Significant Digits Calculations

Significant Digits in Calculations Now you know how to determine the number of significant digits in a number How do you decide what to do when adding, subtracting, multiplying, or dividing?

Rules for Addition and Subtraction When you add or subtract measurements, your answer must have the same number of decimal places as the one with the fewest For example: 20.4 + 1.322 + 83 = 104.722

Addition & Subtraction Continued Because you are adding, you need to look at the number of decimal places 20.4 + 1.322 + 83 = 104.722 (1) (3) (0) Since you are adding, your answer must have the same number of decimal places as the one with the fewest The fewest number of decimal places is 0 Therefore, you answer must be rounded to have 0 decimal places Your answer becomes 105

Addition & Subtraction Problems 1.23056 + 67.809 = 23.67 – 500 = 40.08 + 32.064 = 22.9898 + 35.453 = 95.00 – 75.00 = 69.03956  69.040 - 476.33  -476 72.1440  72.14 58.4428  58.443 20  20.00

Rules for Multiplication & Division When you multiply and divide numbers you look at the TOTAL number of significant digits NOT just decimal places For example: 67.50 x 2.54 = 171.45

Multiplication & Division Because you are multiplying, you need to look at the total number of significant digits not just decimal places 67.50 x 2.54 = 171.45 (4) (3) Since you are multiplying, your answer must have the same number of significant digits as the one with the fewest The fewest number of significant digits is 3 Therefore, you answer must be rounded to have 3 significant digits Your answer becomes 171

Multiplication & Division Problems 890.15 x 12.3 = 88.132 / 22.500 = (48.12)(2.95) = 58.30 / 16.48 = 307.15 / 10.08 = 10948.845  1.09 x 104 3916.977  3917.0 141.954  142 3.5376  3.538 30.47123  30.47

More Significant Digit Problems 18.36 g / 14.20 cm3 105.40 °C –23.20 °C 324.5 mi / 5.5 hr 21.8 °C + 204.2 °C 460 m / 5 sec = 1.293 g/cm3 = 82.20 °C = 59 mi / hr = 226.0 °C = 90 or 9 x 101 m/sec