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

[Robert Cohen <Robert.Cohen@PO-BOX.ESU.EDU>]

I wrote:

> And, for those situations where the student provides a
> resolution that
> is unreasonable for the situation (i.e., too many digits), I would
> tend to just remind them that they are implying a much smaller
> uncertainty than is probably valid

to which John Denker responded:

> I would never say that.  It is against my religion to infer
> anything about uncertainty (or significance) from the digit-count.

You may not but other people do.

For example, a car travels 2 m in 7 s.  What is the car's average
speed?  Can the student give an answer of 0.285714286 m/s and leave
it at that?

As I wrote before, I wouldn't take off but I would remind the
student that people typically interpret (correctly or incorrectly)
the uncertainty of such a number as being around +/- 0.0000000005
m/s.  In this case, given typical measurement devices, the
uncertainty in distance is probably not much smaller than a millimeter
(if that) and the uncertainty in time is probably not much smaller
than a millisecond (if that).  These "reasonable" estimates of the
uncertainties don't support an uncertainty in speed as small as
0.0000000005 m/s.  And, rightly or wrongly, that is what
0.285714286 m/s (without any further information) seems to imply.

Again, this assumes that no comparisons are being made (between
two or more measurements/predictions); tracking the uncertainties
would be crucial in that case.

Maybe I'm still missing the point between significance and uncertainty.

____________________________________________________
Robert Cohen; 570-422-3428; www.esu.edu/~bbq
East Stroudsburg University; E. Stroudsburg, PA 18301
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