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.