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[Phys-L] Re: infinite sig. figs.



Robert Cohen wrote:

Given that sig figs is a poor method, one must decide whether it is
better to err on the side of underestimating the uncertainties or
overestimating the uncertainties. I've tended to err on the side of
underestimating the uncertainties (so I typically add an extra digit
beyond that predicted by the sig fig method) but I'm not sure if that
is the best approach. I'd appreciate further guidance on this.

The problem here, as is so horribly often the case, is confusing
number of digits with significance or uncertainty.
-- Adding a guard digit is almost always a good thing to do, and
-- There is no reason that adding a guard digit should cause you
to over- *or* under-estimate the uncertainty.

Example: Suppose you have the number 2.54, and you think for some
reason there are 2 counts of uncertainty in the last digit. You
can write it as
2.54(2)
or you can equally well write it as
2.540(20)
which means exactly the same thing, but gives you more wiggle room
in case the next number that comes along is a little higher or
a little lower:
2.543(20)
2.537(20)

Roundoff error is only one contribution to the uncertainty budget,
one contribution among many. Keeping a goodly number of guard digits
reduces the roundoff error. There is no reason why it should cause
you to over- or under-estimate the other sources of uncertainty.



Why spend so much energy on sig figs in such situations when it is
only approximate anyway?

BTHOM.

(Beats the heck outta me.)

And, for those situations where the student provides a resolution
that is unreasonable for the situation (i.e., too many digits), I
would tend to just remind them that they are implying a much smaller
uncertainty than is probably valid

I would never say that. It is against my religion to infer anything
about uncertainty (or significance) from the digit-count.

If I cared about the uncertainty (which I might or might not) I
would ask the student to go back and estimate the uncertainty. I
would expect the uncertainty to be stated explicitly and separately,
not encoded in the digit-count.
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