[Phys-L] Re: fall cleanup: sig figs

[s.goelzer at COMCAST.NET (Scott Goelzer)]

I followed the discussion on this thread with great interest and read
the link provided by John Denker:
<http://www.av8n.com/physics/uncertainty.htm>.

I have taught SF for years and am aware of the problems it raises
with some data sets and situations. I am rethinking whether to
present SF this year, but this raises some unanswered issues for me:

1) If I do not teach SF and they encounter them in college, have I
prepared my students? I recall needing to round my results using SF
rules in labs and exams in many classes.

2) How do I deal with the problem of rounding answers to text book
problems where there is no uncertainty given other than that implied
by the rules of SF? I constantly fight the standard problem of
students reporting 10 places for the answer of a homework problem
without considering which places are realistic. It is mighty nice to
have a rounding system that produces one correct answer for all
students. How does one decide that a student's answer to a problem
has too many places and validate that to a student? The Giancoli text
and answer book uses SF rules in rounding its answers.


Scott


*******************************************
Scott Goelzer
Physics Teacher
Coe-Brown Northwood Academy
Northwood NH 03261
sgoelzer@coebrownacademy.com
*******************************************


On Aug 10, 2005, at 12:39 PM, John Denker wrote:

> A message from the SPCD (Society for the Prevention of Cruelty
> to Data):
>
> Every September, in classrooms all over the country, kids are taught
> about "significant figures".
>
> This has got to stop.  The notion of "sig figs" is garbage.  If
> you see a number such as 2.54 in isolation, you cannot know
> whether it has 10% uncertainty, 1% uncertainty, or no uncertainty
> at all.
>
> Different texts tout wildly inconsistent versions of the "rules"
> for using sig figs.
>
> People who care about their data don't use sig figs at all;  they
> state the number and its uncertainty separately, explicitly, as in
>        1.672 621 71(29) e-27 kg
>
>
> Let's be clear:  Uncertainty needs to be expressed.  It doesn't
> need to be expressed using the method of "sig figs".
>
> Uncertainty is not the same as significance.  A number that has
> uncertainty at the .01 level may be significant at the .001
> level, for instance if there is signal-averaging going on.
>
> Roundoff is not the same as uncertainty or significance.  The
> proper roundoff rules are:
>   -- keep many enough digits to avoid unintended loss of
>    precision.
>   -- keep few enough digits to be reasonably convenient.
>
> In particular, rounding things off in accordance with the
> usual "sig figs" rules commonly results in disastrous loss
> of precision.  Don't do it.
>
> For details on all this, see
>         http://www.av8n.com/physics/uncertainty.htm
>
> Even if you don't read that page, your students will.  It gets a
> lot of hits ... especially during September.