Rules for Significant Figures

1. All nonzero figures are significant: 112.6^oC has four significant figures.
2. All zeros between nonzero figures are significant: 108.005 m has six significant figures.
3. Zeros to the right of a nonzero figure, but to the left of an understood decimal point, are not significant unless specifically indicated to be significant. The right most such zero which is significant is indicated by a bar placed above it: 109000 km contains three significant figures;

        _

109000 km contains five significant figures.

4. All zeros to the right of a decimal point but to the left of a nonzero figure are not significant: 0.000647 kg has three significant figures. The single zero placed to the left of the decimal point in such an expression servers to call attention to the decimal point and is never significant.
5. All zeros to the right of a decimal point and following a nonzero figure are significant: both 0.07080 cm and 20.00 cm have four significant figures.
6. Rule for addition and subtraction. Remember that the right most significant figure in a measurement is uncertain. The rightmost significant figure in a sun or difference will be determined by the leftmost place at which an uncertain figure occurs in any of the measurements being added or subtracted. The following example of addition illustrates this rule:

                     13.05   cm

309.2      cm ------- The 2 is the leftmost place of uncertain figure in    

    3.785 cm                 measurements being added

326.035 cm ------- The 0 is the rightmost significant figure in the  

                                     answer    

Since the answer should have only one uncertain figure (the rightmost one), it should be recorded as 326.0 cm.      

7. Rule for multiplication and division. Remember that when an uncertain figure is multiplied or divided by a number, the answer is likewise uncertain. Therefore the product or quotient should not have more significant figures than the least precise factor. The following example illustrates the rule for multiplication:

       3.54 cm X 4.8 cm X 0.5421 cm = 9.211363 cm³

        Note: 4.8 is the least precise factor

                  The 2 in the answer is the rightmost significant figure.

Consequently, the answer should be recorded as 9.2 cm³ .

8. Rule for rounding. If the first figure to be dropped in rounding off is ro or less, the receding figure is not changed: if it is 6 or more, the receding figure is raised by 1. If the figures to be dropped in rounding off are a 5 followed by figures other than zeros, the preceding figure is raised by 1. If the figure to be dropped in rounding off is a 5 followed by zeros (or if the figure is exactly 5), the preceding figure is not changed if it is even; but if it is odd, it is raised by l.