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It is unusual but not impossible for a counting operation to result
in a number such as 12.5. For example, it is perfectly reasonable
to carry 12.5 dollars in your pocket, with zero uncertainty in the
amount.
Entirely analogously, there are EXACTLY 0.048 kstudents registered in
my class that meets for the first time tomorrow (the required
preparation for which I am avoiding by reading and responding to
posts on phys-l.)
Help stamp out sig figs!
Although I understand the motivation, I won't sign on to that
crusade. The concept of sig figs is just too useful and important to
"stamp out."
I don't always require numerical values to be quoted with
uncertainties (in fact, outside of lab, I almost NEVER do), but I
insist on them being quoted to a reasonable number of sig figs.
Students lose points for giving me 5 sig figs when a number deserves
3 or fewer. They lose points for giving me 1 sig fig when the number
deserves at least two, even when that second one is a zero, even when
it comes just after the decimal point.
These are not, IMO, trivial concerns, understanding the concept of
sig figs and putting it into practice reflects a healthy number sense
and an appreciation of measurement uncertainty. Sig figs may not do
full justice to the uncertainty in numbers, but there are lots of
numbers that simply do not require full justice in that regard.
--
John "Slo" Mallinckrodt
Professor of Physics, Cal Poly Pomona
<http://www.csupomona.edu/~ajm>
and
Lead Guitarist, Out-Laws of Physics
<http://www.csupomona.edu/~hsleff/OoPs.html>