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Re: Significant figures - a Modest Proposal



I think I disagree here (although I certainly cut students some slack if
they happen to present their lab analyses with one too many sig figs). In
fact, especially for my 'liberal arts' class, I think the principle
(measurements and resulting calculated quantities have limited precision) is
one of the more important aspects of their lab experience. My college has
continually taken course evaluations (questions with a 1-5 rubric) and
published college and individual averages to 4 significant figures. I've
seen social science talks present 4 sig fig percentages on samples of 25-35
people. The topic needs to be taught, but in a laboratory atmosphere where
the relevance can be clearly demonstrated. I do this in one of our very
first labs--a basic measurement lab--where I have students measure the
density of various objects to identify their materials. One of those
objects is a piece of relatively thick copper wire, about 1mm in diameter
and about 30. cm long. Given the measuring instruments used, the density
measurement warrants _at best_ two significant figures (often only one). I
spend some time subsequently examining WHY these limits make sense.

Besides, without the disregard for significant figures and missing units to
penalize, how would I grade lab books? ;-)

The normal rules also need to be seen as 'conservative', usually providing a
bigger margin of error than might be warranted by a more detailed analysis
(Leigh's quantized argument), but to me, that's OK. More trouble is caused
by assuming a figure is MORE accurate (reliable) than it really is, rather
than less.

Rick

P.S. Only old curmudgeons like Leigh can get away with 'sarcastic remarks'
to students anymore. If any young faculty try this they will get buried
under negative course evals.

*******************************************************
Richard W. Tarara
Department of Chemistry & Physics
Notre Dame, IN 46556
219-284-4664
rtarara@saintmarys.edu

FREE Physics Educational Software
Available for Download

see: www.saintmarys.edu/~rtarara/ for details

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----- Original Message -----
From: Leigh Palmer <palmer@SFU.CA>

Has anyone got the impression I've had for years that teaching the
topic of significant figures is counterproductive? It really adds
nothing to the sudents' conceptual grasp of Nature, and the students
often think that the topic is important, like Newton's second law. My
inclination has always been to ignore the subject until a really
egregious example occurs (I may even generate one myself in lecture)
and then treat it by pointing out the *uncertainty* in the result,
*not* the "number of significant digits".

The big problem with rules for significant digits is that the number is
necessarily quantized. Uncertainty is not quantized to factors of ten.
I could construct many examples of the application of significant digit
rules where the baby gets thrown out and the bathwater gets retained
because of these rules, but I won't. It is sufficient to say the
significant digit rules are not part of the laws of Nature, and they
play no part in reporting results in the scientific literature. Why,
then, do some teachers become obsessive about the application of these
rules?

My practice is *lazy fair* with regard to the sin of excessive
precision. I am content to make sarcastic remarks on students' papers
rather than taking marks off. The lesson is there. There are many other
sins which are comparable and worse for which we do not penalize them,
and I treat these similarly. One I might point out is the
precision-losing practice of writing down intermediate results in a
calculation and then reentering them from the keyboard, often after
rounding and truncating. Surely this is an even worse sin.

I think that learning the concepts of physics is sufficiently difficult
for students without clouding their minds with somewhat arbitrary
procedures which will be of no long term use to them. The concepts of
precision and accuracy, and of uncertainty and error, do need to be
taught, but they can be deferred until the students have learned some
science to which to apply them. Let's get rid of this traditional
dinosaur and see if it helps students learn.

Leigh