Significant Figures Why significant figures are important Please remember that, in science, all numbers are based upon measurements (except for a very few that are defined). Since all measurements are uncertain, we must only use those numbers that are meaningful. A common ruler cannot measure something to be 22.4072643 cm long. Not all of the digits have meaning (significance) and, therefore, should not be written down. In science, only the numbers that have significance (derived from measurement) are written.

Significant Figures There are two rules for determining the number of significant figures Note: significant figures is abbreviated sig. figs.

Significant Figures Rule 1 If there is no decimal point Start at the RIGHT Count, beginning with the first non-zero digit. Examples 340 2 sig.figs. 30400 3 sig.figs. 34955 5 sig.figs.

Significant Figures Rule 2 If there is a decimal point Start at the LEFT Count, beginning with the first non-zero digit. Examples 340. 3 sig.figs. 30400. 5 sig.figs. 0.34955 5 sig.figs. 0.00040 2 sig.figs.

Significant Figures There are two rules for determining the number of significant figures to display in a reported number

Significant Figures When you multiply and/or divide Count the sig. figs. in the numbers you are multiplying and/or dividing. Your answer should be rounded off to the smallest number of sig. figs. in your problem. Examples 28.33 x 3.12 (4 sig.figs. and 3 sig. figs., respectively) 88.3896 - calculator answer 88.4 - reported answer (must have 3 sig. figs.)     28.44 x 3.12 (4 sig.figs. and 3 sig. figs., respectively) 9.080128205 - calculator answer 9.08 - reported answer (must have 3 sig. figs.) Reminder: Rounding-off rules: Go to next number. If it is 0-4, round down. If it is 5-9, round up

Significant Figures When you add and/or subtract Count the sig. figs. in the numbers you are adding and/or subtracting The answer should have the same number of decimal places as that of the number with the least number of decimals. Examples 4.838 g +1.0023 g = 5.3853 g Only 3 digits to right of decimal are allowed 4th decimal to right, 3, is 0-4, so round down 5.358 is reported answer 486.58 g + 421. g = 65.58 g No digits to right of decimal are allowed 1st decimal to right, 5 is 5-9, so round up 66 g reported answer Reminder: In addition and subtraction, decimals must be lined up

Significant Figures Complete the significant figures worksheet