1. Significant Figures in Operations
© R. A. Hill

2. Odd Even Rounding Rule:
If the digit after the digit to be retained is:
1) < 5, then round down = 2.3
2) > 5, “ “ up = 2.4
3) = 5 & the digit to be retained is odd, round up = 2.4
4) = 5 “ “ “ “ “ “ “ even, “ down = 2.4

3. 2 key characteristics of measurements:
# of S.F.  # of digits coming directly from the measuring device.
accuracy – how close a real measurement is to the immeasurable
measurement containing an infinite number of digits.
3.1
3.12
3.123 …
Which measurement
is most accurate
as compared to

4. 3.123 is more accurate than the other 2 measurements
2 key characteristics of measurements:
# of S.F.  # of digits coming directly from the measuring device.
accuracy – how close a real measurement is to the immeasurable
measurement containing an infinite number of digits.
3.1
3.12
3.123 …
3.123 is more accurate than the other 2 measurements

5. 3.123 is more accurate than the other 2 measurements
2 key characteristics of measurements:
# of S.F.  # of digits coming directly from the measuring device.
accuracy – how close a real measurement is to the immeasurable
measurement containing an infinite number of digits.
(…“how far to the right” a measurement has been made)
3.1
3.12
3.123 …
3.123 is more accurate than the other 2 measurements

6. 2 key characteristics of measurements:
# of S.F.  # of digits coming directly from the measuring device.
accuracy – how close a real measurement is to the immeasurable
measurement containing an infinite number of digits.
(…“how far to the right” a measurement has been made)
Ex: or
is more accurate
has more S.F.

7. 5 . 0 4 3 + 1 . 2 6 . 2 4 3 Addition & Subtraction
The answer cannot be any more or less accurate than the
# used during the calculation which was least accurate.
Recall

8. 5 . 0 4 3 + 1 . 2 6 . 2 4 3 Addition & Subtraction
The answer cannot be any more or less accurate than the
# used during the calculation which was least accurate.
Recall

9. 5 . 0 4 3 + 1 . 2 6 . 2 4 3 Addition & Subtraction
The answer cannot be any more or less accurate than the
# used during the calculation which was least accurate.
Recall

10. 5 . 0 4 3 + 1 . 2 6 . 2 Addition & Subtraction
The answer cannot be any more or less accurate than the
# used during the calculation which was least accurate.
6 . 2
Recall
Final Answer

11. Assume that the following numbers are measurements and determine the answer with the appropriate number of significant figures.
(1)
32.12

12. Assume that the following numbers are measurements and determine the answer with the appropriate number of significant figures.
(1)
32.12

13. Assume that the following numbers are measurements and determine the answer with the appropriate number of significant figures.
(1)
32.12

14. Assume that the following numbers are measurements and determine the answer with the appropriate number of significant figures.
(1)
32.12

15. Assume that the following numbers are measurements and determine the answer with the appropriate number of significant figures.
(1)
32.1

16. Assume that the following numbers are measurements and determine the answer with the appropriate number of significant figures.
(1)
32.1

17. Assume that the following numbers are measurements and determine the answer with the appropriate number of significant figures.
(1) (2)

18. Assume that the following numbers are measurements and determine the answer with the appropriate number of significant figures.
(1) (2)

19. Assume that the following numbers are measurements and determine the answer with the appropriate number of significant figures.
(1) (2)

20. Assume that the following numbers are measurements and determine the answer with the appropriate number of significant figures.
(1) (2)

21. Assume that the following numbers are measurements and determine the answer with the appropriate number of significant figures.
(1) (2)

22. Assume that the following numbers are measurements and determine the answer with the appropriate number of significant figures.
(1) (2)
176.5

23. Assume that the following numbers are measurements and determine the answer with the appropriate number of significant figures.
(1) (2)
176.5

24. Assume that the following numbers are measurements and determine the answer with the appropriate number of significant figures.
(1) (2) (3) 
176.5

25. Assume that the following numbers are measurements and determine the answer with the appropriate number of significant figures.
How many S.F.?
What is the accuracy?
(1) (2) (3) 
176.5

26. Assume that the following numbers are measurements and determine the answer with the appropriate number of significant figures.
(1) (2) (3) 
176.5

27. Assume that the following numbers are measurements and determine the answer with the appropriate number of significant figures.
(1) (2) (3) 
176.5

28. Assume that the following numbers are measurements and determine the answer with the appropriate number of significant figures.
(1) (2) (3) 
176.5

29. Assume that the following numbers are measurements and determine the answer with the appropriate number of significant figures.
(1) (2) (3) 
176.5
When in doubt as the # of S.F. in a measurement,
assume the least # of S.F. are present.

30. Assume that the following numbers are measurements and determine the answer with the appropriate number of significant figures.
(1) (2) (3) 
176.5
When in doubt as the # of S.F. in a measurement,
assume the least # of S.F. are present.

31. Assume that the following numbers are measurements and determine the answer with the appropriate number of significant figures.
(1) (2) (3) 
176.5
When in doubt as the # of S.F. in a measurement,
assume the least # of S.F. are present.

32. Assume that the following numbers are measurements and determine the answer with the appropriate number of significant figures.
(1) (2) (3) 
176.5
When in doubt as the # of S.F. in a measurement,
assume the least # of S.F. are present.

33. Assume that the following numbers are measurements and determine the answer with the appropriate number of significant figures.
(1) (2) (3) 
176.5
When in doubt as the # of S.F. in a measurement,
assume the least # of S.F. are present.

34. Assume that the following numbers are measurements and determine the answer with the appropriate number of significant figures.
(1) (2) (3) (4) 32.4 

35. Assume that the following numbers are measurements and determine the answer with the appropriate number of significant figures.
(1) (2) (3) (4) 32.4 

36. Assume that the following numbers are measurements and determine the answer with the appropriate number of significant figures.
(1) (2) (3) (4) 32.4 

37. Assume that the following numbers are measurements and determine the answer with the appropriate number of significant figures.
(1) (2) (3) (4) 32.4 

38. Assume that the following numbers are measurements and determine the answer with the appropriate number of significant figures.
(1) (2) (3) (4) 32.4 

39. Assume that the following numbers are measurements and determine the answer with the appropriate number of significant figures.
(1) (2) (3) (4) 32.4 

40. Assume that the following numbers are measurements and determine the answer with the appropriate number of significant figures.
(1) (2) (3) (4) 32.4 

41. Multiplication & Division
The answer cannot have any more or less S.F. than the
# used in the calculation which has the least # of S.F.

42. Multiplication & Division
The answer cannot have any more or less S.F. than the
# used in the calculation which has the least # of S.F.
(1) x =

43. Multiplication & Division
The answer cannot have any more or less S.F. than the
# used in the calculation which has the least # of S.F.
(1) x =

44. Multiplication & Division
The answer cannot have any more or less S.F. than the
# used in the calculation which has the least # of S.F.
(1) x =

45. Multiplication & Division
The answer cannot have any more or less S.F. than the
# used in the calculation which has the least # of S.F.
(1) x =

46. Multiplication & Division
The answer cannot have any more or less S.F. than the
# used in the calculation which has the least # of S.F.
(1) x =
(2) / = …

47. Multiplication & Division
The answer cannot have any more or less S.F. than the
# used in the calculation which has the least # of S.F.
(1) x =
(2) / = …

48. Multiplication & Division
The answer cannot have any more or less S.F. than the
# used in the calculation which has the least # of S.F.
(1) x =
(2) / =

49. Multiplication & Division
The answer cannot have any more or less S.F. than the
# used in the calculation which has the least # of S.F.
(1) x =
(2) / =

50. Multiplication & Division
The answer cannot have any more or less S.F. than the
# used in the calculation which has the least # of S.F.
(1) x =
(2) / =
(3) x =

51. Multiplication & Division
The answer cannot have any more or less S.F. than the
# used in the calculation which has the least # of S.F.
(1) x =
(2) / =
(3) x =

52. Multiplication & Division
The answer cannot have any more or less S.F. than the
# used in the calculation which has the least # of S.F.
(1) x =
(2) / =
(3) x =

53. Multiplication & Division
The answer cannot have any more or less S.F. than the
# used in the calculation which has the least # of S.F.
(1) x =
(2) / =
(3) x =

54. Multiplication & Division
The answer cannot have any more or less S.F. than the
# used in the calculation which has the least # of S.F.
(1) x =
(2) / =
(3) x =

55. Multiplication & Division
The answer cannot have any more or less S.F. than the
# used in the calculation which has the least # of S.F.
(1) x =
(2) / =
(3) x =

56. Multiplication & Division
The answer cannot have any more or less S.F. than the
# used in the calculation which has the least # of S.F.
(1) x =
(2) / =
(3) x =
(4) / = 2

57. Multiplication & Division
The answer cannot have any more or less S.F. than the
# used in the calculation which has the least # of S.F.
(1) x =
(2) / =
(3) x =
(4) / = 2

58. Multiplication & Division
The answer cannot have any more or less S.F. than the
# used in the calculation which has the least # of S.F.
(1) x =
(2) / =
(3) x =
(4) / = 2

59. Multiplication & Division
The answer cannot have any more or less S.F. than the
# used in the calculation which has the least # of S.F.
(1) x =
(2) / =
(3) x =
(4) / =

60. Multiplication & Division
The answer cannot have any more or less S.F. than the
# used in the calculation which has the least # of S.F.
(1) x =
(2) / =
(3) x =
(4) / =

61. 3.45 x 0.45 = 0.5175 3 Sequential Operations
When multiple operations are done in sequence,
rounding to the proper # of S.F. is done only in the last step.
When all the operations belong to the same category,
i.e. all + and or  or all x and or ,
then use the appropriate pattern to round in the last step.
3.45 x 0.45 = 3

62. 3.45 x 0.45 = 0.5175 3 Sequential Operations
When multiple operations are done in sequence,
rounding to the proper # of S.F. is done only in the last step.
When all the operations belong to the same category,
i.e. all + and or  or all x and or ,
then use the appropriate pattern to round in the last step.
3.45 x 0.45 = 3

63. 3.45 x 0.45 = 0.5 3 Sequential Operations
When multiple operations are done in sequence,
rounding to the proper # of S.F. is done only in the last step.
When all the operations belong to the same category,
i.e. all + and or  or all x and or ,
then use the appropriate pattern to round in the last step.
3.45 x 0.45
= 0.5 3

64. 3.45 x 0.45 = 0.5 3 Sequential Operations
When multiple operations are done in sequence,
rounding to the proper # of S.F. is done only in the last step.
When all the operations belong to the same category,
i.e. all + and or  or all x and or ,
then use the appropriate pattern to round in the last step.
3.45 x 0.45
= 0.5 3

65. Sequential Operations
When multiple operations are done in sequence,
rounding to the proper # of S.F. is done only in the last step.
When all the operations belong to the same category,
i.e. all + and or  or all x and or ,
then use the appropriate pattern to round in the last step.
When mixed operations are involved,
some + and or  and some x and or ,
then the estimate must be tracked (underlined) in order to
round in the last step.

66. Sequential Operations
When multiple operations are done in sequence,
rounding to the proper # of S.F. is done only in the last step.
When mixed operations are involved,
some + and or  and some x and or ,
then the estimate must be tracked (underlined) in order to
round in the last step.

67. 3.45 x 0.45 + 1.01 = 1.5275 3 o.5175 Sequential Operations
When multiple operations are done in sequence,
rounding to the proper # of S.F. is done only in the last step.
When mixed operations are involved,
some + and or  and some x and or ,
then the estimate must be tracked (underlined) in order to
round in the last step.
3.45 x 0.45 = 3
o.5175

68. 3.45 x 0.45 + 1.01 = 1.5 3 o.5175 Sequential Operations
When multiple operations are done in sequence,
rounding to the proper # of S.F. is done only in the last step.
When mixed operations are involved,
some + and or  and some x and or ,
then the estimate must be tracked (underlined) in order to
round in the last step.
3.45 x 0.45
= 1.5 3
o.5175

69. 56.2 x 0.081 = 7.00338… 2.15 − 1.5 Sequential Operations
When multiple operations are done in sequence,
rounding to the proper # of S.F. is done only in the last step.
When mixed operations are involved,
some + and or  and some x and or ,
then the estimate must be tracked (underlined) in order to
round in the last step. x
= …
− 1.5

70. 56.2 x 0.081 4.5522 = = 7.00338… 2.15 − 1.5 0.65 Sequential Operations
When multiple operations are done in sequence,
rounding to the proper # of S.F. is done only in the last step.
When mixed operations are involved,
some + and or  and some x and or ,
then the estimate must be tracked (underlined) in order to
round in the last step. x
4.5522 =
= …
− 1.5
0.65

71. 56.2 x 0.081 4.5522 = = 7 2.15 − 1.5 0.65 Sequential Operations
When multiple operations are done in sequence,
rounding to the proper # of S.F. is done only in the last step.
When mixed operations are involved,
some + and or  and some x and or ,
then the estimate must be tracked (underlined) in order to
round in the last step. x
4.5522 =
= 7
− 1.5
0.65

72. 3.4 + 0.71 = 0.101631…. 36.4 x 1.111 Sequential Operations
When multiple operations are done in sequence,
rounding to the proper # of S.F. is done only in the last step.
When mixed operations are involved,
some + and or  and some x and or ,
then the estimate must be tracked (underlined) in order to
round in the last step.
= …. x

73. Sequential Operations
When multiple operations are done in sequence,
rounding to the proper # of S.F. is done only in the last step.
When mixed operations are involved,
some + and or  and some x and or ,
then the estimate must be tracked (underlined) in order to
round in the last step.
4.11 =
= …. x

74. 3.4 + 0.71 4.11 = = 0.10 36.4 x 1.111 40.4404 Sequential Operations
When multiple operations are done in sequence,
rounding to the proper # of S.F. is done only in the last step.
When mixed operations are involved,
some + and or  and some x and or ,
then the estimate must be tracked (underlined) in order to
round in the last step.
4.11 =
= 0.10 x

75. Significant figures will be used in every calculation in this course from this point on…
It is used in college physical science courses for all calculations…