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Significant Digits

Significant Digits. By Michelle Lamary and Caitlin Ostrowski. Counting Significant Digit Rules. All non-zero digits are significant (725 , 2, 12) Trapped zeros are significant (101, 2003) Ending zeros are significant only if the decimal point can be seen ( 100. , 1.10, 100, 20 )

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Significant Digits

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  1. Significant Digits By Michelle Lamary and Caitlin Ostrowski

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

  3. Example 1 • 401700.0900

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

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

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

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

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

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

  10. Example 2 • 0.007050

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

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

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

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

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

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

  17. Example 3 • 700.

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

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

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

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

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

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

  24. Example 4 • 8500

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

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

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

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

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

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

  31. Example 5 • 8500.

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

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

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

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

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

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

  38. Example 6 • 0.0000001

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

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

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

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

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

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

  45. Example 7 • 200009

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

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

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

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

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

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