Sig figs is all about having an implied but unstated level of precision.
If the precision really matters, you need to do actual error analysis.
However, a thorough treatment of numerical error analysis is beyond
many if not most high school students, and would take more time than
most curricula allow.
The problem, as John Denker so often points out, is that sig figs imply
that we know more about the precision just from the number of digits
that are reported than we can actually know. Sig figs often but not
always give a decent order-of-magnitude estimate of the precision, but I
don't think anyone can seriously claim that they're better than a rule
of thumb that works much of the time.
I think the problem with the way educators treat sig figs in high
schools is that the existence of rigid and precise rules imply that sig
figs are more reliable about estimating precision than they actually
are. I think the use of sig figs for high school students should be
simply to say, "don't give me eight digits of answer from your
calculator if I've only given you three in the numbers in the problem."
My students were taught sig figs badly in chemistry, so they know that
they need to round their answers off, but they've spent so much time
being confused that any attempt I make to teach them how to figure out
where is a reasonable place to round doesn't stick in their minds. I
expect my students to round their answers off to a "reasonable" number
of "sig figs", but because what's "reasonable" is arguable, I don't take
off any points as long as they're within about +/-2 of what a formal
treatment of sig figs would call for.
--
Jeff Bigler
"Magic" is what we call Science before we understand it.