Re: [Phys-L] Significant Figures

[John Denker <jsd@av8n.com>]

On 09/16/2017 02:06 PM, Richard Tarara wrote:

> [...] finite precision which is usually indicated by the number of 
> digits (more than likely decimal places) in the value reported.

Au contraire, real-world instruments generally do not follow the
sig figs rules, and you wouldn't want them to.

The five instruments closest to where I am sitting right now are 
a ruler, a thermometer, a high-quality voltmeter, a digital caliper,
and a bicycle cyclometer ... precisely none of which exhibit an
uncertainty limited by the readability of the display (or of the
analog scale).

Furthermore, if you're a masochist you could modify the instruments
to make them conform to the sig figs rules ... but this would make
them markedly less useful.

> In my experience it is more likely that such students will report
> too few digits.

If you teach them the sig figs rules, they will virtually always
report too few digits, by which I mean too few to faithfully
represent the physics.  So don't do that.

> All measurements have a finite precision

That's not true, several times over.
 -- Some observations have no uncertainty, for all practical purposes.
 -- Even if there is some uncertainty, it might be unimportant, i.e.
  immaterial for all practical purposes.
 -- Sig figs makes the far stronger claim that virtually every number
  (when expressed as a decimal numeral) has some uncertainty.  This
  is false and corrosive to the most fundamental understanding of
  what a number is.

> All the complex details of 'real' uncertainties can wait a course or
> two--or forever.

I agree.

However, just because the right thing is complicated doesn't make
it OK to teach the wrong thing.

Instead, rely on the simple notion of tolerances, which is widely
used in the real world, in everyday life and in the research lab.
This is not a new idea:
  Clifford E. Swartz,
  ``EDITORIAL: Insignificant figures''
  Phys. Teach. _6_, 125 (March 1968).
  https://dx.doi.org/10.1119/1.2352406