Thread: Decimal places
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Old 04-10-2021, 11:34 PM   #3 (permalink)
Vman455
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This is an important point. First semester of an engineering or sciences degree, multiple professors will spend class time on this (in the degree I'm finishing now, we covered this in Chemistry 101, Physics 141, and Engineering Science 201. Yes, it was duplicative. Yes, it's that important).

This is the concept of "significant figures," or, as we referred to it in school, "sig figs." The basic rules are:

1) The last digit is uncertain--it's an estimate. Measure something from a tape measure marked in centimeters, and you estimate the decimal point (between the marks), eg 23.7 cm. Measure it with a tape marked in millimeters, and the decimal point is again estimated, eg 236.7 mm. Accuracy depends on the measuring device, but in all cases the last digit--just beyond the resolution of the device--is estimated. It's uncertain.*

2) Addition and subtraction: The uncertain digit is taken from the smallest significant figure of the two numbers, eg 0.067 + 1.40 = 1.467.

3) Multiplication and division: The answer is rounded to the smallest number of significant figures of the input data, eg 0.067 * 1.40 = 0.094 (not 0.0938; one number has only two significant figures, so the answer is rounded to two significant figures).

*Note that this says nothing about the calibration of the device. If you use a tape marked in millimeters but each mark is actually 1.1 mm, you're going to be way off regardless of correct rounding.
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