The document discusses measured numbers and significant figures. It provides examples of reading measurement tools like metersticks and explains how to estimate digits. Measured numbers are obtained through measurement, while exact numbers come from counting or definitions. The document also distinguishes between exact and measured numbers, giving examples like temperature, length conversions, and counted items.

1. Chapter 1 Measurements Measured Numbers and Significant Figures

2. Measured Numbers When you use a measuring tool is used to determine a quantity such as your height or weight, the numbers you obtain are called measured numbers .

3. Reading a Meterstick . l 2 . . . . I . . . . I 3 . . . .I . . . . I 4 . . cm First digit (known) = 2 2 .?? cm Second digit (known) = 0 .7 2.7 ? cm Third digit (estimated) between 0.05- 0.07 Length reported = 2.75 cm or 2.76 cm or 2.77 cm

4. Known + Estimated Digits Known digits 2 and 7 are 100% certain The third digit 6 is estimated (uncertain) In the reported length, all three digits (2.76 cm) are significant including the estimated one

5. Learning Check . l 8 . . . . I . . . . I 9 . . . .I . . . . I 10 . . cm What is the length of the line? 1) 9.2 cm 2) 9.22 cm 3) 9.23 cm How your answer compare with your neighbor’s answer? Why or why not?

6. Solution . l 8 . . . . I . . . . I 9 . . . .I . . . . I 10 . . cm Estimate to the hundreth’s place (0.01 cm) 2) 9.22 cm 3) 9.23 cm The estimated digit may be slightly different. Both readings are acceptable.

7. Learning Check l 5 . . . . I . . . . I 6 . . . .I . . . . I 7 . . cm What is the length of the line? 1) 6.0 cm 2) 6.06 cm 3) 6.60 cm

8. Solution l 5 . . . . I . . . . I 6 . . . .I . . . . I 7 . . cm Estimate to the hundreth’s place (0.01 cm). The reading is between 6.0 and 6.1. You may have estimated 6.07 cm as well. 2) 6.06 cm

9. Zero as a Measured Number . l 3 . . . . I . . . . I 4 . . . . I . . . . I 5 . . cm What is the length of the line? First digit 4.?? cm Second digit 4 .5? cm Last (estimated) digit is 4.5 0 cm (not to the left or right of .5)

10. Exact Numbers Obtained when you count objects 2 soccer balls 1 watch 4 pizzas Obtained from a defined relationship 1 foot = 12 inches 1 meters = 100 cm Not obtained with measuring tools

11. Learning Check A. Exact numbers are obtained by 1. measuring 2. counting 3. definition B. Measured numbers are obtained by 1. measuring 2. counting 3. definition

12. Solution A. Exact numbers are obtained by 2. counting 3. definition B. Measured numbers are obtained by 1. Using a measuring tool

13. Learning Check Classify each of the following as an exact (1) or a measured (2) number. A.___Gold melts at 1064°C B.___1 yard = 3 feet C.___A red blood cell with diameter 6 x 10 -4 cm D.___There were 6 hats on the shelf E.___A can of soda contains 355 mL of soda

14. Solution Classify each of the following as an exact (1) or a measured(2) number. Give reason. A. 2 Requires a thermometer(measuring tool) B. 1 From a definition in U.S. system C. 2 Need measuring tool to determine D. 1 Counted the hats E. 2 Measured

15. % Yield Actual/Theoretical x 100% If you are attempting an experiment and the theoretical yield is 100g and your group’s yield is 79g, determine the % error.

17. Variables Independent Variable: A variable that stands alone and is not changed. Not changed by what we measure. Dependent Variable: Depends on other factors. This is what changes in the experiment.