Physics Tutorial: Significant Figures


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Significant figures are the number of reliably known digits used to locate a decimal point reported in a measurement. Proper use of significant figures ensures that you correctly represent the uncertainty of your measurements. For example, scientists immediately realize that a reported measurement of 1.2345 m is much more accurate than a reported length of 1.2 m.

Care must be taken when determining the number of significant figures to use. Your driver's license may state that your height is 5 feet 3 inches, or 5.25 feet. Measuring a little more carefully, we may find that your height is found to be 5.257 feet. However if you said you were 5.257186 feet tall the scientific community would look upon that measurement with serious skepticism because you stated your height accurate to the nearest micron! When a measurement is properly stated in scientific notation all of the digits will be significant. For example: 0.0035 has 2 significant figures which can be easily seen when written in scientific notation as 3.5 x 10-3. Fortunately, there are a few general guidelines that are used to determine significant figures:

Whole Numbers: The following numbers are all represented by three significant digits. Note that zeros are often place holders and are not significant.

  • 0.00123
  • 0.123
  • 1.23
  • 12.3
  • 123
  • 12300 (The zeros here often cause confusion. As written here, the zeros are not significant. If they were, in fact, significant, then the use of scientific notation would remove all ambiguity and the number would be written 1.2300 x 104.)
The following numbers are all represented by one significant digit.

  • 0.005
  • 0.5
  • 5
  • 500
  • 5,000,000

The following numbers are all represented by four significant figures.
  • 0.004001
  • 0.004000
  • 40.01
  • 40.00
  • 4321
  • 432.1
  • 43,210,000

Integers and Defined Quantities: Integers are assumed to have an infinite number of significant figures. For example, the 2 in C = 2pr, is exactly two and we can assume that the number has an infinite number of significant figures. However, the conversion factor 2.54 cm which is used to convert inches to centimeters has three significant figures.

Multiplication and Division: When multiplying or dividing numbers, the result should have only as many significant figures as the quantity with the smallest number of significant figures being used in the calculation. For example, with your calculator multiply 4.7 and 5.93. The calculator returns 27.871 as the answer. A common mistake students make is to record what comes out of the calculator as the correct answer. However, since 4.7 has only 2 significant figures, the result must be truncated to 2 significant figures as well. Taking all this into account and remembering to round appropriately, the result should be reported as 28.

Addition and Subtraction: When adding or subtracting numbers, keep all figures up to the smallest quantity being used in the calculation. For example, 3.14 + 0.00159 = 3.14159.

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Last Modified on 01/27/2006 14:25:18.