(Or How many decimal places should I keep?)
In physics, all experimental measurements have some uncertainty involved. The accuracy of any measurement is expressed by the number of significant digits written when the measurement is reported.
There are several rules for determining the number of significant digits (or significant figures) in a measurement. In general significant figures are determined starting with the leftmost digit.
The general rule of thumb in this class is that calculated results can have no more than 3 significant figures (sig figs). This usually means that results shown on a calculator must be rounded off to 3 sig figs.
For example, 252,194,701 would be rounded to 252,000,000.
Sometimes more or fewer than 3 sig figs would be allowed according to the following rules:
MULTIPLICATION or DIVISION
Example: 1.2 x 4.56 = 5.472 on the calculator. But since the one factor has only 2 sig figs, the answer must be rounded to 2 sig figs or 5.5.
ADDITION or SUBTRACTION
Example: 1.234 + 5.67 = 6.904 on the calculator. But since the one factor has only 2 decimal places, so must the answer. Thus the result must be rounded to 6.90 (where the zero is significant. See rule 3 above.)
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31 January 2000