There is such a thing as a /null measurement/. For example,
suppose you are trying to measure the difference between
inertial mass and gravitational mass ... the Eötvös experiment.
You are expecting the difference to be zero.
If you repeat the experiment N times, you will have a
distribution of measured values, and the distribution
will have some mean and standard deviation.
In favorable cases (albeit not all cases) it would make
sense to report the mean and standard deviation. You
could use the representation A ± B, with the expectation
that B is enormous compared to A.
In this case B is the *absolute* uncertainty, at the
1σ level.
In contrast, for such an experiment, it would be
madness to report the relative uncertainty. There
is no way to make sense of relative uncertainty in
a measurement of this kind. Don't bother trying.
As a corollary: In such a case, "sig figs" are
even more obviously absurd than usual. There is
no way to make sense of sig figs. Don't bother
trying.
Constructive suggestion #1: In many cases, the best
thing is to report that absolute uncertainty and
leave it at that.
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At the university level (not the HS level), it might
be appropriate to /understand/ the sources of
uncertainty.
a) For example, one source is the plain old uncertainty
of measurement. How good are the instruments? How
repeatable are the readings under the best of conditions?
b) Another source is friction and other perturbations.
How much does the momentum of a cart decay in the
absence of a collision? You can measure this over
a long baseline, to help separate this item (b) from
the previous item (a).
*) et cetera
Then you get to have some fun. You get to do some
physics. I predict that in a well-designed experiment,
nearly all of the uncertainty seen in the collision
experiment can be explained by contributions such as
those itemized above, i.e. having nothing to do with
the collision.
Let's be clear:
i) There will be instrumental uncertainty on P1(before),
on P2(before), and P12(after). These can be measured
under non-collision conditions.
ii) There will be some measured spread in the amount of
momentum "lost" in the collision. I predict that nearly
all of this can be explained by contributions not
related to the collision.
If you want to put the measured spread in context, this
comparison (i) versus (ii) is the way to do it.
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If that doesn't answer the question, please ask a more
specific question.