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Re: [Phys-l] formatting uncertainties



Hi all-
The particle data group at LBL (Lawrence Berkeley Lab), quotes all numbers up to and including the uncertain digits, which are specified in parentheses (http://pdg.lbl.gov) For example, they give
G=6.6742(10)x10^{11} (in the usual units)
and they seem to follow the same convention throughout, e.g.,
h= 6.6260693(11)x10^{-34} Js,
except when the uncertainties are asymmetric.
Regards,
Ja

On Thu, 24 Jan 2008, Robert Cohen wrote:

There have been a number of good points raised in this discussion. One is that it adds nothing to round if the uncertainty is already provided. On the other hand, if the uncertainty is not provided, one uses the number of digits (sig figs) to ascertain a "vague sense" of the uncertainty.

The question that generated this discussion, though, is not what to do when there is no uncertainty provided but rather what to do when there is an uncertainty provided. In that case, one must remember that a rounding error is introduced whenever you round (as pointed out by JD). So, it doesn't make sense to do that on purpose.

Still, does this mean one should *never* round? It seems to me that it depends on how large the rounding error is relative to the stated uncertainty.

For 6.67255 ± 0.001, rounding to 6.673 causes an error (or at least an uncertainty) of 0.0045, which seems pretty significant relative to the 0.001. You are definitely *increasing* the error/uncertainty by rounding in that situation.

However, suppose you are given 6.67255 ± 1. In that case, it seems you can probably round to 6.673 and your uncertainty/error would still be ± 1. Are you losing significant information by rounding in that case? I used to think it was okay to round in that case but I can see if this number is used in another calculation it may be important to keep the extra digits (as in the GM example). Is rounding ever acceptable?

P.S. As for the other question of what to do when no uncertainty is stated, in that case we have to ascertain a vague sense of the uncertainty from the number of digits provided. One very rough way of doing that is the sig fig method (although, in order to ensure that no data is lost, I would add an extra digit to whatever the sig fig method predicts). However, I would stress that this is not a good way to go about it and I certainly wouldn't want students to think this is the *ideal* or *best* way (which, I might add, many students appear to believe).

----------------------------------------------------------
Robert A. Cohen, Department of Physics, East Stroudsburg University
570.422.3428 rcohen@po-box.esu.edu http://www.esu.edu/~bbq

-----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-----
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?

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_______________________________________________
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