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Math1003 1.13 - Significant Digits, Accuracy, Precision

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Math1003 1.13 - Significant Digits, Accuracy, Precision

1. 1. 1.1310110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001 Signiﬁcant Digits, Accuracy, and Precision MATH1003
2. 2. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001 Goal To be able to deﬁne the concepts of signiﬁcant digits, accuracy, and precision with respect to numbers. MATH1003
3. 3. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001 Signiﬁcant Digits “A crowd of 7,000 people had gathered to watch the parade.” MATH1003
4. 4. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001 Signiﬁcant Digits “They planted 2,124 daffodils this year.” MATH1003
5. 5. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001 Signiﬁcant Digits 7000 2214 The number of important, or “signiﬁcant,” digits in these numbers are different. MATH1003
6. 6. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001 Signiﬁcant Digits 7000 2214 In 7000, there is only one signiﬁcant digit. MATH1003
7. 7. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001 Signiﬁcant Digits 7000 2214 In 7000, there is only one signiﬁcant digit. MATH1003
8. 8. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001 Signiﬁcant Digits 7000 2214 In 7000, there is only one signiﬁcant digit. In 2214, there are four signiﬁcant digits. MATH1003
9. 9. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001 Signiﬁcant Digits MATH1003
10. 10. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001 Signiﬁcant Digits Rules MATH1003
11. 11. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001 Signiﬁcant Digits Rules ❖ All non-zero digits are signiﬁcant. MATH1003
12. 12. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001 Signiﬁcant Digits Rules ❖ All non-zero digits are signiﬁcant. ❖ Zero (0) is a signiﬁcant digit if it is between two signiﬁcant digits. MATH1003
13. 13. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001 Signiﬁcant Digits Rules ❖ All non-zero digits are signiﬁcant. ❖ Zero (0) is a signiﬁcant digit if it is between two signiﬁcant digits. ❖ Leading 0s are not signiﬁcant. MATH1003
14. 14. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001 Signiﬁcant Digits Rules ❖ All non-zero digits are signiﬁcant. ❖ Zero (0) is a signiﬁcant digit if it is between two signiﬁcant digits. ❖ Leading 0s are not signiﬁcant. ❖ Trailing 0s are signiﬁcant only if the number contains a decimal point. MATH1003
15. 15. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001 Signiﬁcant Digits Rules ❖ All non-zero digits are signiﬁcant. ❖ Zero (0) is a signiﬁcant digit if it is between two signiﬁcant digits. ❖ Leading 0s are not signiﬁcant. ❖ Trailing 0s are signiﬁcant only if the number contains a decimal point. MATH1003
16. 16. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001 Signiﬁcant Digits 527 Rules ❖ All non-zero digits are signiﬁcant. ❖ Zero (0) is a signiﬁcant digit if it is between two signiﬁcant digits. ❖ Leading 0s are not signiﬁcant. ❖ Trailing 0s are signiﬁcant only if the number contains a decimal point. MATH1003
17. 17. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001 Signiﬁcant Digits 527 Rules ❖ All non-zero digits are signiﬁcant. ❖ Zero (0) is a signiﬁcant digit if it is between two signiﬁcant digits. ❖ Leading 0s are not signiﬁcant. ❖ Trailing 0s are signiﬁcant only if the number contains a decimal point. MATH1003
18. 18. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001 Signiﬁcant Digits 527 527 has 3 signiﬁcant digits Rules ❖ All non-zero digits are signiﬁcant. ❖ Zero (0) is a signiﬁcant digit if it is between two signiﬁcant digits. ❖ Leading 0s are not signiﬁcant. ❖ Trailing 0s are signiﬁcant only if the number contains a decimal point. MATH1003
19. 19. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001 Signiﬁcant Digits 527 527 has 3 signiﬁcant digits Rules ❖ All non-zero digits are signiﬁcant. ❖ Zero (0) is a signiﬁcant digit if it is between two signiﬁcant digits. ❖ Leading 0s are not signiﬁcant. ❖ Trailing 0s are signiﬁcant only if the number contains a decimal point. MATH1003
20. 20. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001 Signiﬁcant Digits 527 527 has 3 signiﬁcant digits Rules ❖ All non-zero digits are signiﬁcant. ❖ Zero (0) is a signiﬁcant digit if it is between two signiﬁcant digits. ❖ Leading 0s are not signiﬁcant. ❖ Trailing 0s are signiﬁcant only if the number contains a decimal point. MATH1003
21. 21. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001 Signiﬁcant Digits 527 527 has 3 signiﬁcant digits Rules ❖ All non-zero digits are signiﬁcant. ❖ Zero (0) is a signiﬁcant digit if it is between two signiﬁcant digits. ❖ Leading 0s are not signiﬁcant. ❖ Trailing 0s are signiﬁcant only if the number contains a decimal point. MATH1003
22. 22. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001 Signiﬁcant Digits -5,032 Rules ❖ All non-zero digits are signiﬁcant. ❖ Zero (0) is a signiﬁcant digit if it is between two signiﬁcant digits. ❖ Leading 0s are not signiﬁcant. ❖ Trailing 0s are signiﬁcant only if the number contains a decimal point. MATH1003
23. 23. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001 Signiﬁcant Digits -5,032 Rules ❖ All non-zero digits are signiﬁcant. ❖ Zero (0) is a signiﬁcant digit if it is between two signiﬁcant digits. ❖ Leading 0s are not signiﬁcant. ❖ Trailing 0s are signiﬁcant only if the number contains a decimal point. MATH1003
24. 24. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001 Signiﬁcant Digits -5,032 -5,032 has 4 signiﬁcant digits Rules ❖ All non-zero digits are signiﬁcant. ❖ Zero (0) is a signiﬁcant digit if it is between two signiﬁcant digits. ❖ Leading 0s are not signiﬁcant. ❖ Trailing 0s are signiﬁcant only if the number contains a decimal point. MATH1003
25. 25. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001 Signiﬁcant Digits -5,032 -5,032 has 4 signiﬁcant digits Rules ❖ All non-zero digits are signiﬁcant. ❖ Zero (0) is a signiﬁcant digit if it is between two signiﬁcant digits. ❖ Leading 0s are not signiﬁcant. ❖ Trailing 0s are signiﬁcant only if the number contains a decimal point. MATH1003
26. 26. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001 Signiﬁcant Digits -5,032 -5,032 has 4 signiﬁcant digits Rules ❖ All non-zero digits are signiﬁcant. ❖ Zero (0) is a signiﬁcant digit if it is between two signiﬁcant digits. ❖ Leading 0s are not signiﬁcant. ❖ Trailing 0s are signiﬁcant only if the number contains a decimal point. MATH1003
27. 27. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001 Signiﬁcant Digits -5,032 -5,032 has 4 signiﬁcant digits Rules ❖ All non-zero digits are signiﬁcant. ❖ Zero (0) is a signiﬁcant digit if it is between two signiﬁcant digits. ❖ Leading 0s are not signiﬁcant. ❖ Trailing 0s are signiﬁcant only if the number contains a decimal point. MATH1003
28. 28. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001 Signiﬁcant Digits -5,032 -5,032 has 4 signiﬁcant digits Rules ❖ All non-zero digits are signiﬁcant. ❖ Zero (0) is a signiﬁcant digit if it is between two signiﬁcant digits. ❖ Leading 0s are not signiﬁcant. ❖ Trailing 0s are signiﬁcant only if the number contains a decimal point. MATH1003
29. 29. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001 Signiﬁcant Digits 3.68 Rules ❖ All non-zero digits are signiﬁcant. ❖ Zero (0) is a signiﬁcant digit if it is between two signiﬁcant digits. ❖ Leading 0s are not signiﬁcant. ❖ Trailing 0s are signiﬁcant only if the number contains a decimal point. MATH1003
30. 30. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001 Signiﬁcant Digits 3.68 Rules ❖ All non-zero digits are signiﬁcant. ❖ Zero (0) is a signiﬁcant digit if it is between two signiﬁcant digits. ❖ Leading 0s are not signiﬁcant. ❖ Trailing 0s are signiﬁcant only if the number contains a decimal point. MATH1003
31. 31. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001 Signiﬁcant Digits 3.68 3.68 has 3 signiﬁcant digits Rules ❖ All non-zero digits are signiﬁcant. ❖ Zero (0) is a signiﬁcant digit if it is between two signiﬁcant digits. ❖ Leading 0s are not signiﬁcant. ❖ Trailing 0s are signiﬁcant only if the number contains a decimal point. MATH1003
32. 32. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001 Signiﬁcant Digits 3.68 3.68 has 3 signiﬁcant digits Rules ❖ All non-zero digits are signiﬁcant. ❖ Zero (0) is a signiﬁcant digit if it is between two signiﬁcant digits. ❖ Leading 0s are not signiﬁcant. ❖ Trailing 0s are signiﬁcant only if the number contains a decimal point. MATH1003
33. 33. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001 Signiﬁcant Digits 3.68 3.68 has 3 signiﬁcant digits Rules ❖ All non-zero digits are signiﬁcant. ❖ Zero (0) is a signiﬁcant digit if it is between two signiﬁcant digits. ❖ Leading 0s are not signiﬁcant. ❖ Trailing 0s are signiﬁcant only if the number contains a decimal point. MATH1003
34. 34. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001 Signiﬁcant Digits 3.68 3.68 has 3 signiﬁcant digits Rules ❖ All non-zero digits are signiﬁcant. ❖ Zero (0) is a signiﬁcant digit if it is between two signiﬁcant digits. ❖ Leading 0s are not signiﬁcant. ❖ Trailing 0s are signiﬁcant only if the number contains a decimal point. MATH1003
35. 35. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001 Signiﬁcant Digits -0.0019 Rules ❖ All non-zero digits are signiﬁcant. ❖ Zero (0) is a signiﬁcant digit if it is between two signiﬁcant digits. ❖ Leading 0s are not signiﬁcant. ❖ Trailing 0s are signiﬁcant only if the number contains a decimal point. MATH1003
36. 36. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001 Signiﬁcant Digits -0.0019 Rules ❖ All non-zero digits are signiﬁcant. ❖ Zero (0) is a signiﬁcant digit if it is between two signiﬁcant digits. ❖ Leading 0s are not signiﬁcant. ❖ Trailing 0s are signiﬁcant only if the number contains a decimal point. MATH1003
37. 37. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001 Signiﬁcant Digits -0.0019 -0.0019 has 2 signiﬁcant digits Rules ❖ All non-zero digits are signiﬁcant. ❖ Zero (0) is a signiﬁcant digit if it is between two signiﬁcant digits. ❖ Leading 0s are not signiﬁcant. ❖ Trailing 0s are signiﬁcant only if the number contains a decimal point. MATH1003
38. 38. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001 Signiﬁcant Digits -0.0019 -0.0019 has 2 signiﬁcant digits Rules ❖ All non-zero digits are signiﬁcant. ❖ Zero (0) is a signiﬁcant digit if it is between two signiﬁcant digits. ❖ Leading 0s are not signiﬁcant. ❖ Trailing 0s are signiﬁcant only if the number contains a decimal point. MATH1003
39. 39. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001 Signiﬁcant Digits -0.0019 -0.0019 has 2 signiﬁcant digits Rules ❖ All non-zero digits are signiﬁcant. ❖ Zero (0) is a signiﬁcant digit if it is between two signiﬁcant digits. ❖ Leading 0s are not signiﬁcant. ❖ Trailing 0s are signiﬁcant only if the number contains a decimal point. MATH1003
40. 40. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001 Signiﬁcant Digits 15,009 Rules ❖ All non-zero digits are signiﬁcant. ❖ Zero (0) is a signiﬁcant digit if it is between two signiﬁcant digits. ❖ Leading 0s are not signiﬁcant. ❖ Trailing 0s are signiﬁcant only if the number contains a decimal point. MATH1003
41. 41. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001 Signiﬁcant Digits 15,009 Rules ❖ All non-zero digits are signiﬁcant. ❖ Zero (0) is a signiﬁcant digit if it is between two signiﬁcant digits. ❖ Leading 0s are not signiﬁcant. ❖ Trailing 0s are signiﬁcant only if the number contains a decimal point. MATH1003
42. 42. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001 Signiﬁcant Digits 15,009 15,009 has 5 signiﬁcant digits Rules ❖ All non-zero digits are signiﬁcant. ❖ Zero (0) is a signiﬁcant digit if it is between two signiﬁcant digits. ❖ Leading 0s are not signiﬁcant. ❖ Trailing 0s are signiﬁcant only if the number contains a decimal point. MATH1003
43. 43. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001 Signiﬁcant Digits 15,009 15,009 has 5 signiﬁcant digits Rules ❖ All non-zero digits are signiﬁcant. ❖ Zero (0) is a signiﬁcant digit if it is between two signiﬁcant digits. ❖ Leading 0s are not signiﬁcant. ❖ Trailing 0s are signiﬁcant only if the number contains a decimal point. MATH1003
44. 44. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001 Signiﬁcant Digits 15,009 15,009 has 5 signiﬁcant digits Rules ❖ All non-zero digits are signiﬁcant. ❖ Zero (0) is a signiﬁcant digit if it is between two signiﬁcant digits. ❖ Leading 0s are not signiﬁcant. ❖ Trailing 0s are signiﬁcant only if the number contains a decimal point. MATH1003
45. 45. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001 Signiﬁcant Digits 15,009 15,009 has 5 signiﬁcant digits Rules ❖ All non-zero digits are signiﬁcant. ❖ Zero (0) is a signiﬁcant digit if it is between two signiﬁcant digits. ❖ Leading 0s are not signiﬁcant. ❖ Trailing 0s are signiﬁcant only if the number contains a decimal point. MATH1003
46. 46. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001 Signiﬁcant Digits 15,009 15,009 has 5 signiﬁcant digits Rules ❖ All non-zero digits are signiﬁcant. ❖ Zero (0) is a signiﬁcant digit if it is between two signiﬁcant digits. ❖ Leading 0s are not signiﬁcant. ❖ Trailing 0s are signiﬁcant only if the number contains a decimal point. MATH1003
47. 47. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001 Signiﬁcant Digits 15,009 15,009 has 5 signiﬁcant digits Rules ❖ All non-zero digits are signiﬁcant. ❖ Zero (0) is a signiﬁcant digit if it is between two signiﬁcant digits. ❖ Leading 0s are not signiﬁcant. ❖ Trailing 0s are signiﬁcant only if the number contains a decimal point. MATH1003
48. 48. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001 Signiﬁcant Digits 23.004 Rules ❖ All non-zero digits are signiﬁcant. ❖ Zero (0) is a signiﬁcant digit if it is between two signiﬁcant digits. ❖ Leading 0s are not signiﬁcant. ❖ Trailing 0s are signiﬁcant only if the number contains a decimal point. MATH1003
49. 49. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001 Signiﬁcant Digits 23.004 Rules ❖ All non-zero digits are signiﬁcant. ❖ Zero (0) is a signiﬁcant digit if it is between two signiﬁcant digits. ❖ Leading 0s are not signiﬁcant. ❖ Trailing 0s are signiﬁcant only if the number contains a decimal point. MATH1003
50. 50. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001 Signiﬁcant Digits 23.004 23.004 has 5 signiﬁcant digits Rules ❖ All non-zero digits are signiﬁcant. ❖ Zero (0) is a signiﬁcant digit if it is between two signiﬁcant digits. ❖ Leading 0s are not signiﬁcant. ❖ Trailing 0s are signiﬁcant only if the number contains a decimal point. MATH1003
51. 51. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001 Signiﬁcant Digits 23.004 23.004 has 5 signiﬁcant digits Rules ❖ All non-zero digits are signiﬁcant. ❖ Zero (0) is a signiﬁcant digit if it is between two signiﬁcant digits. ❖ Leading 0s are not signiﬁcant. ❖ Trailing 0s are signiﬁcant only if the number contains a decimal point. MATH1003
52. 52. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001 Signiﬁcant Digits 23.004 23.004 has 5 signiﬁcant digits Rules ❖ All non-zero digits are signiﬁcant. ❖ Zero (0) is a signiﬁcant digit if it is between two signiﬁcant digits. ❖ Leading 0s are not signiﬁcant. ❖ Trailing 0s are signiﬁcant only if the number contains a decimal point. MATH1003
53. 53. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001 Signiﬁcant Digits 23.004 23.004 has 5 signiﬁcant digits Rules ❖ All non-zero digits are signiﬁcant. ❖ Zero (0) is a signiﬁcant digit if it is between two signiﬁcant digits. ❖ Leading 0s are not signiﬁcant. ❖ Trailing 0s are signiﬁcant only if the number contains a decimal point. MATH1003
54. 54. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001 Signiﬁcant Digits 23.004 23.004 has 5 signiﬁcant digits Rules ❖ All non-zero digits are signiﬁcant. ❖ Zero (0) is a signiﬁcant digit if it is between two signiﬁcant digits. ❖ Leading 0s are not signiﬁcant. ❖ Trailing 0s are signiﬁcant only if the number contains a decimal point. MATH1003
55. 55. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001 Signiﬁcant Digits 23.004 23.004 has 5 signiﬁcant digits Rules ❖ All non-zero digits are signiﬁcant. ❖ Zero (0) is a signiﬁcant digit if it is between two signiﬁcant digits. ❖ Leading 0s are not signiﬁcant. ❖ Trailing 0s are signiﬁcant only if the number contains a decimal point. MATH1003
56. 56. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001 Signiﬁcant Digits -27,500 Rules ❖ All non-zero digits are signiﬁcant. ❖ Zero (0) is a signiﬁcant digit if it is between two signiﬁcant digits. ❖ Leading 0s are not signiﬁcant. ❖ Trailing 0s are signiﬁcant only if the number contains a decimal point. MATH1003
57. 57. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001 Signiﬁcant Digits -27,500 Rules ❖ All non-zero digits are signiﬁcant. ❖ Zero (0) is a signiﬁcant digit if it is between two signiﬁcant digits. ❖ Leading 0s are not signiﬁcant. ❖ Trailing 0s are signiﬁcant only if the number contains a decimal point. MATH1003
58. 58. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001 Signiﬁcant Digits -27,500 -27,500 has 3 signiﬁcant digits Rules ❖ All non-zero digits are signiﬁcant. ❖ Zero (0) is a signiﬁcant digit if it is between two signiﬁcant digits. ❖ Leading 0s are not signiﬁcant. ❖ Trailing 0s are signiﬁcant only if the number contains a decimal point. MATH1003
59. 59. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001 Signiﬁcant Digits -27,500 -27,500 has 3 signiﬁcant digits Rules ❖ All non-zero digits are signiﬁcant. ❖ Zero (0) is a signiﬁcant digit if it is between two signiﬁcant digits. ❖ Leading 0s are not signiﬁcant. ❖ Trailing 0s are signiﬁcant only if the number contains a decimal point. MATH1003
60. 60. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001 Signiﬁcant Digits -27,500 -27,500 has 3 signiﬁcant digits Rules ❖ All non-zero digits are signiﬁcant. ❖ Zero (0) is a signiﬁcant digit if it is between two signiﬁcant digits. ❖ Leading 0s are not signiﬁcant. ❖ Trailing 0s are signiﬁcant only if the number contains a decimal point. MATH1003
61. 61. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001 Signiﬁcant Digits -27,500 -27,500 has 3 signiﬁcant digits Rules ❖ All non-zero digits are signiﬁcant. ❖ Zero (0) is a signiﬁcant digit if it is between two signiﬁcant digits. ❖ Leading 0s are not signiﬁcant. ❖ Trailing 0s are signiﬁcant only if the number contains a decimal point. MATH1003
62. 62. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001 Signiﬁcant Digits 3,000.00 Rules ❖ All non-zero digits are signiﬁcant. ❖ Zero (0) is a signiﬁcant digit if it is between two signiﬁcant digits. ❖ Leading 0s are not signiﬁcant. ❖ Trailing 0s are signiﬁcant only if the number contains a decimal point. MATH1003
63. 63. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001 Signiﬁcant Digits 3,000.00 Rules ❖ All non-zero digits are signiﬁcant. ❖ Zero (0) is a signiﬁcant digit if it is between two signiﬁcant digits. ❖ Leading 0s are not signiﬁcant. ❖ Trailing 0s are signiﬁcant only if the number contains a decimal point. MATH1003
64. 64. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001 Signiﬁcant Digits 3,000.00 3,000.00 has 6 signiﬁcant digits Rules ❖ All non-zero digits are signiﬁcant. ❖ Zero (0) is a signiﬁcant digit if it is between two signiﬁcant digits. ❖ Leading 0s are not signiﬁcant. ❖ Trailing 0s are signiﬁcant only if the number contains a decimal point. MATH1003
65. 65. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001 Signiﬁcant Digits 3,000.00 3,000.00 has 6 signiﬁcant digits Rules ❖ All non-zero digits are signiﬁcant. ❖ Zero (0) is a signiﬁcant digit if it is between two signiﬁcant digits. ❖ Leading 0s are not signiﬁcant. ❖ Trailing 0s are signiﬁcant only if the number contains a decimal point. MATH1003
66. 66. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001 Signiﬁcant Digits 3,000.00 3,000.00 has 6 signiﬁcant digits Rules ❖ All non-zero digits are signiﬁcant. ❖ Zero (0) is a signiﬁcant digit if it is between two signiﬁcant digits. ❖ Leading 0s are not signiﬁcant. ❖ Trailing 0s are signiﬁcant only if the number contains a decimal point. MATH1003
67. 67. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001 Signiﬁcant Digits 3,000.00 3,000.00 has 6 signiﬁcant digits Rules ❖ All non-zero digits are signiﬁcant. ❖ Zero (0) is a signiﬁcant digit if it is between two signiﬁcant digits. ❖ Leading 0s are not signiﬁcant. ❖ Trailing 0s are signiﬁcant only if the number contains a decimal point. MATH1003
68. 68. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001 Signiﬁcant Digits 3,000.00 3,000.00 has 6 signiﬁcant digits Rules ❖ All non-zero digits are signiﬁcant. ❖ Zero (0) is a signiﬁcant digit if it is between two signiﬁcant digits. ❖ Leading 0s are not signiﬁcant. ❖ Trailing 0s are signiﬁcant only if the number contains a decimal point. MATH1003
69. 69. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001 Signiﬁcant Digits 3,000.00 3,000.00 has 6 signiﬁcant digits Rules ❖ All non-zero digits are signiﬁcant. ❖ Zero (0) is a signiﬁcant digit if it is between two signiﬁcant digits. ❖ Leading 0s are not signiﬁcant. ❖ Trailing 0s are signiﬁcant only if the number contains a decimal point. MATH1003
70. 70. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001 Signiﬁcant Digits 3,000.00 3,000.00 has 6 signiﬁcant digits Rules ❖ All non-zero digits are signiﬁcant. ❖ Zero (0) is a signiﬁcant digit if it is between two signiﬁcant digits. ❖ Leading 0s are not signiﬁcant. ❖ Trailing 0s are signiﬁcant only if the number contains a decimal point. MATH1003
71. 71. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001 Accuracy MATH1003
72. 72. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001 Accuracy Deﬁnition The accuracy of a number is the number of signiﬁcant digits in the number. MATH1003
73. 73. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001 Accuracy Deﬁnition The accuracy of a number is the number of signiﬁcant digits in the number. 3.02 MATH1003
74. 74. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001 Accuracy Deﬁnition Definition The accuracy of a number is the number of signiﬁcant digits in the number. 3.02 This number is accurate to 3 signiﬁcant digits. MATH1003
75. 75. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001 Accuracy Deﬁnition Definition The accuracy of a number is the number of signiﬁcant digits in the number. MATH1003
76. 76. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001 Accuracy Deﬁnition Definition The accuracy of a number is the number of signiﬁcant digits in the number. -1,470 MATH1003
77. 77. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001 Accuracy Deﬁnition Definition The accuracy of a number is the number of signiﬁcant digits in the number. -1,470 This number is accurate to 3 signiﬁcant digits. MATH1003
78. 78. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001 Precision MATH1003
79. 79. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001 Precision Deﬁnition The precision of a number is the place value of the rightmost signiﬁcant digit. MATH1003
80. 80. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001 Precision Deﬁnition The precision of a number is the place value of the rightmost signiﬁcant digit. 3.02 MATH1003
81. 81. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001 Precision Deﬁnition Definition The precision of a number is the place value of the rightmost signiﬁcant digit. 3.02 This number has a precision of 0.01 MATH1003
82. 82. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001 Precision Deﬁnition Definition The precision of a number is the place value of the rightmost signiﬁcant digit. 3.02 This number has a precision of 0.01 MATH1003
83. 83. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001 Precision Deﬁnition Definition The precision of a number is the place value of the rightmost signiﬁcant digit. -1,470 MATH1003
84. 84. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001 Precision Deﬁnition Definition The precision of a number is the place value of the rightmost signiﬁcant digit. -1,470 This number has a precision of 10 MATH1003
85. 85. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001 Precision Deﬁnition Definition The precision of a number is the place value of the rightmost signiﬁcant digit. -1,470 This number has a precision of 10 MATH1003
86. 86. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001 Precision Deﬁnition Definition The precision of a number is the place value of the rightmost signiﬁcant digit. -0.006043 MATH1003
87. 87. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001 Precision Deﬁnition Definition The precision of a number is the place value of the rightmost signiﬁcant digit. -0.006043 This number has a precision of 0.000001 or 10-6 MATH1003
88. 88. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001 Precision Deﬁnition Definition The precision of a number is the place value of the rightmost signiﬁcant digit. -0.006043 This number has a precision of 0.000001 or 10-6 MATH1003
89. 89. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001 Exercises MATH1003
90. 90. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001 Exercises On Monday, the Canadian dollar was trading against the US dollar at 0.9985 MATH1003
91. 91. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001 Exercises On Monday, the Canadian dollar was trading against the US dollar at 0.9985 What is the accuracy and precision of the exchange rate? Accuracy ______ Precision ________________________ MATH1003
92. 92. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001 Exercises On Monday, the Canadian dollar was trading against the US dollar at 0.9985 What is the accuracy and precision of the exchange rate? Accuracy ______ Precision ________________________ MATH1003
93. 93. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001 Exercises On Monday, the Canadian dollar was trading against the US dollar at 0.9985 What is the accuracy and precision of the exchange rate? 4 Accuracy ______ Precision ________________________ MATH1003
94. 94. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001 Exercises On Monday, the Canadian dollar was trading against the US dollar at 0.9985 What is the accuracy and precision of the exchange rate? 4 Accuracy ______ Precision ________________________ MATH1003
95. 95. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001 Exercises On Monday, the Canadian dollar was trading against the US dollar at 0.9985 What is the accuracy and precision of the exchange rate? 4 Accuracy ______ Precision ________________________ -4 .0001 or 10 MATH1003
96. 96. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001 Exercises MATH1003
97. 97. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001 Exercises On this sign, it is posted that the population of Toronto is 2,482,000 MATH1003
98. 98. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001 Exercises On this sign, it is posted that the population of Toronto is 2,482,000 What is the accuracy and precision of the polpulation count? Accuracy ______ Precision ________________________ MATH1003
99. 99. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001 Exercises On this sign, it is posted that the population of Toronto is 2,482,000 What is the accuracy and precision of the polpulation count? Accuracy ______ Precision ________________________ MATH1003
100. 100. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001 Exercises On this sign, it is posted that the population of Toronto is 2,482,000 What is the accuracy and precision of the polpulation count? 4 Accuracy ______ Precision ________________________ MATH1003
101. 101. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001 Exercises On this sign, it is posted that the population of Toronto is 2,482,000 What is the accuracy and precision of the polpulation count? 4 Accuracy ______ Precision ________________________ MATH1003
102. 102. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001 Exercises On this sign, it is posted that the population of Toronto is 2,482,000 What is the accuracy and precision of the polpulation count? 4 Accuracy ______ Precision ________________________ 3 1000 or 10 MATH1003
103. 103. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001 Exercises MATH1003
104. 104. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001 Exercises The distance between Toronto, Canada and Dublin, Ireland is 5300 kilometers MATH1003
105. 105. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001 Exercises The distance between Toronto, Canada and Dublin, Ireland is 5300 kilometers MATH1003
106. 106. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001 Exercises The distance between Toronto, Canada and Dublin, Ireland is 5300 kilometers MATH1003
107. 107. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001 Exercises The distance between Toronto, Canada and Dublin, Ireland is 5300 kilometers What is the accuracy and precision of the distance? Accuracy ______ Precision ________________________ MATH1003
108. 108. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001 Exercises The distance between Toronto, Canada and Dublin, Ireland is 5300 kilometers What is the accuracy and precision of the distance? Accuracy ______ Precision ________________________ MATH1003
109. 109. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001 Exercises The distance between Toronto, Canada and Dublin, Ireland is 5300 kilometers What is the accuracy and precision of the distance? 2 Accuracy ______ Precision ________________________ MATH1003
110. 110. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001 Exercises The distance between Toronto, Canada and Dublin, Ireland is 5300 kilometers What is the accuracy and precision of the distance? 2 Accuracy ______ Precision ________________________ MATH1003
111. 111. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001 Exercises The distance between Toronto, Canada and Dublin, Ireland is 5300 kilometers What is the accuracy and precision of the distance? 2 Accuracy ______ Precision ________________________ 2 100 or 10 MATH1003
112. 112. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001 Exercises MATH1003
113. 113. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001 Exercises In a previous federal election, the percentage of registered voters that voted was 64.9 MATH1003
114. 114. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001 Exercises In a previous federal election, the percentage of registered voters that voted was 64.9 What is the accuracy and precision of the percentage? Accuracy ______ Precision ________________________ MATH1003
115. 115. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001 Exercises In a previous federal election, the percentage of registered voters that voted was 64.9 What is the accuracy and precision of the percentage? Accuracy ______ Precision ________________________ MATH1003
116. 116. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001 Exercises In a previous federal election, the percentage of registered voters that voted was 64.9 What is the accuracy and precision of the percentage? 3 Accuracy ______ Precision ________________________ MATH1003
117. 117. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001 Exercises In a previous federal election, the percentage of registered voters that voted was 64.9 What is the accuracy and precision of the percentage? 3 Accuracy ______ Precision ________________________ MATH1003
118. 118. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001 Exercises In a previous federal election, the percentage of registered voters that voted was 64.9 What is the accuracy and precision of the percentage? 3 Accuracy ______ Precision ________________________ -1 0.1 or 10 MATH1003