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Significant Digits

Significant Digits. 0 1 2 3 4 5 6 7 8 9. Mr. Gabrielse. How Long is the Pencil?. Mr. Gabrielse. Use a Ruler. Mr. Gabrielse. Can’t See?. Mr. Gabrielse. How Long is the Pencil?. Look Closer. How Long is the Pencil?. 5.8 cm or 5.9 cm ?. 5.9 cm. 5.8 cm. How Long is the Pencil?.

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Significant Digits

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  1. Significant Digits 0 1 2 3 4 5 6 7 8 9 . . . Mr. Gabrielse

  2. How Long is the Pencil? Mr. Gabrielse

  3. Use a Ruler Mr. Gabrielse

  4. Can’t See? Mr. Gabrielse

  5. How Long is the Pencil? Look Closer

  6. How Long is the Pencil? 5.8 cm or 5.9 cm ? 5.9 cm 5.8 cm

  7. How Long is the Pencil? Between 5.8 cm & 5.9 cm 5.9 cm 5.8 cm

  8. How Long is the Pencil? At least: 5.8 cm Not Quite: 5.9 cm 5.9 cm 5.8 cm

  9. Solution: Add a Doubtful Digit • Guess an extra doubtful digit between 5.80 cm and 5.90 cm. • Doubtful digits are always uncertain, never precise. • The last digit in a measurement is always doubtful. 5.9 cm 5.8 cm

  10. Pick a Number:5.80 cm, 5. 81 cm, 5.82 cm, 5.83 cm, 5.84 cm, 5.85 cm, 5.86 cm, 5.87 cm, 5.88 cm, 5.89 cm, 5.90 cm 5.9 cm 5.8 cm

  11. Pick a Number:5.80 cm, 5. 81 cm, 5.82 cm, 5.83 cm, 5.84 cm, 5.85 cm, 5.86 cm, 5.87 cm, 5.88 cm, 5.89 cm, 5.90 cm 5.9 cm I pick 5.83 cm because I think the pencil is closer to 5.80 cm than 5.90 cm. 5.8 cm

  12. Extra Digits 5.837 cm I guessed at the 3 sothe 7 is meaningless. 5.9 cm 5.8 cm

  13. Extra Digits 5.837 cm I guessed at the 3 sothe 7 is meaningless. Digits after the doubtful digit are insignificant (meaningless). 5.9 cm 5.8 cm

  14. Example Problem • Example Problem: What is the average velocity of a student that walks 4.4 m in 3.3 s? • d = 4.4 m • t = 3.3 s • v = d / t • v = 4.4 m / 3.3 s = 1.3 m/s not 1.3333333333333333333 m/s

  15. Identifying Significant Digits Examples: 45 [2] 19,583.894 [8] .32 [2] 136.7 [4] Rule 1: Nonzero digits are always significant.

  16. Identifying Significant Digits Zeros make this interesting! FYI: 0.000,340,056,100,0 Beginning Zeros MiddleZeros EndingZeros Beginning, middle, and endingzeros are separated by nonzero digits.

  17. Identifying Significant Digits Examples: 0.005,6 [2] 0.078,9 [3] 0.000,001 [1] 0.537,89 [5] Rule 2: Beginningzeros are never significant.

  18. Identifying Significant Digits Examples: 7.003 [4] 59,012 [5] 101.02 [5] 604 [3] Rule 3: Middlezeros are always significant.

  19. Identifying Significant Digits Examples: 430 [2] 43.0 [3] 0.00200 [3] 0.040050 [5] Rule 4: Endingzeros are only significant if there is a decimal point.

  20. Your TurnCounting Significant DigitsClasswork: start it, Homework: finish it

  21. Using Significant Digits Measure how fast the car travels.

  22. Example Measure the distance: 10.21 m

  23. Example Measure the distance: 10.21 m

  24. Example Measure the distance: 10.21 m Measure the time: 1.07 s 1.07 s 0.00 s start stop

  25. speed = distance time Measure the distance: 10.21 m Measure the time: 1.07 s Physicists take data (measurements) and use equations to make predictions.

  26. speed = distance = 10.21 m time 1.07 s Measure the distance:10.21 m Measure the time:1.07 s Physicists take data (measurements) and use equations to make predictions. Use a calculator to make a prediction.

  27. speed = 10.21 m =9.542056075 m1.07 s s Physicists take data (measurements) and use equations to make predictions. Too many significant digits! We need rules for doing math with significant digits.

  28. speed = 10.21 m =9.542056075 m1.07 s s Physicists take data (measurements) and use equations to make predictions. Too many significant digits! We need rules for doing math with significant digits.

  29. Math with Significant Digits The result can never be more precise than the least precise measurement.

  30. speed = 10.21 m =9.54 m1.07 s s we go over how to round next 1.07 s was the least precise measurement since it had the least number of significant digits The answer had to be rounded to 9.54 so it wouldn’t have more significant digits than 1.07 s.

  31. Rounding Off to X X: the new last significantdigit Y: the digit after the new last significant digit If Y≥ 5, increase X by 1 If Y < 5, leave X the same Example: Round 345.0 to 2 significant digits.

  32. Rounding Off to X X: the new last significantdigit Y: the digit after the new last significant digit If Y≥ 5, increase X by 1 If Y < 5, leave X the same Example: Round 345.0 to 2 significant digits. X Y

  33. Fill in till the decimal place with zeroes. Rounding Off to X X: the new last significantdigit Y: the digit after the new last significant digit If Y≥ 5, increase X by 1 If Y < 5, leave X the same Example: Round 345.0 to 2 significant digits. 345.0  350 X Y

  34. Multiplication & Division You can never have more significant digits than any of your measurements.

  35. Multiplication & Division Round the answer so it has the same number of significant digits as the least precise measurement. (3.45 cm)(4.8 cm)(0.5421cm) = 8.977176 cm3 (3) (2) (4) = (?)

  36. Multiplication & Division Round the answer so it has the same number of significant digits as the least precise measurement. (3.45 cm)(4.8 cm)(0.5421cm) = 8.977176 cm3 (3) (2) (4) = (2)

  37. Multiplication & Division Round the answer so it has the same number of significant digits as the least precise measurement. (3.45 cm)(4.8 cm)(0.5421cm) = 9.000000 cm3 (3) (2) (4) = (2)

  38. Multiplication & Division (3) Round the answer so it has the same number of significant digits as the least precise measurement. (?) (2)

  39. Multiplication & Division (3) Round the answer so it has the same number of significant digits as the least precise measurement. (2) (2)

  40. Multiplication & Division (3) Round the answer so it has the same number of significant digits as the least precise measurement. (2) (2)

  41. Addition & Subtraction Example: 13.05 309.2 + 3.785 326.035 Rule: You can never have more decimal places than any of your measurements.

  42. Addition & Subtraction Example: 13.05 309.2 + 3.785 326.035 Rule: The answer’s doubtful digit is in the same decimal place as the measurement with the leftmost doubtful digit. leftmost doubtful digit in the problem Hint: Line up your decimal places.

  43. Addition & Subtraction Example: 13.05 309.2 + 3.785 326.035 Rule: The answer’s doubtful digit is in the same decimal place as the measurement with the leftmost doubtful digit. Hint: Line up your decimal places.

  44. Your TurnClasswork: Using Significant Digits

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