Re: [Phys-l] formatting uncertainties

["Jeffrey Schnick" <JSchnick@Anselm.Edu>]

It would make no sense to me to report
(6.67259 +/- 0.001) * 10^(-11) m^3kg^(-1)s^(-2)
as
(6.673 +/- 0.001) * 10^(-11) m^3kg^(-1)s^(-2)
because the purpose of rounding to 6.673 in the method of significant
figures is to communicate a vague sense in the uncertainty of the value
(at the cost of throwing away some information), and in this case, the
uncertainty is already provided in a more precise manner.  Still, I
think there are times when the method of significant figures is
appropriate.  For instance:

The standard uncertainty in the value of G at 
http://physics.nist.gov/cgi-bin/cuu/Value?bg 
is quoted to two significant digits.  In using exactly two significant
digits in the value of the standard uncertainty, I think the author is
intentionally communicating some vague sense of the uncertainty in the
value of the standard uncertainty.

The value of the standard uncertainty itself represents the mean of a
distribution.  Using the method of significant figures (more
specifically, rounding the value of the standard uncertainty to two
significant digits) to convey a vague idea of the width of that
distribution is appropriate both because the width is not known very
precisely and because the precise width of the distribution is likely to
be of little relevance.  Likewise, the digits eliminated by the rounding
are likely to be of little relevance.

> -----(Part of) Original Message-----
> From: phys-l-bounces@carnot.physics.buffalo.edu [mailto:phys-l-
> bounces@carnot.physics.buffalo.edu] On Behalf Of John Denker
> Sent: Thursday, January 24, 2008 10:40 AM
> To: Forum for Physics Educators
> Subject: Re: [Phys-l] formatting uncertainties
>
>
> Did everybody notice that all of the fundamental constants on
> the NIST site e.g.
>   http://physics.nist.gov/cgi-bin/cuu/Value?bg 
> are quoted with multiple uncertain digits?   Haven't you ever
> wondered if there might be a reason for that?