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-----Original Message-----
From: phys-l-bounces@carnot.physics.buffalo.edu
[mailto:phys-l-bounces@carnot.physics.buffalo.edu] On Behalf
Of Jeffrey Schnick
Sent: Thursday, January 24, 2008 12:49 PM
To: Forum for Physics Educators
Subject: Re: [Phys-l] formatting uncertainties
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-----on the NIST
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
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?
Forum for Physics Educators
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