s
rather than writing 2.00 m/s. Why throw extra hurdles at myself when I
am writing exams and problem sets?

(3) Three significant digits are generally satisfactory for typical
problems on exams and problem sets. They are many enough to show what
needs shown, and few enough to be convenient.

I suspect the AP folks are thinking the same thing. Don't throw sig-fig
stuff or error analysis baggage on every problem. Just test the
physics.

=======================

Let me add that even when "significant digits" refer to significance, they
are a lousy way to do it. Counting digits is never a good way to represent
anything . There are much better ways.

For instance, in situations like the above, instead of saying 3 digits,
you could say 0.1%. Instead of 5 digits, you could say 10 ppm. This
has numerous advantages, not least of which is that you can express the
idea of 30 ppm, which would be hard to represent in terms of counting
the digits ... writing four and a half digits is remarkably ugly.
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