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Re: [Phys-l] formatting uncertainties



1) the number of digits in the reported answer directly relates to the confidence placed in the precision of the result.
3421.675 means that I believe the .67 is reproducible by subsequent measurements and the 5 might vary a little bit. 3.42e3 means something close to 3420. The number of significant digits carries information about the result.

2) round-off during intermediate calculations should be minimized because of the dangers of subtractive cancellation and loss of accuracy

3) students should be shown the results of poor experimental design which leads to loss of accuracy due to rounding

4) students should also be shown the fallacy of using too many significant digits. Have them measure the diameter and circumference of a tennis ball and calculate pi. Then compare it to the known value. The comparison should be done to the same number of significant digits that can be obtained from the measurement instruments, otherwise, they'll think they proved that pi is "wrong."

rabbit hole? --> students often (but not uniquely) learn more vividly when they do something wrong and are shown why it's wrong, than when they memorize the right way and never see the wrong.

BN
Union University
Jackson, TN

On 01/23/2008 11:09 AM, Rick Tarara wrote:
<snip>
The only way I can make sense of this situation is in the case
where the cure is worse than the original disease. That is,
if you round off sufficiently brutally that roundoff error is
the dominant source of uncertainty, then you know what the
uncertainty is. But why would you want to do that? Designing
an experiment or a calculation such that roundoff error is the
dominant source of uncertainty is the hallmark of bad design.
Why should we tempt (let alone require) students to go down
that rabbit-hole?
<snip>
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