The following set of significant figure rules helps to define which figures are significant, allowing one to count the number of significant figures in the entire number.
1. All nonzero digits are always significant. For example, all of the digits in the number 471.9 are significant and there are a total of 4 significant figures.
2. All zeros that are located between nonzero digits are always significant. For example, all of the digits in the number 800,007, including the 4 zeros in between the 8 and the 7. Therefore, the total number of significant figures in this number is 6.
3. Leading zeros that occur to the left of the first nonzero digit are not considered significant. For example, the number 0.0037 has only 2 significant figures because none of the zeros to the left of the number 3 are considered significant. This is a good example of how zeros sometimes act as placeholders but do not necessarily denote any precision of the measurement.
4. Whole numbers with trailing zeros that occur to the right of the last nonzero digit are significant if the whole number ends in a decimal point. If the whole number does not end in a decimal point, then the trailing zeros are not significant. An example of this is the number "4,500." vs "4,500"; both of the zeros in the number "4,500." are significant with a total of 4 significant figures whereas neither of the zeros in the number "4,500" are significant and the number only has 2 significant figures total. This is another example of how to identify which zeros were truly measured and which are just placeholders.
5. Trailing zeros occurring after a decimal point are considered significant. An example is 34.00, where both zeros are significant, bringing the total number of significant figures to 4.
6. A number can be written in scientific notation to reflect the number of significant figures it should have.
Here is an example of how the number 6,800 can be written in scientific notation with either 2, 3, or 4 significant figures based on the precision of the instrument:
- 6,800 with 2 significant figures would be written as 6.8 X 103
- 6,800 with 3 significant figures would be written as 6.80 X 103
- 6,800 with 4 significant figures would be written as 6.800 X 103
Table 1 provides more examples of numbers and their correct number of significant figures based on the aforementioned rules.
Table 1. Examples of Applying the Significant Figures Rules.| Example | # of Significant Figures |
| 51,373 | 5 |
| 25 | 2 |
| 5.09 | 3 |
| 5.00 | 3 |
| 0.066 | 2 |
| 12,000 | 2 |
| 1.2 x 103 (12,000 written in scientific notation) | 2 |
| 800 | 1 |
| 800. | 3 |
| 530,530,530 | 8 |
| 0.00020 | 2 |
