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

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