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Re: [Phys-l] Significant figures -- again



On 3/12/2012 3:49 PM, John Mallinckrodt wrote:

I see no reason whatsoever not to expect people (including students) to express numerical data using an appropriate number of digits. It's simply a matter of using proper "numerical grammar." There may be no "right number of digits," but there are most certainly "wrong numbers of digits." I wouldn't and don't waste any time on "the rules for sig figs" and I would never penalize a student for using, say 2 or 4 digits to express a number that "the rules" would say should have 3, but I will continue to penalize them for using, say 1 digit or 6 or more in such a case.

Sig figs are insidious because they pretend to communicate more about
uncertainty than they actually are able to. This makes sig figs the
numeric equivalent of the arrogant fool who makes bold assertions that
he can't back up.

However, one of the problems with education is that we're expected to
teach students social conventions as well as "content" (things that fit
the data and observations that we know about--things the nonscientific
world calls "facts").

In this case, teachers are supposed to teach our students the social
convention of not giving extraneous or meaningless information. In the
measurement 3.8675309 ± 0.5 cm, I would argue that the digits beyond the
hundredths place are extraneous. It would be polite to leave them out.
Most people would think it reasonable to quote a measurement of 3.9 ±
0.5 cm or 3.87 ± 0.5 cm, but might waste time wondering about the string
of digits in 3.8675309 ± 0.5 cm. The latter is not wrong; it's just a
little impolite.

However, the problem I see is that many students don't have any kind of
sense of uncertainty in measurements. So instead of communicating
anything with any meaning, to most students, the question of sig figs
becomes a guessing game of "Where should I round off the number so I
don't lose points?" I think it would be a lot more useful to point out
that most high school laboratory equipment can't measure more than about
three sig figs. Therefore, for most calculations, teaching them to keep
four sig figs through the calculations would probably serve them better
than trying to teach them to estimate from the sig fig rules every time.

--
Jeff Bigler
"Magic" is what we call Science before we understand it.