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Dealing correctly with significant figures can save you time! Often,
students copy down numbers from their calculators with eight significant
figures of precision, then type them back in for a later calculation. That’s a
waste of time, unless your original data had that kind of incredible preci-
sion.
The rules about significant figures are only rules of thumb, and are not
a substitute for careful thinking. For instance, $20.00 + $0.05 is $20.05. It
need not and should not be rounded off to $20. In general, the sig fig rules
work best for multiplication and division, and we also apply them when
doing a complicated calculation that involves many types of operations. For
simple addition and subtraction, it makes more sense to maintain a fixed
number of digits after the decimal point.
When in doubt, don’t use the sig fig rules at all. Instead, intentionally
change one piece of your initial data by the maximum amount by which
you think it could have been off, and recalculate the final result. The digits
on the end that arecompletely reshuffled are the ones that are meaningless,
and should be omitted.
How many significant figures are there in each of the following measurements.
(a) 9.937 m
(b) 4.0 s
(c) 0.0000037 kg
(a) (b) 4; (c) 2; (d) 2
Section 0.10Significant Figures