1. Section 5.2 Uncertainty in Measurement and Significant Figures 1.To learn how uncertainty in a measurement arises 2.To learn to indicate a measurement’s uncertainty by using significant figures 3.To learn to determine the number of significant figures in a calculated result Objectives

2. Section 5.2 Uncertainty in Measurement and Significant Figures A. Uncertainty in Measurement A measurement always has some degree of uncertainty.

3. Section 5.2 Uncertainty in Measurement and Significant Figures A. Uncertainty in Measurement Different people estimate differently. Record all certain numbers and one estimated number.

4. Section 5.2 Uncertainty in Measurement and Significant Figures B. Significant Figures Numbers recorded in a measurement. –All the certain numbers plus first estimated number

5. Section 5.2 Uncertainty in Measurement and Significant Figures B. Significant Figures Rules for Counting Significant Figures 1.Nonzero integers always count as significant figures. 1457 4 significant figures

6. Section 5.2 Uncertainty in Measurement and Significant Figures B. Significant Figures Rules for Counting Significant Figures 2.Zeros a.Leading zeros - never count 0.0025 2 significant figures b.Captive zeros - always count 1.008 4 significant figures c.Trailing zeros - count only if the number is written with a decimal point 100 1 significant figure 100. 3 significant figures 120.0 4 significant figures

7. Section 5.2 Uncertainty in Measurement and Significant Figures B. Significant Figures Rules for Counting Significant Figures 3.Exact numbers - unlimited significant figures Not obtained by measurement Determined by counting 3 apples Determined by definition 1 in. = 2.54 cm

8. Section 5.2 Uncertainty in Measurement and Significant Figures Count the number of significant figures in each number A)2050 B)315.0 C)0.00253 D)1.030 E)6.45x10 5 F)0.0056 G)1.0x10 -4 2050 = 3 sig figs 315.0 = 4 sig figs 0.00253 = 3 sig figs 1.030 = 4 sig figs 6.45x10 5 = 3 sig figs 0.0056 = 2 sig figs 1.0x10 -4 = 2 sig figs

9. Section 5.2 Uncertainty in Measurement and Significant Figures B. Significant Figures

10. Section 5.2 Uncertainty in Measurement and Significant Figures Round each number to 3 significant figures A)4055 B)315.3 C)0.006572 D)1.0880 E)6.415x10 5 F)2.0056 G)5.608x10 -4 4060 315 0.00657 1.09 6.42x10 5 2.01 5.61x10 -4

11. Section 5.2 Uncertainty in Measurement and Significant Figures B. Significant Figures Rules for Multiplication and Division The number of significant figures in the result is the same as in the measurement with the smallest number of significant figures.

12. Section 5.2 Uncertainty in Measurement and Significant Figures How many sig figs should the answer have? A)1.25 x 3.055 = B)0.20 x 4550 = C)1250 x 1.3 = D)1440 ÷ 35 = E)0.1050 ÷ 22.0 = round answer to 3 sig figs round answer to 2 sig figs round answer to 3 sig figs

13. Section 5.2 Uncertainty in Measurement and Significant Figures B. Significant Figures Rules for Addition and Subtraction The number of significant figures in the result is the same as in the measurement with the smallest number of decimal places.

14. Section 5.2 Uncertainty in Measurement and Significant Figures How many decimal places should the answer have? A)1.25 + 3.055 = B)0.20 + 455.0 = C)1.250 + 1.3 = D)6.43 – 0.35 = E)0.1050 - 0.015 = round answer to 2 decimals round answer to 1 decimal round answer to 2 decimals round answer to 3 decimals

15. Section 5.2 Uncertainty in Measurement and Significant Figures Solve each problem and round the answer correctly. A)421 x 3.5 = B)0.210 x 1.255 = C)24.0 ÷ 2.3 = D)144.0 + 35.55 = E)0.1050 – 0.0433 = F)3.055 + 8.73 = 1473.5  1500 0.26355  0.264 10.43478  10. 179.55  179.6 0.0617 11.785  11.79

16. Section 5.2 Uncertainty in Measurement and Significant Figures Count the sig figs in all of these measurements. A)325.10 mL B)0.20 g C)20.0 mL D)123.08 g E)1.10 mL F)35.05 g 5 sig figs 2 sig figs 3 sig figs 5 sig figs 3 sig figs 4 sig figs

17. Section 5.2 Uncertainty in Measurement and Significant Figures Find the area of each figure and round to the correct number of significant figures. 3.5 m 4.7 m 125.25 cm 33.83 cm 4.7x3.5 = 16.45 16 m 2 33.83x125.25 = 4237.2075 4237 cm 2

18. Section 5.2 Uncertainty in Measurement and Significant Figures Find the sum of each set of measurements and round to the correct number of significant figures. 12300 cm 4550 cm + 88473 cm 105323 105300 cm 23.45 m 112.78 m + 5.5 m 141.73 m 141.7 m

19. Section 5.2 Uncertainty in Measurement and Significant Figures C. Density Density is the amount of matter present in a given volume of substance.

20. Section 5.2 Uncertainty in Measurement and Significant Figures C. Density

21. Section 5.2 Uncertainty in Measurement and Significant Figures What is the density of an object with a mass of 10.0 g and a volume of 2.0 cm 3 ? 10.0 g 2.0 cm 3 = 5.0 g/cm 3

22. Section 5.2 Uncertainty in Measurement and Significant Figures What is the mass of a sample with a density of 0.15 g/mL and a volume of 40.0 mL? mass volume = density mass = densityXvolume = 0.15 g/mL X 40.0 mL = 6.0 g