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John D responded in part:
|
| 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?
|
[Joel Rauber] Excellent point above, I'm not sure how much, if any of the below applies, as I'm talking about the number read off of an instrument and not the subsequent interpretation (calculation) of an uncertainty from sets of data using those numbers; i.e. use of sig figs to say something about the fineness of the scale on the measuring instrument itself. Your example with a non-decimal fraction (common in a 12 inch ruler) above is an excellent counter example as well as a previous post where you used rational fractions to address a different question than the above, but never the less related to sig figs.
| -- 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.
|
| <snip>
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