Significant Figures and Rounding Off Numbers

You need to know how to count the number of significant figures in a number, because they affect the way answers are stated in calculations. Zeros can be a problem. A zero may or may not be significant depending on how it is used. To handle this zero problem, follow this set of six rules  

Rule 2. A zero standing alone to the left of a decimal point is not significant. For example, in 0.63 and 0.0055, the 0 to the left of the decimal only helps you see the decimal point. It has no other use. 

Rule 3. For a number less than 1, any zeros between the decimal point and the first nonzero digit are not significant. These zeros are simply placing the decimal point. The zeros in bold type in 0.00457 and 0.0000864 are not significant. Both numbers have three significant figures 457 in the first number and 864 in the second. 

Rule 4. A zero between two nonzero digits is significant. In 2.0056 and 0.0040558, both numbers have 5 significant figures. Because the second number is less than 1, only the 4, 0, 5,5, and 8 are significant. 

Rule 5. If the number has a decimal point, any zeros at the end of the number are significant. Both of these numbers have 4 significant figures 4.500 and 0.01380. 

---

If you missed 2, go to Significant Figures and Rounding Off Numbers, page 13. 

---