Thanks, Paul, for giving us the link to the Wired article. In the past when we have had these discussions on uncertainties, I have stayed silent, but I guess I'll enter the fray.
Rhett Allain (the Wired blogger) and others are obviously correct in showing that sig figs is not the most accurate way of treating uncertainties, but I would urge us to consider at what level this is emphasized. As a college prof of physics, I emphasize sig figs to my intro level students, both majors and non-majors, so that they do not just blindly report all of the digits their calculator gives them. In our upper-level experimental physics courses, we do expect our students to use the calculus method. Even the three-crank method is too much for us to expect from our student's in every calculation they do (most of our students are not physics or even chemistry majors) and even on exams, we want them to think about uncertainties. We do not use multiple-choice exams but actually have them write out calculations in answers to problems.
So there is my two-cents.
BTW, generally if one reports a measurement of 3.12 cm in the sig figs method, then the usual implication is that due to rounding the uncertainty is +/- 0.005 cm not the 0.01 cm that Rhett Allain used in the Wired article. This reduces the extreme error in his sig fig example.
Richard
Richard L. Bowman, PhD | Department of Physics | Professor of Physics
BRIDGEWATER COLLEGE, Bridgewater, VA 22812, USA
phone: 540-828-5441 | online: www.bridgewater.edu/~rbowman