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Significant Figures
The rules for propagation of errors hold true for cases when we are in the lab, but doing propagation of
errors is time consuming. The rules for
significant figures
allow a much quicker method to get results
that are approximately correct even when we have no uncertainty values.
A significant figure is any digit 1 to 9 and any zero which is not a place holder. Thus, in 1.350 there are
4 significant figures since the zero is not needed to make sense of the number. In a number like 0.00320
there are 3 significant figures the first three zeros are just place holders. However the number 1350 is
ambiguous. You cannot tell if there are 3 significant figures the 0 is only used to hold the units place 
or if there are 4 significant figures and the zero in the units place was actually measured to be zero.
How do we resolve ambiguities that arise with zeros when we need to use zero as a place holder as well
as a significant figure? Suppose we measure a length to three significant figures as 8000 cm. Written this
way we cannot tell if there are 1, 2, 3, or 4 significant figures. To make the number of significant figures
apparent we use scientific notation, 8 x 10
3
cm (which has one significant figure), or 8.00 x 10
3
cm
(which has three significant figures), or whatever is correct under the circumstances.
We start then with numbers each with their own number of significant figures and compute a new
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This note was uploaded on 11/26/2011 for the course PHY 2053 taught by Professor Lind during the Fall '09 term at FSU.
 Fall '09
 LIND

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