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Re: [Phys-L] Significant Figures

Sig-figs has been a recurring topic here, fueled mostly by those who oppose their use.  Most of us know (have experienced) that in actual research figuring out and presenting meaningful uncertainties can be arduous and at least slightly complicated. I'm thinking of having several factors that come to play in a experimental value some of which can present random uncertainties and others that can by systematic.  But all that aside, for the BEGINNING science student or for the 'lay' student taking their one and only science course, the two issues involved here are:  1) All measurements have a finite precision which is usually indicated by the number of digits (more than likely decimal places) in the value reported.  In my experience it is more likely that such students will report too few digits.  2)  That mathematical operations in of themselves should not increase nor decrease the precision of the result reported.  The simple example is that of measuring an area with width and length measurements.  This can be used to show how the 'rules' of sig-figs do a pretty good job of preventing one from overstating the accuracy of an area measurement.

All the complex details of 'real' uncertainties can wait a course or two--or forever.

RWT (who once chided one of our psychologists for presenting a study done with 35 employees and presenting percentages to two decimal places.)


On 9/16/2017 4:51 PM, John Denker via Phys-l wrote:
On 09/16/2017 09:41 AM, John Sohl wrote:

Then, some news report comes out that says something stupid like:
"The new roadway into the university's campus will cost $204,531.18
and will be paid for by..."

When has any large project come in, on-budget, to an accuracy down
to the penny?????
On the bright side, I can show these articles in class and ask "what
do you think is wrong with this number?"
What if somebody says there is nothing wrong?

AFAICT it only becomes a problem if you interpret the numeral
as a claim of uncertainty, comparable to 1 count in the last
digit. However:
a) Representing uncertainty that way would be bad practice, and
b) The more insignificant digits there are, the more obvious
it is that no such claim was intended.

The cost of writing an abundance of guard digits is infinitesimal,
so tell me again, what is wrong with that number?
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