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

[John Denker <jsd@AV8N.COM>]

Dwight K. Souder wrote:

> It's been a few days, but I believe the question asked was, if you counted
> 12.5 oranges, is it still an infinite number of sig. figs. or are there 3
> sig. figs.?

First of all, I'm going to flame any sentence that uses the
term "sig figs."  People who care about their data do not follow
the "sig figs rules" in any form.  Instead, they talk about the
_uncertainty_ in their data.  They represent the uncertainty
separately and explicitly.

For more information on how to think about uncertainty, and how
to express uncertainty,  see
   http://www.av8n.com/physics/uncertainty.htm

For more information on "sig figs", look in your thesaurus under
"B" for "Bad".  :-)

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

To answer a slightly reworded question:
   1) Yes, it is very common for counting operations to result in
    numbers with zero uncertainty.

   2) Uncertainty is not the same as insignificance, nor vice versa.
    Bean counting is one of the canonical counterexamples.  See the
    discussion leading up to
      http://www.av8n.com/physics/uncertainty.htm#fig-sig-unc

   3) It is unusual but not impossible for a counting operation to result
    in a number such as 12.5.   For example, it is perfectly reasonable
    to carry 12.5 dollars in your pocket, with zero uncertainty in the
    amount.

   4) You simply cannot judge the uncertainty (or the significance) of a
    number by counting digits.  If you see the number 2.54 in the window
    of a calculator,
     -- It could have much less than .01 units of uncertainty.  Calculators
      are notorious for displaying insignificant digits.
     -- It might (by accident!!!) have just .01 units of uncertainty.
     -- It might have much less than 0.01 units of uncertainty.
     -- It might have no uncertainty whatsoever, for instance if it represents
      the number of centimeters in an inch, which is exact by definition.

Help stamp out sig figs!
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