Lesson Objectives Know how perform mathematical operations using significant figures

Operations w/Significant Figures When performing mathematical operations, you are dealing with more than one measurement Each measurement you use in an equation may come from a different measuring device Your final answer must reflect least precise of your measurements

Operations w/Significant Figures To show this, in equations we must find this measurement which is known as the limiting term or limiting measurement In multiplication and division, this measurement is the one with the least number of significant figures

Limiting Term Examples 32 6,921 96 8 328 911 8

Limiting Term Examples 0.0724 0.0021 0.030 0.93 0.32 0.04 0.04

Limiting Term Examples 43.78 0.052 582 9.4 300 1,745 300

Operations w/Significant Figures After you know the limiting term, you use your calculator to perform the operation If the calculator displays more significant figures than the limiting measurement, you must round to that many significant figures If the calculator does not display enough significant figures, you must add zeros after the decimal point

Multiplication Examples Calculator  22.784 Round  23

Multiplication Examples Calculator  11.2949 Round  11.3

Multiplication Examples Calculator  0.008 Round  0.00800

Multiplication Examples Calculator  164,100 Round  200,000

Division Examples 3.6 / 5 Calculator  0.72 Round  0.7

Division Examples 0.00761 / 0.020 Calculator  0.3805 Round  0.38

570 / 56 Calculator  10.17857143 Round  10 Scientific  1.0 x 101 Division Examples 570 / 56 Calculator  10.17857143 Round  10 Scientific  1.0 x 101

Operations w/Significant Figures In addition and subtraction, the limiting measurement is the one with the least number of decimal places If both numbers have no decimal places, the limiting term is the one with the most trailing zeros

Limiting Term Examples 30.0 0.009 1,099 78.3 0.32 803.8 1,099

Limiting Term Examples 53.31 0.827 780.2 8.91 0.0081 15.66 780.2

Limiting Term Examples 32 6,921 96 8 328 911 All the same

Operations w/Significant Figures After you know the limiting term, you use your calculator to perform the operation If the calculator displays more places than the limiting measurement, you must round to that decimal place or to the place of the rightmost significant figure

Operations w/Significant Figures If the calculator does not display enough places, you must add zeros after the decimal point to fill those places

Addition Examples 14.8 + 9.275 Calculator  24.075 Round  24.1

Addition Examples 2,000.0 + 890.00 Calculator  2,890 Round  2,890.0

Subtraction Examples 45.82 – 22.7 Calculator  23.12 Round  23.1

Subtraction Examples 1,870 – 0.42 Calculator  1,869.58 Round  1,870