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Chapter 2 Measurements. Measured Numbers and Significant Figures. 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. Reading a Meterstick.

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## Chapter 2 Measurements

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**Chapter 2Measurements**Measured Numbers and Significant Figures**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.**Reading a Meterstick**. l2. . . . I . . . . I3 . . . .I . . . . I4. . 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**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**Learning Check**. l8. . . . I . . . . I9. . . .I . . . . I10. . 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?**Solution**. l8. . . . I . . . . I9. . . .I . . . . I10. . 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.**Learning Check**l5. . . . I . . . . I6. . . .I . . . . I7. . cm What is the length of the line? 1) 6.0 cm 2) 6.06 cm 3) 6.60 cm**Solution**l5. . . . I . . . . I6. . . .I . . . . I7. . 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**Zero as a Measured Number**. l3. . . . I . . . . I4 . . . . I . . . . I5. . 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)**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**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**Solution**A. Exact numbers are obtained by 2. counting 3. definition B. Measured numbers are obtained by 1. Using a measuring tool**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**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**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.**Sig Fig Inquiry**• Determine the rules for finding the number of significant digits.**Rules**• All non-zero numbers are significant. • Zeros at the end without a decimal point are not significant. • Zeros at the end with a decimal point are significant. • Zeros in the middle of other numbers are significant. • Zeros at the beginning are NOT significant**Adding and Subtracting**The answer has the same number of decimal places as the measurement with the fewest decimal places. 25.2one decimal place + 1.34two decimal places 26.54 answer 26.5 one decimal place Timberlake lecture plus**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**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) 256.8 3) 257 B. 58.925 - 18.2 = 1) 40.725 2) 40.73 3) 40.7 Timberlake lecture plus**Solution**A. 235.05 + 19.6 + 2.1 = 2) 256.8 B. 58.925 - 18.2 = 3) 40.7 Timberlake lecture plus**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. Timberlake lecture plus**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 cm3, after rounding to the correct number of sig figs, V=23.9 cm3**Learning Check**A. 2.19 X 4.2 = 1) 9 2) 9.2 3) 9.198 B. 4.311 ÷ 0.07 = 1)61.582) 62 3) 60 C. 2.54 X 0.0028 = 0.0105 X 0.060 1) 11.3 2) 11 3) 0.041 Timberlake lecture plus**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 Timberlake lecture plus

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