A message from the SPCD (Society for the Prevention of Cruelty
to Data):
Every September, in classrooms all over the country, kids are taught
about "significant figures".
This has got to stop. The notion of "sig figs" is garbage. If
you see a number such as 2.54 in isolation, you cannot know
whether it has 10% uncertainty, 1% uncertainty, or no uncertainty
at all.
Different texts tout wildly inconsistent versions of the "rules"
for using sig figs.
People who care about their data don't use sig figs at all; they
state the number and its uncertainty separately, explicitly, as in
1.672 621 71(29) e-27 kg
Let's be clear: Uncertainty needs to be expressed. It doesn't
need to be expressed using the method of "sig figs".
Uncertainty is not the same as significance. A number that has
uncertainty at the .01 level may be significant at the .001
level, for instance if there is signal-averaging going on.
Roundoff is not the same as uncertainty or significance. The
proper roundoff rules are:
-- keep many enough digits to avoid unintended loss of
precision.
-- keep few enough digits to be reasonably convenient.
In particular, rounding things off in accordance with the
usual "sig figs" rules commonly results in disastrous loss
of precision. Don't do it.