1. Significant Digits
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

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
Pick a Number: 5.80 cm, cm, 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
Pick a Number: 5.80 cm, cm, 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. I guessed at the 3 so the 7 is meaningless.
Extra Digits
5.837 cm
I guessed at the 3 so the 7 is meaningless.
5.9 cm
5.8 cm

13. Extra Digits 5.837 cm I guessed at the 3 so the 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 m/s

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

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

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

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

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

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

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

22. Measure the distance: 10.21 m
Example
Measure the distance: m

23. Measure the distance: 10.21 m
Example
Measure the distance: m

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

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

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

27. Too many significant digits!
speed = m = m 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. Too many significant digits!
speed = m = m 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 = m = 9.54 m 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 so it wouldn’t have
more significant digits than 1.07 s.

31. Round 345.0 to 2 significant digits.
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 to 2 significant digits.

32. Round 345.0 to 2 significant digits.
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 to 2 significant digits. X Y

33. Rounding Off to X X Y 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 to 2 significant digits.
345.0  350 X Y
Fill in till the decimal place with zeroes.

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

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

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

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

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

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

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

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

42. Addition & Subtraction
Example:
13.05
309.2
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
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 Turn Classwork: Using Significant Digits