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Significant Figures ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Chapter Two
Exact Numbers ,[object Object],Counting objects are always exact 2 soccer balls 4 pizzas Exact relationships, predefined values, not measured 1 foot = 12 inches 1 meter = 100 cm For instance is 1 foot = 12.000000000001 inches? No  1 ft is EXACTLY 12 inches.
Learning Check  ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Solution ,[object Object],[object Object],[object Object],[object Object],[object Object]
Learning Check ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Solution
2.4 Measurement and Significant Figures ,[object Object],[object Object],[object Object],[object Object],Chapter Two
What is the Length? ,[object Object],[object Object],[object Object],[object Object],[object Object]
Learning Check What is the length of the wooden stick? 1)  4.5 cm  2)  4.54 cm  3)  4.547 cm
8.00 cm or 3 (2.2/8) ?
Measured Numbers ,[object Object],[object Object],[object Object]
Chapter Two Below are two measurements of the mass of the same object. The same quantity is being described at two different levels of precision or certainty.
Note the 4 rules ,[object Object],[object Object],[object Object],Chapter Two
[object Object],[object Object],Chapter Two
[object Object],45.8736 .000239  .00023900  48000.  48000  3.982  10 6   1.00040 6 3 5 5 2 4 6 ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
2.5 Scientific Notation ,[object Object],[object Object],[object Object],[object Object],Chapter Two
Chapter Two Two examples of converting standard notation to scientific notation are shown below.
Chapter Two Two examples of converting scientific notation back to  standard notation are shown below.
[object Object],[object Object],[object Object],[object Object],Chapter Two
2.6 Rounding Off Numbers ,[object Object],[object Object],[object Object],Chapter Two
[object Object],[object Object],[object Object],[object Object],Chapter Two
Practice Rule #2 Rounding ,[object Object],1.5587 .0037421 1367 128,522 1.6683   10 6   1.56 .00374 1370 129,000 1.67   10 6 Your Final number must be of the same value as the number you started with, 129,000 and  not  129
Examples of Rounding ,[object Object],4965.03   780,582   1999.5   0 is dropped, it is <5 8 is dropped, it is >5; Note you must include the 0’s 5 is dropped it is = 5; note you need a 4 Sig Fig 4965 780,600 2000.
[object Object],Chapter Two
[object Object],Chapter Two
Multiplication and division 32.27    1.54 = 49.6958 3.68    .07925 = 46.4353312 1.750    .0342000 = 0.05985 3.2650  10 6     4.858 = 1.586137    10 7   6.022  10 23     1.661  10 -24  = 1.000000 49.7 46.4 .05985 1.586   10 7   1.000
Addition/Subtraction ,[object Object],[object Object],[object Object],[object Object]
Addition and Subtraction __  ___  __ .56 + .153 = .713 82000 + 5.32 = 82005.32 10.0 - 9.8742 = .12580 10 – 9.8742 = .12580 .71 82000 .1 0 Look for the last important digit
Mixed Order of Operation 8.52  + 4 .1586    18.73 + 153.2 =   (8.52  + 4 .1586)    (18.73 + 153.2) = 239.6 2180. =  8.52  + 77.89  + 153.2 = 239.61 = = 12.68    171.9 = 2179.692 =
Try Find the standard deviation for the following numbers:  7.691 g, 7.23 g, 7.892 g
Try 7.691 g  7.23  g  7.892 g 22.813  g 22.81  g   = 7.603 g 3 7.691 g, 7.23 g, 7.892 g
Try    = 7.603 g 7.691 g – 7.603 g =  .088 g  7.23  g – 7.603 g =  -.37 g 7.892 g – 7.603 g =  .289 g   .01 g
Try .25 .01  = .01 g

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Sig Figs

  • 1.
  • 2.
  • 3.
  • 4.
  • 5.
  • 6.
  • 7.
  • 8.
  • 9. Learning Check What is the length of the wooden stick? 1) 4.5 cm 2) 4.54 cm 3) 4.547 cm
  • 10. 8.00 cm or 3 (2.2/8) ?
  • 11.
  • 12. Chapter Two Below are two measurements of the mass of the same object. The same quantity is being described at two different levels of precision or certainty.
  • 13.
  • 14.
  • 15.
  • 16.
  • 17. Chapter Two Two examples of converting standard notation to scientific notation are shown below.
  • 18. Chapter Two Two examples of converting scientific notation back to standard notation are shown below.
  • 19.
  • 20.
  • 21.
  • 22.
  • 23.
  • 24.
  • 25.
  • 26. Multiplication and division 32.27  1.54 = 49.6958 3.68  .07925 = 46.4353312 1.750  .0342000 = 0.05985 3.2650  10 6  4.858 = 1.586137  10 7 6.022  10 23  1.661  10 -24 = 1.000000 49.7 46.4 .05985 1.586  10 7 1.000
  • 27.
  • 28. Addition and Subtraction __ ___ __ .56 + .153 = .713 82000 + 5.32 = 82005.32 10.0 - 9.8742 = .12580 10 – 9.8742 = .12580 .71 82000 .1 0 Look for the last important digit
  • 29. Mixed Order of Operation 8.52 + 4 .1586  18.73 + 153.2 = (8.52 + 4 .1586)  (18.73 + 153.2) = 239.6 2180. = 8.52 + 77.89 + 153.2 = 239.61 = = 12.68  171.9 = 2179.692 =
  • 30. Try Find the standard deviation for the following numbers: 7.691 g, 7.23 g, 7.892 g
  • 31. Try 7.691 g 7.23 g 7.892 g 22.813 g 22.81 g = 7.603 g 3 7.691 g, 7.23 g, 7.892 g
  • 32. Try  = 7.603 g 7.691 g – 7.603 g = .088 g 7.23 g – 7.603 g = -.37 g 7.892 g – 7.603 g = .289 g .01 g
  • 33. Try .25 .01 = .01 g