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Here is how I do it. The level of discussion regarding uncertainty
analysis depends on the group. I have two presentations on
propagating error/uncertainty:
the first one is required by the IB
exams and contains typical HS rules of thumb.
The second presentation
is introduced if I feel that my students are up to it. It makes use
of partial derivatives and discusses assuptions underlying the Least
Square Fit and so on (still elementary but a bit more demanding than
the first take).
Do you find any merit in discussing significant figure rules for the
simple silly but practical reason that students may be tested on them?
Also, for the reason that they may have to communicate with folks who
talk about those rules?