Significant Figures
Significant figures are all of the digits that are known in a measurement, plus one additional digit, which is an estimate. In the figure below, the length of a turtle's shell is being measured using a centimeter ruler. The ruler has unnumbered divisions representing millimeters. In this case, two numbers can be determined exactly: the number of centimeters and the number of millimeters. One additional digit can be estimated. So, the measurement of this turtle's shell can be recorded with three significant figures as 8.80 centimeters.
Rules for Significant Digits
Follow these rules to determine the number of significant figures in a number.
All nonzero numbers are significant.
Example: 3217 has four significant digits.
Zeros are significant if
They are between nonzero digits. Example: 509
They follow a decimal point and a nonzero digit.
Example: 7.00
Zeros are not significant if
They follow nonzero digits in a number without a decimal. Example: 7000
They precede nonzero digits in a number with a decimal. Example: 0.0098
Calculating With Significant Figures
When measurements are added or subtracted, the precision of the result is determined by the precision of the least-precise measurement. The result may need to be rounded so the number of digits after the decimal is the same as the least-precise measurement.
Example
Follow these steps to determine the correct number of significant figures when adding 4.51 g, 3.27 g, and 6.0 g.
Determine which measurement is reported with the least degree of precision. In this case, the least-precise measurement, 6.0 g, has one digit after the decimal point.
The result must be rounded so that it also has one digit after the decimal point. After rounding, the result of this calculation is 13.8 g.
When measurements are multiplied or divided, the answer must have the same number of significant figures as the measurement with the fewest number of significant figures.
Example
Follow these steps to determine the correct number of significant figures when multiplying 120 m by 6.32 m.
Determine the number of significant figures in each of the measurements. In this case, the measurement 120 m has two significant figures; the measurement 6.32 m has three significant figures.
The result must be rounded to have only two significant figures. After rounding, the result of this calculation is 760 m2.
Table of Contents
- Formulas and Equations
- Applying Formulas and Equations
- Mean, Median, and Mode
- Estimation
- Using Measurements in Calculations
- Effects of Measurement Errors
- Accuracy
- Precision
- Comparing Accuracy and Precision
- Significant Figures
- Calculating With Significant Figures
- Scientific Notation
- Calculating With Scientific Notation
- Dimensional Analysis
- Applying Dimensional Analysis