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Significant Digits Notes

Significant Digits Notes. You will need your own paper. Purpose: Significant digits (or significant figures) is a communication tool to express where you rounded any particular number. Question (do not need to copy): If you won one million dollars, where would you want that rounded?

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Significant Digits Notes

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  1. Significant Digits Notes You will need your own paper

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

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

  4. The Four Rules for Significant Digits:

  5. The Four Rules for Significant Digits: 1) All nonzero digits are significant

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

  21. Significant Digits Practice

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

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

  24. How many Significant Digits is in: 84.10

  25. How many Significant Digits is in: 84.10 4

  26. How many Significant Digits is in: 0.039100

  27. How many Significant Digits is in: 0.039100 5

  28. How many Significant Digits is in: 77.6670

  29. How many Significant Digits is in: 77.6670 6

  30. How many Significant Digits is in: 0.060

  31. How many Significant Digits is in: 0.060 2

  32. How many Significant Digits is in: 78000

  33. How many Significant Digits is in: 78000 2

  34. How many Significant Digits is in: 8.52800

  35. How many Significant Digits is in: 8.52800 6

  36. How many Significant Digits is in: 0.00090

  37. How many Significant Digits is in: 0.00090 2

  38. How many Significant Digits is in: 0.006

  39. How many Significant Digits is in: 0.006 1

  40. How many Significant Digits is in: 7080

  41. How many Significant Digits is in: 7080 3

  42. How many Significant Digits is in: 30050

  43. How many Significant Digits is in: 30050 4

  44. How many Significant Digits is in: 0.0206

  45. How many Significant Digits is in: 0.0206 3

  46. How many Significant Digits is in: 4000400

  47. How many Significant Digits is in: 4000400 5

  48. How many Significant Digits is in: 9200001

  49. How many Significant Digits is in: 9200001 7

  50. How many Significant Digits is in: 600.00

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