Understanding Significant Figures in Measurements

1. Significant Figures

2. True/Accepted Value: 21.00 cm Group 1 Group 2 Group 3 21.00 cm 21.01 cm 21.00 cm 21.02 cm 20.98 cm 21.00 cm 22.00 cm 18.00 cm 23.00 cm 21.00 cm 17.50 cm 17.52 cm 17.48 cm 17.45 cm 17.51 cm 17.49 cm Avg 21.00 cm 21.00 cm Accurate and precise Accurate not precise Precise not accurate

3. Significant Figures • The digits in a measurement that are known with certainty plus the first estimated digit.

4. Determining the # of Sig. Figs • All non-zero digits ARE significant. Ex) 345.26 g 5 sig figs • Zeros before non-zero digits are NOT significant Ex) 0.00023 2 sig figs

5. Zeros between significant figures ARE significant Ex) 108 mm 3 sig figs • Zeros after non-zero digits AND after the decimal ARE significant Ex) 18,1.00 mm 5 sig figs Zeros after non-zero digits but before the decimal are NOT significant Ex) 1200 2 sig figs

6. Scientific Notation: 1.810 x 104 mm 4 sig figs • Bar above the significant zero: 18,100 4 sig figs

7. Sig Fig Examples – state how many each # has 2 • 82 • 408.3 • 9706.2 • 0.00060085 • 3.80600 • 8.42 • 0.0100200 • 900086.003 • 234860 4 5 5 6 3 6 9 5

8. 2 3 2 • 25000 • 1.26 x 10-5 • 3.8 x 1020 • 4.6583 x 10-7 • 8.9620 x 104 • 1.00004 x 10-24 • 0.000125000 • 0.123 • 5900 • 40010 • 0.01010101 5 5 6 6 3 2 4 7

9. Rules for Sig Fig Calculations • Multiplication and Division The number of significant figures in the answer is the same as the number with the lowest number of sig figs in the problem. Ex) 65.01m x 3.4m = 221. 034m2 (calc) 4 sf 2sf 2sf If you cross off a # in front of the decimal replace it with a zero 221.034m2 220 m2

10. Rules for Sig Fig Calculations • Addition and Subtraction The answer has the same number of places to the right of the decimal as the number in the problem with the smallest number of digits to the right of the decimal. Ex) 65.01g + 3.4 g = 68.41g (calc) 2 places 1 place 1 place 68.4g