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

[Brian Whatcott <betwys1@SBCGLOBAL.NET>]

At 03:06 PM 9/22/2005, Ken F., you wrote:
> [JD]
> > First of all, I'm going to flame any sentence that uses the
> > term "sig figs."  People who care about their data do not follow
> > the "sig figs rules" in any form.  Instead, they talk about the
> > _uncertainty_ in their data.  They represent the uncertainty
> > separately and explicitly.
>
> First off I am in this camp philosophically but have a question as I teach
> high school introductory level and the "evil" words are part of the
> curriculum.
>
> 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%)
>
> I do not like this very much as the 0.54 has the same certainty as the
> others.
> I would prefer:
> 2.67 +- 0.39 cc
> but not
>  2.673 +- 0.388 cc
>
> I have tried to take the approach that we are multiplying 3.7x by 1.3x by
> 0.5x  (where the x represents an uncetain number). When I do this I get
> 2.4xxx  which I think supports my choice of 2.67 cc.
>
> I wonder if I am misleading my students with what I call a reasonable
> approach?
>
> Ken Fox


This brings back to mind the recent thread concerning the asymmetry of
the uncertainty around  multiplied factors, each having symetrically
disposed uncertainty. Multiplying three factors each with given
uncertainty could lead to twenty seven estimates of the product,
of which the bounds are 2.67 cc -0.37 cc +0.40 cc
In a more comprehensive model, given a likely distribution of the
individual factorial  values, one could arrive at an (asymmetrical)
  product distribution.



Brian Whatcott    Altus OK    Eureka!
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