Multiplication and Division

Now that we can identify significant figures, we can consider the rules for significant figures in calculations. When multiplying two numbers, the important value is the number of significant figures. If the numbers being multiplied have three significant figures, then the product will have three significant figures. For example, if you wanted to find the area of a rectangular yard, you would measure the length and width. If the length was L = 3.2 meters, and the width was W = 2.8 meters, then the area would be A = L x W = (3.2 m)(2.8 m) = 8.96 m². But since the length and width only have two significant figures, the area will only have two significant figures. You therefore report the area as A = 9.0 m².

When the two factors being multiplied don't have the same number of significant digits, the product will have the smaller of the two numbers of sig-digs. If the width of your yard was 5.2 meters and the length was 13.5 meters, you would still only report the area with two significant figures: A = 7.0 x 10¹ m². This is an example of a more general rule for significant figures:

The uncertainty in a calculated value is determined by the uncertainty of the least certain original number.

Division is just the inverse of multiplication, so the significant figures for a quotient will be determined in the same way as the significant figures of a product. We can summarize the rule for division and multiplication as

When multiplying or dividing two or more numbers, count the significant figures in each of the original numbers. Take the smallest of the numbers of significant figures. The product or quotient will have that minimum number of significant figures.