1. Significant Digits By Michelle Lamary and and Caitlin Ostrowski

2. Counting Significant Digit Rules 1. All non-zero digits are significant (725, 2, 12) 2. Trapped zeros are significant (101, 2003) 3. Ending zeros are significant only if the decimal point can be seen (100., 1.10, 100, 20) 4. Leading (beginning) zeros are never significant (0.001, 0.9)

3. Example 1 401700.0900 401700.0900

4. Example 1 - Answer 401700.0900 401700.0900 Rule 1 – 4 sig digs non-zero digits Rule 1 – 4 sig digs non-zero digits

5. Example 1 - Answer 401700.0900 401700.0900 Rule 1 – 4 sig digs non-zero digits Rule 1 – 4 sig digs non-zero digits Rule 2 – 4 sig digs trapped zeros Rule 2 – 4 sig digs trapped zeros

6. Example 1 - Answer 401700.0900 401700.0900 Rule 1 – 4 sig digs non-zero digits Rule 1 – 4 sig digs non-zero digits Rule 2 – 4 sig digs trapped zeros Rule 2 – 4 sig digs trapped zeros Rule 3 – 2 ending zeros Rule 3 – 2 ending zeros

7. Example 1 - Answer 401700.0900 401700.0900 Rule 1 – 4 sig digs non-zero digits Rule 1 – 4 sig digs non-zero digits Rule 2 – 4 sig digs trapped zeros Rule 2 – 4 sig digs trapped zeros Rule 3 – 2 sig digs ending zeros with decimal point shown Rule 3 – 2 sig digs ending zeros with decimal point shown

8. Example 1 - Answer 401700.0900 401700.0900 Rule 1 – 4 sig digs non-zero digits Rule 1 – 4 sig digs non-zero digits Rule 2 – 4 sig digs trapped zeros Rule 2 – 4 sig digs trapped zeros Rule 3 – 2 sig digs ending zeros with decimal point shown Rule 3 – 2 sig digs ending zeros with decimal point shown Rule 4 – 0 beginning zeros Rule 4 – 0 beginning zeros

9. Example 1 - Answer 401700.0900 401700.0900 Rule 1 – 4 sig digs non-zero digits Rule 1 – 4 sig digs non-zero digits Rule 2 – 4 sig digs trapped zeros Rule 2 – 4 sig digs trapped zeros Rule 3 – 2 sig digs ending zeros with decimal point shown Rule 3 – 2 sig digs ending zeros with decimal point shown Rule 4 – 0 beginning zeros Rule 4 – 0 beginning zeros 10 Significant Digits 10 Significant Digits

10. Example 2 0.007050 0.007050

11. Example 2 - Answer 0.007050 0.007050 Rule 1 – 2 sig digs non-zero numbers Rule 1 – 2 sig digs non-zero numbers

12. Example 2 - Answer 0.007050 0.007050 Rule 1 – 2 sig digs non-zero numbers Rule 1 – 2 sig digs non-zero numbers Rule 2 – 1 sig dig trapped zero Rule 2 – 1 sig dig trapped zero

13. Example 2 - Answer 0.007050 0.007050 Rule 1 – 2 sig digs non-zero numbers Rule 1 – 2 sig digs non-zero numbers Rule 2 – 1 sig dig trapped zero Rule 2 – 1 sig dig trapped zero Rule 3 – 1 ending zero Rule 3 – 1 ending zero

14. Example 2 - Answer 0.007050 0.007050 Rule 1 – 2 sig digs non-zero numbers Rule 1 – 2 sig digs non-zero numbers Rule 2 – 1 sig dig trapped zero Rule 2 – 1 sig dig trapped zero Rule 3 – 1 sig dig ending zero with decimal point is shown Rule 3 – 1 sig dig ending zero with decimal point is shown

15. Example 2 - Answer 0.007050 0.007050 Rule 1 – 2 sig digs non-zero numbers Rule 1 – 2 sig digs non-zero numbers Rule 2 – 1 sig dig trapped zero Rule 2 – 1 sig dig trapped zero Rule 3 – 1 sig dig ending zero with decimal point is shown Rule 3 – 1 sig dig ending zero with decimal point is shown Rule 4 – beginning zeros are not significant (3 beginning zeros) Rule 4 – beginning zeros are not significant (3 beginning zeros)

16. Example 2 - Answer 0.007050 0.007050 Rule 1 – 2 sig digs non-zero numbers Rule 1 – 2 sig digs non-zero numbers Rule 2 – 1 sig dig trapped zero Rule 2 – 1 sig dig trapped zero Rule 3 – 1 sig dig ending zero with decimal point is shown Rule 3 – 1 sig dig ending zero with decimal point is shown Rule 4 – beginning zeros are not significant (3 beginning zeros) Rule 4 – beginning zeros are not significant (3 beginning zeros) 4 significant digits 4 significant digits

17. Example 3 700. 700.

18. Example 3 - Answer 700. 700. Rule 1 – 1 sig dig non-zero number Rule 1 – 1 sig dig non-zero number

19. Example 3 - Answer 700. 700. Rule 1 – 1 sig dig non-zero number Rule 1 – 1 sig dig non-zero number Rule 2 – 0 sig dig trapped zeros Rule 2 – 0 sig dig trapped zeros

20. Example 3 - Answer 700. 700. Rule 1 – 1 sig dig non-zero number Rule 1 – 1 sig dig non-zero number Rule 2 – 0 sig dig trapped zeros Rule 2 – 0 sig dig trapped zeros Rule 3 – 2 ending zeros Rule 3 – 2 ending zeros

21. Example 3 - Answer 700. 700. Rule 1 – 1 sig dig non-zero number Rule 1 – 1 sig dig non-zero number Rule 2 – 0 sig dig trapped zeros Rule 2 – 0 sig dig trapped zeros Rule 3 – 2 sig digs ending zeros with decimal point shown Rule 3 – 2 sig digs ending zeros with decimal point shown

22. Example 3 - Answer 700. 700. Rule 1 – 1 sig dig non-zero number Rule 1 – 1 sig dig non-zero number Rule 2 – 0 sig dig trapped zeros Rule 2 – 0 sig dig trapped zeros Rule 3 – 2 sig digs ending zeros with decimal point shown Rule 3 – 2 sig digs ending zeros with decimal point shown Rule 4 – 0 leading zeros Rule 4 – 0 leading zeros

23. Example 3 - Answer 700. 700. Rule 1 – 1 sig dig non-zero number Rule 1 – 1 sig dig non-zero number Rule 2 – 0 sig dig trapped zeros Rule 2 – 0 sig dig trapped zeros Rule 3 – 2 sig digs ending zeros with decimal point shown Rule 3 – 2 sig digs ending zeros with decimal point shown Rule 4 – 0 leading zeros Rule 4 – 0 leading zeros 3 significant digits 3 significant digits

24. Example 4 8500 8500

25. Example 4 - Answer 8500 8500 Rule 1 – 2 sig digs non-zero numbers Rule 1 – 2 sig digs non-zero numbers

26. Example 4 - Answer 8500 8500 Rule 1 – 2 sig digs non-zero numbers Rule 1 – 2 sig digs non-zero numbers Rule 2 – 0 sig digs trapped zeros Rule 2 – 0 sig digs trapped zeros

27. Example 4 - Answer 8500 8500 Rule 1 – 2 sig digs non-zero numbers Rule 1 – 2 sig digs non-zero numbers Rule 2 – 0 sig digs trapped zeros Rule 2 – 0 sig digs trapped zeros Rule 3 – 2 ending zeros Rule 3 – 2 ending zeros

28. Example 4 - Answer 8500 8500 Rule 1 – 2 sig digs non-zero numbers Rule 1 – 2 sig digs non-zero numbers Rule 2 – 0 sig digs trapped zeros Rule 2 – 0 sig digs trapped zeros Rule 3 – 0 sig digs (2 ending zeros but decimal point is NOT shown) Rule 3 – 0 sig digs (2 ending zeros but decimal point is NOT shown)

29. Example 4 - Answer 8500 8500 Rule 1 – 2 sig digs non-zero numbers Rule 1 – 2 sig digs non-zero numbers Rule 2 – 0 sig digs trapped zeros Rule 2 – 0 sig digs trapped zeros Rule 3 – 0 sig digs (2 ending zeros but decimal point is NOT shown) Rule 3 – 0 sig digs (2 ending zeros but decimal point is NOT shown) Rule 4 – 0 beginning zeros Rule 4 – 0 beginning zeros

30. Example 4 - Answer 8500 8500 Rule 1 – 2 sig digs non-zero numbers Rule 1 – 2 sig digs non-zero numbers Rule 2 – 0 sig digs trapped zeros Rule 2 – 0 sig digs trapped zeros Rule 3 – 0 sig digs (2 ending zeros but decimal point is NOT shown) Rule 3 – 0 sig digs (2 ending zeros but decimal point is NOT shown) Rule 4 – 0 beginning zeros Rule 4 – 0 beginning zeros 2 significant digits 2 significant digits

31. Example 5 8500. 8500.

32. Example 5 - Answer 8500. 8500. Rule 1 – 2 sig digs non-zero digits Rule 1 – 2 sig digs non-zero digits

33. Example 5 - Answer 8500. 8500. Rule 1 – 2 sig digs non-zero digits Rule 1 – 2 sig digs non-zero digits Rule 2 – 0 sig dig trapped zeros Rule 2 – 0 sig dig trapped zeros

34. Example 5 - Answer 8500. 8500. Rule 1 – 2 sig digs non-zero digits Rule 1 – 2 sig digs non-zero digits Rule 2 – 0 sig dig trapped zeros Rule 2 – 0 sig dig trapped zeros Rule 3 – 2 ending zeros Rule 3 – 2 ending zeros

35. Example 5 - Answer 8500. 8500. Rule 1 – 2 sig digs non-zero digits Rule 1 – 2 sig digs non-zero digits Rule 2 – 0 sig dig trapped zeros Rule 2 – 0 sig dig trapped zeros Rule 3 – 2 sig digs ending zeros with decimal point shown Rule 3 – 2 sig digs ending zeros with decimal point shown

36. Example 5 - Answer 8500. 8500. Rule 1 – 2 sig digs non-zero digits Rule 1 – 2 sig digs non-zero digits Rule 2 – 0 sig dig trapped zeros Rule 2 – 0 sig dig trapped zeros Rule 3 – 2 sig digs ending zeros with decimal point shown Rule 3 – 2 sig digs ending zeros with decimal point shown Rule 4 – 0 beginning zeros Rule 4 – 0 beginning zeros

37. Example 5 - Answer 8500. 8500. Rule 1 – 2 sig digs non-zero digits Rule 1 – 2 sig digs non-zero digits Rule 2 – 0 sig dig trapped zeros Rule 2 – 0 sig dig trapped zeros Rule 3 – 2 sig digs ending zeros with decimal point shown Rule 3 – 2 sig digs ending zeros with decimal point shown Rule 4 – 0 beginning zeros Rule 4 – 0 beginning zeros 4 significant digits 4 significant digits

38. Example 6 0.0000001 0.0000001

39. Example 6 - Answer 0.0000001 0.0000001 Rule 1 – 1 sig dig non-zero number Rule 1 – 1 sig dig non-zero number

40. Example 6 - Answer 0.0000001 0.0000001 Rule 1 – 1 sig dig non-zero number Rule 1 – 1 sig dig non-zero number Rule 2 - 0 sig digs trapped zeros Rule 2 - 0 sig digs trapped zeros

41. Example 6 - Answer 0.0000001 0.0000001 Rule 1 – 1 sig dig non-zero number Rule 1 – 1 sig dig non-zero number Rule 2 - 0 sig digs trapped zeros Rule 2 - 0 sig digs trapped zeros Rule 3 – 0 sig digs ending zeros Rule 3 – 0 sig digs ending zeros

42. Example 6 - Answer 0.0000001 0.0000001 Rule 1 – 1 sig dig non-zero number Rule 1 – 1 sig dig non-zero number Rule 2 - 0 sig digs trapped zeros Rule 2 - 0 sig digs trapped zeros Rule 3 – 0 sig digs ending zeros (decimal point is shown) Rule 3 – 0 sig digs ending zeros (decimal point is shown)

43. Example 6 - Answer 0.0000001 0.0000001 Rule 1 – 1 sig dig non-zero number Rule 1 – 1 sig dig non-zero number Rule 2 - 0 sig digs trapped zeros Rule 2 - 0 sig digs trapped zeros Rule 3 – 0 sig digs ending zeros Rule 3 – 0 sig digs ending zeros Rule 4 – beginning zeros are not significant (7 non significant beginning zeros) Rule 4 – beginning zeros are not significant (7 non significant beginning zeros)

44. Example 6 - Answer 0.0000001 0.0000001 Rule 1 – 1 sig dig non-zero number Rule 1 – 1 sig dig non-zero number Rule 2 - 0 sig digs trapped zeros Rule 2 - 0 sig digs trapped zeros Rule 3 – 0 sig digs ending zeros Rule 3 – 0 sig digs ending zeros Rule 4 – beginning zeros are not significant (7 non significant beginning zeros) Rule 4 – beginning zeros are not significant (7 non significant beginning zeros) 1 significant digit 1 significant digit

45. Example 7 200009 200009

46. Example 7 - Answer 200009 200009 Rule 1 – 2 sig digs non-zero numbers Rule 1 – 2 sig digs non-zero numbers

47. Example 7 - Answer 200009 200009 Rule 1 – 2 sig digs non-zero numbers Rule 1 – 2 sig digs non-zero numbers Rule 2 – 4 sig digs trapped zeros Rule 2 – 4 sig digs trapped zeros

48. Example 7 - Answer 200009 200009 Rule 1 – 2 sig digs non-zero numbers Rule 1 – 2 sig digs non-zero numbers Rule 2 – 4 sig digs trapped zeros Rule 2 – 4 sig digs trapped zeros Rule 3 – 0 sig digs ending zeros Rule 3 – 0 sig digs ending zeros

49. Example 7 - Answer 200009 200009 Rule 1 – 2 sig digs non-zero numbers Rule 1 – 2 sig digs non-zero numbers Rule 2 – 4 sig digs trapped zeros Rule 2 – 4 sig digs trapped zeros Rule 3 – 0 sig digs ending zeros (decimal point NOT shown) Rule 3 – 0 sig digs ending zeros (decimal point NOT shown)

50. Example 7 - Answer 200009 200009 Rule 1 – 2 sig digs non-zero numbers Rule 1 – 2 sig digs non-zero numbers Rule 2 – 4 sig digs trapped zeros Rule 2 – 4 sig digs trapped zeros Rule 3 – 0 sig digs ending zeros (decimal point is NOT shown) Rule 3 – 0 sig digs ending zeros (decimal point is NOT shown) Rule 4 – 0 beginning zeros Rule 4 – 0 beginning zeros

51. Example 7 - Answer 200009 200009 Rule 1 – 2 sig digs non-zero numbers Rule 1 – 2 sig digs non-zero numbers Rule 2 – 4 sig digs trapped zeros Rule 2 – 4 sig digs trapped zeros Rule 3 – 0 sig digs ending zeros Rule 3 – 0 sig digs ending zeros Rule 4 – 0 beginning zeros Rule 4 – 0 beginning zeros 6 significant digits 6 significant digits

52. Example 8 10 10

53. Example 8 - Answer 10 10 Rule 1 – 1 sig dig non-zero number Rule 1 – 1 sig dig non-zero number

54. Example 8 - Answer 10 10 Rule 1 – 1 sig dig non-zero number Rule 1 – 1 sig dig non-zero number Rule 2 – 0 sig digs trapped zeros Rule 2 – 0 sig digs trapped zeros

55. Example 8 - Answer 10 10 Rule 1 – 1 sig dig non-zero number Rule 1 – 1 sig dig non-zero number Rule 2 – 0 sig digs trapped zeros Rule 2 – 0 sig digs trapped zeros Rule 3 – 1 ending zero Rule 3 – 1 ending zero

56. Example 8 - Answer 10 10 Rule 1 – 1 sig dig non-zero number Rule 1 – 1 sig dig non-zero number Rule 2 – 0 sig digs trapped zeros Rule 2 – 0 sig digs trapped zeros Rule 3 – 0 sig digs ( 1 ending zero, but decimal point is NOT shown) Rule 3 – 0 sig digs ( 1 ending zero, but decimal point is NOT shown)

57. Example 8 - Answer 10 10 Rule 1 – 1 sig dig non-zero number Rule 1 – 1 sig dig non-zero number Rule 2 – 0 sig digs trapped zeros Rule 2 – 0 sig digs trapped zeros Rule 3 – 0 sig digs ( 1 ending zero, but decimal point is NOT shown) Rule 3 – 0 sig digs ( 1 ending zero, but decimal point is NOT shown) Rule 4 – 0 leading zeros Rule 4 – 0 leading zeros

58. Example 8 - Answer 10 10 Rule 1 – 1 sig dig non-zero number Rule 1 – 1 sig dig non-zero number Rule 2 – 0 sig digs trapped zeros Rule 2 – 0 sig digs trapped zeros Rule 3 – 0 sig digs ( 1 ending zero, but decimal point is NOT shown) Rule 3 – 0 sig digs ( 1 ending zero, but decimal point is NOT shown) Rule 4 – 0 leading zeros Rule 4 – 0 leading zeros 1 significant digit 1 significant digit

59. Example 9 1000.000 1000.000

60. Example 9 - Answer 1000.000 1000.000 Rule 1 – 1 sig dig non-zero number Rule 1 – 1 sig dig non-zero number

61. Example 9 - Answer 1000.000 1000.000 Rule 1 – 1 sig dig non-zero number Rule 1 – 1 sig dig non-zero number Rule 2 – 0 sig digs trapped zeros Rule 2 – 0 sig digs trapped zeros

62. Example 9 - Answer 1000.000 1000.000 Rule 1 – 1 sig dig non-zero number Rule 1 – 1 sig dig non-zero number Rule 2 – 0 sig digs trapped zeros Rule 2 – 0 sig digs trapped zeros Rule 3 – 6 ending zeros Rule 3 – 6 ending zeros

63. Example 9 - Answer 1000.000 1000.000 Rule 1 – 1 sig dig non-zero number Rule 1 – 1 sig dig non-zero number Rule 2 – 0 sig digs trapped zeros Rule 2 – 0 sig digs trapped zeros Rule 3 – 6 sig digs ending zeros with decimal point shown Rule 3 – 6 sig digs ending zeros with decimal point shown

64. Example 9 - Answer 1000.000 1000.000 Rule 1 – 1 sig dig non-zero number Rule 1 – 1 sig dig non-zero number Rule 2 – 0 sig digs trapped zeros Rule 2 – 0 sig digs trapped zeros Rule 3 – 6 sig digs ending zeros with decimal point shown Rule 3 – 6 sig digs ending zeros with decimal point shown Rule 4 – 0 leading zeros Rule 4 – 0 leading zeros

65. Example 9 - Answer 1000.000 1000.000 Rule 1 – 1 sig dig non-zero number Rule 1 – 1 sig dig non-zero number Rule 2 – 0 sig digs trapped zeros Rule 2 – 0 sig digs trapped zeros Rule 3 – 6 sig digs ending zeros with decimal point shown Rule 3 – 6 sig digs ending zeros with decimal point shown Rule 4 – 0 leading zeros Rule 4 – 0 leading zeros 7 significant digits 7 significant digits

66. Example 10 1136 1136

67. Example 10 - Answer 1136 1136 Rule 1 – 4 sig digs non-zero numbers Rule 1 – 4 sig digs non-zero numbers

68. Example 10 - Answer 1136 1136 Rule 1 – 4 sig digs non-zero numbers Rule 1 – 4 sig digs non-zero numbers Rule 2 – 0 sig digs trapped zeros Rule 2 – 0 sig digs trapped zeros

69. Example 10 - Answer 1136 1136 Rule 1 – 4 sig digs non-zero numbers Rule 1 – 4 sig digs non-zero numbers Rule 2 – 0 sig digs trapped zeros Rule 2 – 0 sig digs trapped zeros Rule 3 – 0 ending zeros Rule 3 – 0 ending zeros

70. Example 10 - Answer 1136 1136 Rule 1 – 4 sig digs non-zero numbers Rule 1 – 4 sig digs non-zero numbers Rule 2 – 0 sig digs trapped zeros Rule 2 – 0 sig digs trapped zeros Rule 3 – 0 ending zeros (Decimal point is NOT shown) Rule 3 – 0 ending zeros (Decimal point is NOT shown)

71. Example 10 - Answer 1136 1136 Rule 1 – 4 sig digs non-zero numbers Rule 1 – 4 sig digs non-zero numbers Rule 2 – 0 sig digs trapped zeros Rule 2 – 0 sig digs trapped zeros Rule 3 – 0 ending zeros Rule 3 – 0 ending zeros Rule 4 – 0 leading zeros Rule 4 – 0 leading zeros

72. Example 10 - Answer 1136 1136 Rule 1 – 4 sig digs non-zero numbers Rule 1 – 4 sig digs non-zero numbers Rule 2 – 0 sig digs trapped zeros Rule 2 – 0 sig digs trapped zeros Rule 3 – 0 ending zeros Rule 3 – 0 ending zeros Rule 4 – 0 leading zeros Rule 4 – 0 leading zeros 4 significant digits 4 significant digits

73. Extra Practice 1. 20 2. 20. 3. 101 4. 0.0071 5. 3333 6. 4567. 7. 1001. 8. 0.00005 9. 21 10. 1000 11. 1010 12. 1550 13. 0.0010790 14. 9999990 15. 1 16. 5. 17. 90000009 18. 0.91000270

74. Extra Practice Answers 1. 1 2. 2 3. 3 4. 2 5. 4 6. 4 7. 4 8. 1 9. 2 10. 1 11. 3 12. 3 13. 5 14. 6 15. 1 16. 1 17. 8 18. 8