John Denker said, "Help stamp out sig figs!" I agree whole-heartedly
agree with this.
Jon Mallinckrodt said he cannot sign on to this crusade because the
sig-fig concept is too useful. He then went on to say that he insists
students quote a reasonable number of "sig figs." And he says that for
students to report a reasonable number of digits reflects a healthy
number sense. (I have edited John M's words. I hope my shortened
version maintains the intended message.)
My response to John M is to quote John D's statement about how many
digits to retain. He says...
* * * quoting John Denker * * *
The proper roundoff rules are:
-- keep many enough digits to avoid unintended loss of
precision.
-- keep few enough digits to be reasonably convenient.
* * * end quote * * *
I love this wording and have begun using it in my lectures and in my
handouts. It speaks to John M's concerns directly, and promotes a much
better lesson in "healthy number sense" than the usual sig-fig rules
have ever conveyed. Indeed, I think, and I am sure Denker would agree,
that the usual sig-fig rules promote unhealthy number sense.
In addition to quoting John D, I also tell my students that unintended
loss of precision can endanger the message they need to convey. They
need to ask themselves what their data are telling them, and report the
numbers in a way that conveys the message to the readers.
Here is an example. If students are trying to see how well the velocity
of a glider on a level air track stays constant, and/or to see if air
friction is observable, and their measurements show a velocity of 34.88
cm/s near the start and 34.64 cm/s near the end of the track, then they
would not want to say, "the two velocities were 35 cm/s and 35 cm/s so
the velocity stayed exactly constant."
Why? Well they do this a bunch of times and if the track is truly level
the later velocities are always a bit slower. Clearly the equipment
produces data good enough to demonstrate air friction. Reporting 35 and
35 violates Denker's first rule. The data consistently show a slight
slow down and rounding to the nearest cm/s doesn't consistently show
this. On the other hand, if the student simply writes what the
calculator said... 34.87942367 cm/s and 34.63785211 then the student has
violated Denker's second rule.
I would be happy if the student reported 34.88 and 34.64 cm/s. I would
certainly tolerate 34.879 and 34.638 cm/s and probably would tolerate
34.9 and 34.6 cm/s.
These all adequately show the extent of slow down from air friction, and
they all are convenient to write and read. Isn't this the number sense
we want students to develop? I see no need to go beyond Denker's rules,
and I see harm in going beyond them.
Michael D. Edmiston, Ph.D.
Professor of Chemistry and Physics
Bluffton University
Bluffton, OH 45817
(419)-358-3270
edmiston@bluffton.edu
_______________________________________________
Phys-L mailing list
Phys-L@electron.physics.buffalo.edu https://www.physics.buffalo.edu/mailman/listinfo/phys-l