Measured And Exact Numbers
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Measured And Exact Numbers

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Measured And Exact Numbers Presentation Transcript

  • 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.
  • 16.  
  • 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.