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Re: Significant figures - a Modest Proposal



Try just asking everyone in the classroom to look at their watch and
write done what time it is. Very common place, but it makes the point.

cheers

On
Fri, 27 Aug 1999, John Gastineau wrote:

<-----Original Message-----
<From: phys-l@lists.nau.edu: Forum for Physics Educators
<[mailto:PHYS-L@lists.nau.edu]On Behalf Of Joseph Bellina
<Sent: Friday, August 27, 1999 10:16 AM
<To: PHYS-L@lists.nau.edu
<Subject: Re: Significant figures - a Modest Proposal
<
<
<I'm going to spin this issue a little differently. I think it is
<important to make the following distinction for students. Mathematics
<deals with issues of equality...is one thing equal to another. In
<science, everything rests eventually on some sort of measurement and the
<results of two different measurements, no matter what we do, are not the
<same. So the issue never is equal, rather it is, are two values close
<enough that we are willing to say they are the same. That is a judgment
<call....but you need some basis for making the judgment.


Well said.

One easy to way to work on this concept is to make a single measurement
repeatedly, and then look at the spectrum of values. Is one value "correct"?
Is one value better than the others? Is there a representative value? Is there
a way to characterize the spread of the values?

I've done this two ways with students. One is to measure with a stopwatch the
time it takes a ball to fall from a table to the floor, 50 or 100 times. Use a
digital stopwatch to get the time to 0.01s. If the same student drops the ball
and runs the stopwatch, reaction time is minimized through anticipation,
though not the variation in reaction time. Observing that variation is the
point to the lab.

You can also do an MBL or CBL experiment multiple times. Measure g with a
picket fence and photogate ten times. Now consider your set of measurements.
Compare your set to the set of another group. After this exercise, students
won't be tempted either to write g=9.8104568 m/s^2 or to claim that their
result of 9.81 is better than another group's 9.82.

In my opinion, once a student has done this sort of work, he or she is less
likely to report homework results to nine digits.

I think this sort of thing (uncertainties, but possibly without statistics) is
well worth spending time on, while arbitrary rules of sig figs may not be
worth it.

JEG
__________________________________

John E. Gastineau john@gastineau.org
PMB #163 http://gastineau.home.mindspring.com
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