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

["Folkerts, Timothy J" <FolkertsT@BARTONCCC.EDU>]

> In determining a density of a rectangular soilid I might,
> with my cm ruler get this data:
> l = 3.75 +- .05 cm
> w = 1.32 +- .05 cm
> h = 0.54 +- .05 cm
>
> all the tools I hav been taught to do this gives the volume as:
> 2.7 cc +- 0.4 cc  (14%)

The "best estimate" is, of course, 3.75*1.32*.54 = 2.673

I can think of 3 rules for the uncertainty.
1)  Sig Figs.  The last number has 2 sig figs, so round to 2 sig figs.
      2.7 +/- ???

2) "Worst case" estimate.  Add the relative errors, which would be 1.33%
+ 3.79% + 9.26% = +/- 14.4% = +/- 0.384 cm^3, so the answer could be
       2.67 +/- 0.38
Or     2.7  +/- 0.4

3) "Most likely" estimate.  Add the (relative error)^2 and take the sq
root, which would be (0.00018 + 0.00144 + 0.00857)^0.5 = 0.101 =10.1%
for the relative error or 0.27 for the error.
      2.67 +/- 0.27
Or    2.7  +/- 0.3

The third approach is particularly useful if the uncertainties represent
the st dev of the measurement.

Tim F
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