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Re: [Phys-l] Significant figures -- again



I don't have a problem with your main message. It just seems to me that an example like Bob and Carol illustrates it better.

Or, even simpler...

I worked a year at company A, took some time off, then worked a year at company B. How many days did I work at each company?

Is writing 400 days at each company any better or worse than writing 365.2425 days at each company?

I would say it would be neither better nor worse without some way of conveying the uncertainty. However, lacking that information, it would be worse if someone was using the value to make additional calculations (like the total number of days all together) and better if one was using the number itself to convey some vague idea about the uncertainty (e.g., "about 400 days" vs. "about 365.2425 days").

Is this improper?

Robert A. Cohen, Department of Physics, East Stroudsburg University
570.422.3428 rcohen@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 John Denker
Sent: Thursday, April 12, 2012 5:43 PM
To: Forum for Physics Educators
Subject: Re: [Phys-l] Significant figures -- again

On 04/12/2012 09:11 AM, Robert Cohen wrote:

.... it seems to me that the sig fig examples serve to illustrate the
problems with rounding intermediate steps, not the use of sig figs at
the end.

That argument doesn't work in the real world.

It is as easy as π to come up with examples where one person's "final" output is another person's input, so from the overall point of view virtually everything is an intermediate result.

We have recently (03/29/2012 12:05 PM) seen a specific example of this, where Bob spent all day calculating the matrix elements and then Carol spent all night calculating the eigenvalues. Bob rounded off "at the end" of /his/ calculation, in accordance with the sig- figs rules, with disastrous results.

Seriously, what's the point of calculating a number if nobody is going to use it? Then ... if somebody is going to use your number, it's not really a "final"
result, is it?

AFAICT only case where my counterargument doesn't apply is in connection with ivory-tower busywork assignments, where the answer will not be used for any practical purpose, but instead will simply be checked for compliance with artificial, nonsensical rules.

Just to pound on this a little more: The suggestion to use sig figs only "at the end" is IMHO a last-ditch straw- grasping argument anyway. At this point you have already conceded that for a 25-step calculation, sig figs are no good for (at least!) 24 of the 25 steps, and conceded that sig figs cannot be used for "propagation of error" ... so why is it even worth mentioning sig figs? Other techniques must be learned. Other techniques must be used most of the time ... so why are we bothering to put lipstick on this pig? Who cares if you can find isolated cases where sig figs are not a /complete/ disaster?
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Forum for Physics Educators
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https://carnot.physics.buffalo.edu/mailman/listinfo/phys-l