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

On 03/13/2012 03:21 PM, Rauber, Joel wrote:
Isn't there value in significant figures in the reporting of raw data
for indicating the precision of the measuring instrument. In other
words,

If a student reported measurements of a dimension of an object as

1.2 cm

Vs.

1.200 cm

I hope something meaningfully different is being conveyed about the
instrument they used to obtain the datum in the two different cases.
Something meaningful that is not conveyed by the statement that the
Hindu-Arabic conventions imply equality.

Hope springs eternal, but that particular hope is not well-founded.

There are innumerable unsolvable problems with that approach. Here
are a few examples.

-- What if another student writes 1.125 cm ... accurate to the nearest
1/8th cm, not to the nearest thousandth?

-- What if it's voltage instead of length, and the reading is 1.2 V,
with an uncertainty of 3% of the reading plus 3% of full scale. The
uncertainty is well represented by the rule (3% of the reading plus
3% of full scale) ... whereas it would be madness to try to represent
that using some number of trailing zeros.

-- What if the uncertainty is NOT KNOWN at the time the data is written
down, for instance if the whole purpose of the exercise is to calibrate
the voltmeter?

-- What if the guy who writes down 1.200 intends for it to mean half a
count of uncertainty in the last digit, but the guy who reads the number
later takes it to mean a few counts of uncertainty in the last digit
... or vice versa?

-- etc. etc. etc.


You might get away with sig figs in a classroom busywork situation, where
the teacher poses the problem and grades the results, and nobody will ever
know whether the expected result was factually correct ... but in the real
world, Mother Nature plays by different rules. In my line of work, it
pays to get the actual factual answer ... not necessarily the answer that
the person who posed the question was expecting.