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# Measured And Exact Numbers

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### Measured And Exact Numbers

1. 1. Chapter 1 Measurements <ul><li>Measured Numbers and Significant Figures </li></ul>
2. 2. Measured Numbers <ul><li>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 . </li></ul>
3. 3. Reading a Meterstick <ul><li>. l 2 . . . . I . . . . I 3 . . . .I . . . . I 4 . . cm </li></ul><ul><li>First digit (known) = 2 2 .?? cm </li></ul><ul><li>Second digit (known) = 0 .7 2.7 ? cm </li></ul><ul><li>Third digit (estimated) between 0.05- 0.07 </li></ul><ul><li>Length reported = 2.75 cm </li></ul><ul><li> or 2.76 cm </li></ul><ul><li>or 2.77 cm </li></ul>
4. 4. Known + Estimated Digits <ul><li>Known digits 2 and 7 are 100% certain </li></ul><ul><li>The third digit 6 is estimated (uncertain) </li></ul><ul><li>In the reported length, all three digits </li></ul><ul><li>(2.76 cm) are significant including the estimated one </li></ul>
5. 5. Learning Check <ul><li>. l 8 . . . . I . . . . I 9 . . . .I . . . . I 10 . . cm </li></ul><ul><li>What is the length of the line? </li></ul><ul><li>1) 9.2 cm </li></ul><ul><li>2) 9.22 cm </li></ul><ul><li>3) 9.23 cm </li></ul><ul><li>How your answer compare with your neighbor’s answer? Why or why not? </li></ul>
6. 6. Solution <ul><li>. l 8 . . . . I . . . . I 9 . . . .I . . . . I 10 . . cm </li></ul><ul><li>Estimate to the hundreth’s place (0.01 cm) </li></ul><ul><li>2) 9.22 cm </li></ul><ul><li>3) 9.23 cm </li></ul><ul><li>The estimated digit may be slightly different. Both readings are acceptable. </li></ul>
7. 7. Learning Check <ul><li>l 5 . . . . I . . . . I 6 . . . .I . . . . I 7 . . cm </li></ul><ul><li>What is the length of the line? </li></ul><ul><li>1) 6.0 cm </li></ul><ul><li>2) 6.06 cm </li></ul><ul><li>3) 6.60 cm </li></ul>
8. 8. Solution <ul><li>l 5 . . . . I . . . . I 6 . . . .I . . . . I 7 . . cm </li></ul><ul><li>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. </li></ul><ul><li>2) 6.06 cm </li></ul>
9. 9. Zero as a Measured Number <ul><li>. l 3 . . . . I . . . . I 4 . . . . I . . . . I 5 . . cm </li></ul><ul><li>What is the length of the line? </li></ul><ul><li>First digit 4.?? cm </li></ul><ul><li>Second digit 4 .5? cm </li></ul><ul><li>Last (estimated) digit is 4.5 0 cm </li></ul><ul><li>(not to the left or right of .5) </li></ul>
10. 10. Exact Numbers <ul><li>Obtained when you count objects </li></ul><ul><ul><li>2 soccer balls </li></ul></ul><ul><ul><li>1 watch </li></ul></ul><ul><ul><li>4 pizzas </li></ul></ul><ul><li>Obtained from a defined relationship </li></ul><ul><ul><li>1 foot = 12 inches </li></ul></ul><ul><ul><li>1 meters = 100 cm </li></ul></ul><ul><li>Not obtained with measuring tools </li></ul>
11. 11. Learning Check <ul><li>A. Exact numbers are obtained by </li></ul><ul><li> 1. measuring </li></ul><ul><li>2. counting </li></ul><ul><li>3. definition </li></ul><ul><li>B. Measured numbers are obtained by </li></ul><ul><li> 1. measuring </li></ul><ul><li>2. counting </li></ul><ul><li>3. definition </li></ul>
12. 12. Solution <ul><li>A. Exact numbers are obtained by </li></ul><ul><li> 2. counting </li></ul><ul><li>3. definition </li></ul><ul><li>B. Measured numbers are obtained by </li></ul><ul><li> 1. Using a measuring tool </li></ul>
13. 13. Learning Check <ul><li>Classify each of the following as an exact (1) </li></ul><ul><li>or a measured (2) number. </li></ul><ul><li>A.___Gold melts at 1064°C </li></ul><ul><li>B.___1 yard = 3 feet </li></ul><ul><li>C.___A red blood cell with diameter 6 x 10 -4 cm </li></ul><ul><li>D.___There were 6 hats on the shelf </li></ul><ul><li>E.___A can of soda contains 355 mL of soda </li></ul><ul><li> </li></ul>
14. 14. Solution <ul><li>Classify each of the following as an exact (1) or a measured(2) number. Give reason. </li></ul><ul><li>A. 2 Requires a thermometer(measuring tool) </li></ul><ul><li>B. 1 From a definition in U.S. system </li></ul><ul><li>C. 2 Need measuring tool to determine </li></ul><ul><li>D. 1 Counted the hats </li></ul><ul><li>E. 2 Measured </li></ul>