Significant Figures

Significant figures are the number of digits in a number that indicate its degree of accuracy. Here are some rules to determine the significant figures in a given number:

  • All non-zero digits are significant. For example: 25678, 1.2345, 11.211 have 5 significant figures each.
  • All zeros between non-zero digits are significant. For example: 101, 203, 507, 0.501 have 3 significant figures each.
  • All zeros at the end of a decimal are significant. For example: 0.1000, 5.003, 9.000, 12.00 have 4 significant figures each.
  • All zeros in front of non-zero digits are not significant. For example: 0.12345, 0.00012345, 0.0012300, 0.098765 have 5 significant figures each.

Examples and Solutions

Example 1:

Using a calculator, find the value of the following and give answers to 3 decimal places and 3 significant figures:

  • 3.1213 \times 2.14112
  • \sqrt{8.901} \div 3.001
  • (12.01^2 - 2.99^2) \div \sqrt{24.936}

Using a calculator, we find 3.1213 \times 2.14112 = 6.683077856

To 3 decimal places, this is 6.683.

To 3 significant figures, this is 6.68.

Using a calculator, we find \sqrt{8.901} \div 3.001 = 0.994153406

To 3 decimal places, this is 0.994.

To 3 significant figures, this is 0.994.

Using a calculator, we find (12.01^2 - 2.99^2) \div \sqrt{24.936} = 27.09470344

To 3 decimal places, this is 27.095.

To 3 significant figures, this is 27.1.

Example 2:

Using a calculator, find the value of the following and give answers to 6 decimal places and 2 significant figures:

  • 3.1213 \times 2.14112
  • \sqrt{8.901} \div 3.001
  • (12.01^2 - 2.99^2) \div \sqrt{24.936}

Using a calculator, we find 3.1213 \times 2.14112 = 6.683078

To 6 decimal places, this is 6.683078.

To 2 significant figures, this is 6.7.

Using a calculator, we find \sqrt{8.901} \div 3.001 = 0.994153

To 6 decimal places, this is 0.994153.

To 2 significant figures, this is 0.99.

Using a calculator, we find (12.01^2 - 2.99^2) \div \sqrt{24.936} = 27.09470344

To 6 decimal places, this is 27.094703.

To 2 significant figures, this is 27.