1. Chapter 2 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 or2.76 cm or2.77 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 4.50 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. Significant Figures Significant Figures – The digits that indicate the precision with which a measurement is made; all digits of a measured quantity are significant, including the last digit, which is uncertain.

16. Sig Fig Inquiry Determine the rules for finding the number of significant digits.

17. Rules 1.All non-zero numbers are significant. 2.Zeros at the end without a decimal point are not significant. 3.Zeros at the end with a decimal point are significant. 4.Zeros in the middle of other numbers are significant. 5.Zeros at the beginning are NOT significant

18. Timberlake lecture plus18 Adding and Subtracting The answer has the same number of decimal places as the measurement with the fewest decimal places. 25.2 one decimal place + 1.34 two decimal places 26.54 answer 26.5 one decimal place

19. Addition/Subtraction with Sig Figs Your answer must have the same number of decimal places as the value with the fewest decimal places 28.0 + 23.538 + 25.68 = 77.218 Round so that the answer is 77.2

20. Timberlake lecture plus20 Learning Check In each calculation, round the answer to the correct number of significant figures. A. 235.05 + 19.6 + 2.1 = 1) 256.75 2) 256.83) 257 B. 58.925 - 18.2= 1) 40.725 2) 40.733) 40.7

21. Timberlake lecture plus21 Solution A. 235.05 + 19.6 + 2.1 = 2) 256.8 B. 58.925 - 18.2= 3) 40.7

22. Timberlake lecture plus22 Multiplying and Dividing Round (or add zeros) to the calculated answer until you have the same number of significant figures as the measurement with the fewest significant figures.

23. Multiply/Divide with Sig Figs Your answer must have the same number of sig figs as the measurement with the fewest number of sig figs. Calculate the volume if L = 3.65 cm, W = 3.20 cm, and H = 2.05 cm V = 23.944 cm 3, after rounding to the correct number of sig figs, V=23.9 cm 3

24. Timberlake lecture plus24 Learning Check A. 2.19 X 4.2 = 1) 9 2) 9.2 3) 9.198 B. 4.311 ÷ 0.07 = 1) 61.58 2) 62 3) 60 C. 2.54 X 0.0028 = 0.0105 X 0.060 1) 11.32) 11 3) 0.041

25. Timberlake lecture plus25 Solution A. 2.19 X 4.2 = 2) 9.2 B. 4.311 ÷ 0.07 = 3) 60 C.2.54 X 0.0028 = 2) 11 0.0105 X 0.060 Continuous calculator operation = 2.54 x 0.0028  0.0105  0.060