Significant Figures

Precision describes the limitations of the measuring instrument. It is important to record the precision of your measurements so that other people can understand and interpret your results. A common convention used in science to indicate precision is known as significant figures.

In the case of the measurement of a pencil as about 18.2 cm, the measurement has three significant figures (sig fig). The sig fig of a measurement includes all the digits that are actually measured (18 cm), plus one estimated digit.

In calculations, the number of sig figs in your result depends on the number of sig figs in each measurement. The final answer cannot be more precise than the least precise measurement used to find the answer.

Rules for determining whether zeros are sig figs

 Rule Examples Zeros between other nonzero digits are significant 50.3 meters has three sig figs3.0025 seconds has five sig figs Zeros in front of nonzero digits are not significant. 0.982 kg has three sig figs0.0008 seconds has one sig fig Zeros that are at the end of a number and also to the right of the decimal are significant. 57.00 grams has four sig figs2.000 000 kg has seven sig figs Zeros at the end of a number but to the left of a decimal are significant if they have been measured or are the first estimated digit; otherwise they are not significant. 1000 meters may contain from one to four sig figs, depending on the precision of the measurement20 meters may contain one or two sig figs

Rules for calculating with sig figs

 Type of Calculation Rule Examples Addition or Subtraction The final answer should have the same number of digits to the right of the decimal as the measurement with the smallest number of digits to the right of the decimal. 97.3+ 5.85103.15 --->(round off) 103.2 Multiplication or Division The final answer has the same number of sig figs as the measurement having the smallest number of sig figs. 123x 5.35658.05 ---> (round off) 658

Examples:

1.) 26 x 0.02584 = ? (0.67)
2.) 15.3 % 1.1 = ? (14)
3.) 782.45 - 3.5328 = ? (778.92)
4.) 63.258 + 734.2 = ? (797.5)

Test on Friday, September 12

• Be able to identify the number of sig figs in given examples.
• Be able to do calculations using sig figs.