When working with numbers that have a certain number of significant figures it is often necessary to multiply or divide these numbers. When doing so, you must keep track of the number of significant figures that the answer will have.

The rule for multiplication or division for significant figures is very simple:

When quantities are multiplied or divided, the number of significant figures in the answer is equal to the number of significant figures in the quantity with the smallest number of significant figures.

For example, if you multiply 1.23 and 4.567, you get an answer of 5.61741. 1.23 has three significant figures, 4.567 has four. Therefore, the answer should have three significant figures, since three is less than four. The properly rounded answer would be written as 5.62.

Example: In the following problem, how many significant figures should the answer have?

(8.33*9.1167)/0.004500

Solution: There are three numbers here:

1. 8.33 has three significant figures
2. 9.1167 has five significant figures
3. 0.004500 has four significant figures

Information provided by: http://learn.chem.vt.edu