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Re: Sig Figures



Here are a few comments on sig fig's.

1. I like to remember that significant digit guidelines are most important
as reminders to our students to think about the accuracy or precision in a
given value and not to simply use the calculator results because it is
there.

2. The "rule" for addition and subtraction is to use the least accurate
POSITIONAL value to determine the limit to our value. Thus my jumping up
onto my desk while asking students how far I am from the center of the
Earth makes no difference in the answer, if the distance to the center of
the Earth is given as 6378 km.
6378 km
+ 0.001 km
------------
6378 km
This is also a good opportunity to talk about the limits (conditions) over
which our "constants" are valid. Am I at the Equator or the North Pole? Am
I at sea-level or not? And so on.

3. The usual "rules" of sig fig's are really conservative estimates.

4. The usual "rules" only apply to linear functions. Trigonometric
functions of angles are not linear in angle. However, just getting
students to realize that sig fig's are important, I let my students simply
treat trig functions as if they are linear. Thus three digits in angle
implies three digits in sin or cos, etc.

5. IMHO, never round off intermediate results.

Note: Joe in John Denker's illustration is doing his experiment correctly
due to suggestion #2 above and not due to #5 above. In fact, Denker's
example is a good one showing what one gains by doing an experiment many
times is more precision in the expected value.

Just some thoughts.

Richard
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Dr. Richard L. Bowman
Chair, Dept. of Physics e-mail: rbowman@bridgewater.edu
(and Dir. of Academic Computing) phone: 540-828-5441
Bridgewater College FAX: 540-828-5479
Bridgewater, VA 22812 http://www.bridgewater.edu/~rbowman/
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