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You will need your own paper. Purpose: Significant digits (or significant figures) is a communication tool to express where you rounded any particular.

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Presentation on theme: "You will need your own paper. Purpose: Significant digits (or significant figures) is a communication tool to express where you rounded any particular."— Presentation transcript:

1 You will need your own paper

2 Purpose: Significant digits (or significant figures) is a communication tool to express where you rounded any particular number. Question (do not need to copy): If you won one million dollars, where would you want that rounded? The person paying would want to round it at the millions place, then they only have to pay you $500,000. Significant digits communicates where the rounding occurred! (end of do not need to copy)

3 In science we round for our measurements. We always estimate a digit between the lines on a measurement tool, and with significant digits we can communicate how accurate a measurement tool we used.

4 The Four Rules for Significant Digits:

5 1) All nonzero digits are significant

6 The Four Rules for Significant Digits: 1)All nonzero digits are significant 2)Zeros that are after a decimal and after a nonzero digit (or vice versa) are significant

7 The Four Rules for Significant Digits: 1)All nonzero digits are significant 2)Zeros that are after a decimal and after a nonzero digit (or vice versa) are significant Examples: 4.00000 ← these zeros are sig digs

8 The Four Rules for Significant Digits: 1)All nonzero digits are significant 2)Zeros that are after a decimal and after a nonzero digit (or vice versa) are significant Examples: 4.00000 ← these zeros are sig digs.400000 ← these zeros are sig digs

9 The Four Rules for Significant Digits: 1)All nonzero digits are significant 2)Zeros that are after a decimal and after a nonzero digit (or vice versa) are significant Examples: 4.00000 ← these zeros are sig digs.400000 ← these zeros are sig digs Nonexamples: 400000 ← these zeros are NOT sig digs

10 The Four Rules for Significant Digits: 1)All nonzero digits are significant 2)Zeros that are after a decimal and after a nonzero digit (or vice versa) are significant Examples: 4.00000 ← these zeros are sig digs.400000 ← these zeros are sig digs Nonexamples: 400000 ← these zeros are NOT sig digs.000004 ← these zeros are NOT sig digs

11 The Four Rules for Significant Digits: 1)All nonzero digits are significant 2)Zeros that are after a decimal and after a nonzero digit (or vice versa) are significant Examples: 4.00000 ← these zeros are sig digs.400000 ← these zeros are sig digs Nonexamples: 400000 ← these zeros are NOT sig digs.000004 ← these zeros are NOT sig digs Mixed:.00400 ← only 2 of these zeros are sig digs

12 The Four Rules for Significant Digits: 1)All nonzero digits are significant 2)Zeros that are after a decimal and after a nonzero digit (or vice versa) are significant 3)Zero between significant digits (zeros or nonzeros) are also significant Examples: 4000005 ← these zeros are sig digs

13 The Four Rules for Significant Digits: 1)All nonzero digits are significant 2)Zeros that are after a decimal and after a nonzero digit (or vice versa) are significant 3)Zero between significant digits (zeros or nonzeros) are also significant Examples: 4000005 ← these zeros are sig digs 400.0005 ← these zeros are sig digs

14 The Four Rules for Significant Digits: 1)All nonzero digits are significant 2)Zeros that are after a decimal and after a nonzero digit (or vice versa) are significant 3)Zero between significant digits (zeros or nonzeros) are also significant Examples: 4000005 ← these zeros are sig digs 400.0005 ← these zeros are sig digs.4000005 ← these zeros are sig digs

15 The Four Rules for Significant Digits: 1)All nonzero digits are significant 2)Zeros that are after a decimal and after a nonzero digit (or vice versa) are significant 3)Zero between significant digits (zeros or nonzeros) are also significant Examples: 4000005 ← these zeros are sig digs 400.0005 ← these zeros are sig digs.4000005 ← these zeros are sig digs

16 The Four Rules for Significant Digits: 1)All nonzero digits are significant 2)Zeros that are after a decimal and after a nonzero digit (or vice versa) are significant 3)Zero between significant digits (zeros or nonzeros) are also significant Examples: 4000005 ← these zeros are sig digs 400.0005 ← these zeros are sig digs.4000005 ← these zeros are sig digs Nonexample: 0.0000045 ← these zeros are NOT sig digs

17 The Four Rules for Significant Digits: 1)All nonzero digits are significant 2)Zeros that are after a decimal and after a nonzero digit (or vice versa) are significant 3)Zero between significant digits (zeros or nonzeros) are also significant Examples: 4000005 ← these zeros are sig digs 400.0005 ← these zeros are sig digs.4000005 ← these zeros are sig digs Nonexample: 0.0000045 ← these zeros are NOT sig digs Mixed: 0.004005 ← only 2 of these zeros are sig digs

18 The Four Rules for Significant Digits: 1)All nonzero digits are significant 2)Zeros that are after a decimal and after a nonzero digit (or vice versa) are significant 3)Zero between significant digits (zeros or nonzeros) are also significant 4)Any other zeros are NOT signficiant digits, but still MUST be shown to keep the decimal place correct

19 The Four Rules for Significant Digits: 1)All nonzero digits are significant 2)Zeros that are after a decimal and after a nonzero digit (or vice versa) are significant 3)Zero between significant digits (zeros or nonzeros) are also significant 4)Any other zeros are NOT signficiant digits, but still MUST be shown to keep the decimal place correct Example : 1,000,000 ← only the “1” is a sig dig, so the one is where the rounding occurred (could have been 4,000,000 rounded down or 500,000 rounded up - we don’t know, but we know where it was rounded)

20 Self-Check (do not need to copy): How would you write one million to be as sure as possible of getting all your money?

21

22 Copy down these numbers, then circle the sig digs in each of them: 84.10 0.039100 77.6670 0.060 7800 8.52800 0.00090 0.006 7080 30050 0.0206 4000400 9200001 600.00 500 0.000000100200

23 Copy down these numbers, then round them to the stated amount of sig digs: 84.10 to 3 S.D. 84.10 to 1 S.D. 0.039100 to 2 S.D. 0.9876 to 3 S.D. 0.9876 to 1 S.D. 7080 to 3 S.D. 30050 to 3 S.D. 500 to 2 S.D.

24 How many Significant Digits is in: 84.10

25 How many Significant Digits is in: 84.10 4

26 How many Significant Digits is in: 0.039100

27 How many Significant Digits is in: 0.039100 5

28 How many Significant Digits is in: 77.6670

29 How many Significant Digits is in: 77.6670 6

30 How many Significant Digits is in: 0.060

31 How many Significant Digits is in: 0.060 2

32 How many Significant Digits is in: 78000

33 How many Significant Digits is in: 78000 2

34 How many Significant Digits is in: 8.52800

35 How many Significant Digits is in: 8.52800 6

36 How many Significant Digits is in: 0.00090

37 How many Significant Digits is in: 0.00090 2

38 How many Significant Digits is in: 0.006

39 How many Significant Digits is in: 0.006 1

40 How many Significant Digits is in: 7080

41 How many Significant Digits is in: 7080 3

42 How many Significant Digits is in: 30050

43 How many Significant Digits is in: 30050 4

44 How many Significant Digits is in: 0.0206

45 How many Significant Digits is in: 0.0206 3

46 How many Significant Digits is in: 4000400

47 How many Significant Digits is in: 4000400 5

48 How many Significant Digits is in: 9200001

49 How many Significant Digits is in: 9200001 7

50 How many Significant Digits is in: 600.00

51 How many Significant Digits is in: 600.00 5

52 How many Significant Digits is in: 500

53 How many Significant Digits is in: 500 1

54 How many Significant Digits is in: 0.000000100200

55 How many Significant Digits is in: 0.000000100200 6

56 Round the following number to the amount of Significant Digits: 84.10 to 3 S.D.

57 Round the following number to the amount of Significant Digits: 84.10 to 3 S.D. 84.1

58 Round the following number to the amount of Significant Digits: 84.10 to 1 S.D.

59 Round the following number to the amount of Significant Digits: 84.10 to 1 S.D. 80

60 Round the following number to the amount of Significant Digits: 0.039100 to 2 S.D.

61 Round the following number to the amount of Significant Digits: 0.039100 to 2 S.D. 0.039

62 Round the following number to the amount of Significant Digits: 0.9876 to 3 S.D.

63 Round the following number to the amount of Significant Digits: 0.9876 to 3 S.D. 0.988

64 Round the following number to the amount of Significant Digits: 0.9876 to 1 S.D.

65 Round the following number to the amount of Significant Digits: 0.9876 to 1 S.D. 1

66 Round the following number to the amount of Significant Digits: 7080 to 3 S.D.

67 Round the following number to the amount of Significant Digits: 7080 to 3 S.D. 7080

68 Round the following number to the amount of Significant Digits: 30050 to 3 S.D.

69 Round the following number to the amount of Significant Digits: 30050 to 3 S.D. 30100

70 Round the following number to the amount of Significant Digits: 500 to 2 S.D.

71 Round the following number to the amount of Significant Digits: 500 to 2 S.D. 5.0 x 10 2

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