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[Phys-L] Re: infinite sig. figs.



There are three situations being discussed here:

1. What to do for labs where students are comparing predictions and
measurements.

2. What to do for labs where students are making general observations
in order to develop the general principles and concepts that describe
how the world works.

3. What to do for in-class exams and homework where students are asked
to calculate something and then COMPARE to a given measurement (i.e.,
a simulation of #1 or #2).

4. What to do for in-class exams and homework where one is testing
if students can apply the general principles and concepts to situations
involving numbers and there will be little opportunity to compare to
actual measurements (other than to see if the answer "makes sense").

I have seen no one argue for sig figs in situation #1 and I would argue
that a strict adherence to sig figs is not appropriate for situation #1
because it can lead to wrong conclusions. Using sig figs as a "guide"
for this situation may be acceptable, however, for populations that
cannot handle more rigorous techniques but it must be clear to them
that sig figs is not the best method (the same is true if you use
the "max error" approach of carrying uncertainties but at least you
can make conclusions using that approach).

Given that sig figs is a poor method, one must decide whether it is
better to err on the side of underestimating the uncertainties or
overestimating the uncertainties. I've tended to err on the side of
underestimating the uncertainties (so I typically add an extra digit
beyond that predicted by the sig fig method) but I'm not sure if that
is the best approach. I'd appreciate further guidance on this.

For situation #2, a method of estimating uncertainties is also crucial
because it is too easy to "hand-wave" observations to fit whatever model
you want. Situations #1 and #2 are similar in that respect.

Situation #3, is like situations #1 and #2 and, as such,
should incorporate a good estimate of the uncertainty.

As for situation #4, Michael Edmiston wrote:

... I don't have to worry about how I give my data. I can
write 2 m/s
rather than writing 2.00 m/s. Why throw extra hurdles at
myself when I
am writing exams and problem sets?

Like ME, I have no problem with that approach when dealing with
situation #4. In fact, I think a strict adherence to sig figs is
counter-productive in situation #4. For example, if a cart moves
at 8 m/s (constant speed and direction), how far does it travel
in 0.8 seconds? Do you say 6 m, 6.4 m, 6.40 m, etc.? Does it
matter?

I prefer 6.4 m over 6 m because it is easier for me to see if the
student has applied the principles correctly and because I think that
reporting the answer as 6 m loses valuable information. Yes,
it implies a lower uncertainty than we can probably assume (given
the resolution of the measurements) but I'd rather do that than
lose valuable information about the answer.

Besides, the sig fig method is a poor way of estimating the uncertainty
anyway. Why adhere to it strictly? For example, suppose a cart
moves at 1 m/s for 1 s. If we assume an uncertainty of 0.5 m/s in the
speed and 0.5 s for the time, the answer could be anywhere from 0.25 m
to 2.25 m. Do you report 1 m as the answer and imply that the
uncertainty
is only +/- 0.5 m?

Why spend so much energy on sig figs in such situations when it is
only approximate anyway?

The method of significant figures/digits is a "quick and dirty" way
of estimating uncertainty. It is convenient (read: "relatively easy
to use") but you will sacrifice information in order to have that
convenience. Feel free to use it as a guide but I wouldn't
take off points that don't adhere strictly to it. If anything,
I'd prefer to take off points that did if I thought valuable
information was lost.

And, for those situations where the student provides a resolution
that is unreasonable for the situation (i.e., too many digits), I
would tend to just remind them that they are implying a much smaller
uncertainty than is probably valid and leave the specifics to
situations #1, #2 and #3.

____________________________________________________
Robert Cohen; 570-422-3428; www.esu.edu/~bbq
East Stroudsburg University; E. Stroudsburg, PA 18301
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