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.