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[Phys-L] Re: Rounding results



Hi all-
Here's a better suggestion. Stop comparing with "standard
values". Such comparisons are misleading because they ignore the
subtleties of systematic uncertainties. My experimental colleagues devote
many hours to consideration of these, and I don't think undergrads are
ready for such profundities.
Regards,
Jack

On Fri, 14 Oct 2005, ALVIN BACHMAN wrote:

When lab calcuations were done with slide rules, we could only read 3 or
four figures.
The advent of calculators resulted in the display of 8 or more figures. Iam
not aware of any gudielines, other than the recently discussed "significant
figures" and the blanket "three decimal place" rules, that are in general
use.

Since the lab result is often compared to a "standard" value, and an
estimate of its
uncertainty is obtained, then a rule of thumb might be:

Round to the place p, such that 10^(-p) is of the order of 1/10 of the
uncertatinty.

Example: raw result 3.12415927 +/- 0.025 ,

1/10 of 0.025 = 0.0025 is of the order of 0.001, so report the result as

3.124 +/- 0.025

Note: This is based on the idea that the "comparison" is of the form

ABS( X - Xo)/ u where the result X +/- u is being compared with
Xo.

Values < 2 are considered Good Agreement

2 .. 5 indeterminate, needing further review

and >= 5 as Disagreement, probably blunders.

(These cut points open to revision.)

Al Bachman


--
"Trust me. I have a lot of experience at this."
General Custer's unremembered message to his men,
just before leading them into the Little Big Horn Valley