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

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How Long is the Pencil? Mr. Gabrielse

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Use a Ruler Mr. Gabrielse

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Can’t See? Mr. Gabrielse

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How Long is the Pencil? Look Closer

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Mr. Gabrielse How Long is the Pencil? 5.9 cm 5.8 cm or 5.9 cm ?

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

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

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Mr. Gabrielse Solution: Add a Doubtful Digit 5.9 cm 5.8 cm 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.

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Mr. Gabrielse 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

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Mr. Gabrielse 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 I pick 5.83 cm because I think the pencil is closer to 5.80 cm than 5.90 cm.

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Mr. Gabrielse Extra Digits 5.9 cm 5.8 cm 5.837 cm I guessed at the 3 so the 7 is meaningless.

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

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Mr. Gabrielse 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

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

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Mr. Gabrielse Identifying Significant Digits Zeros make this interesting! FYI: 0.000,340,056,100,0 Beginning Zeros Middle Zeros Ending Zeros Beginning, middle, and ending zeros are separated by nonzero digits.

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

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Mr. Gabrielse Identifying Significant Digits Examples: 7.003[4] 59,012 [5] 101.02[5] 604[3] Rule 3: Middle zeros are always significant.

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

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Mr. Gabrielse Your Turn Counting Significant Digits Classwork: start it, Homework: finish it

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Mr. Gabrielse Using Significant Digits Measure how fast the car travels.

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Mr. Gabrielse Example Measure the distance: 10.21 m

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Mr. Gabrielse Example Measure the distance: 10.21 m

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

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Mr. Gabrielse 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.

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Mr. Gabrielse 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.

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Mr. Gabrielse speed = 10.21 m = 9.542056075 m 1.07 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.

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Mr. Gabrielse speed = 10.21 m = 9.542056075 m 1.07 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.

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

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Mr. Gabrielse speed = 10.21 m = 9.54 m 1.07 s s 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. we go over how to round next

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Mr. Gabrielse Rounding Off to X X: the new last significant digit 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.

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Mr. Gabrielse Rounding Off to X X: the new last significant digit 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

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

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

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Mr. Gabrielse 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 cm 3 (3) (2) (4) = (?)

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Mr. Gabrielse 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 cm 3 (3) (2) (4) = (2)

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Mr. Gabrielse 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 cm 3 (3) (2) (4) = (2)

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

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

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

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

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

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

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Mr. Gabrielse Your Turn Classwork: Using Significant Digits

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