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SIGNIFICANT DIGITS

SIGNIFICANT DIGITS. We’ll call them “S.D.’s” for short. Why Use Them??. To show how precise our instruments are. Whatever you measure you must estimate 1 decimal place past what you measure Represent the uncertainty of a piece of equipment by using + or –

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SIGNIFICANT DIGITS

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  1. SIGNIFICANT DIGITS We’ll call them “S.D.’s” for short

  2. Why Use Them??

  3. To show how precise our instruments are

  4. Whatever you measure you must estimate 1 decimal place past what you measure • Represent the uncertainty of a piece of equipment by using + or – • Read what the ruler/graduated beaker says and estimate 1 number past the marking

  5. The following types of digits are considered significant: • any non-zero number…for example, 562 this number has 3 S.D.’s • all zeros between 2 other S.D.’s…for example, 5006 this number has 4 S.D.’s • If there is a decimal, any zero that follows the last nonzero number…for example 560.0 this number has 4 S.D.’s

  6. The following types of digits arenot considered significant • If there is no decimal point, any zero following the last nonzero digit is not significant…for example, 9050 this number has 3 S.D.’s • all zeros appearing in front of the first nonzero digit…for example, .0091 this number has 2 S.D.’s

  7. Now we can do mathematical operations the RIGHT WAY!!

  8. ADDITION AND SUBTRACTION • Consider the following problem 5.0 + 15.5 + 20.25 = ??? • After you read the problem, do the addition (or subtraction) like you normally would. • Write down the entire answer from your calculator you should have gotten 40.75

  9. ADDITION AND SUBTRACTION • WE ARE NOT DONE!!!! • Decide which was the LEAST PRECISE number in the problem That would be the 5.0 OR the 15.5…..both go to the tenths place • For +/-, the answer goes to the same place!! • 40.75 must go to the tenths……it becomes • 40.8

  10. Whew….DONE!!!

  11. Not Exactly…..

  12. MULTIPLICATION AND DIVISION • Consider the following problem 562 x .0095 = ??? • After you read the problem, do the multiplication (or division) like you normally would. • Write down the entire answer from your calculator you should have gotten 5.339

  13. MULTIPLICATION AND DIVISION • WE ARE NOT DONE!!!! • Decide which number in the problem had the LEAST NUMBER OF S.D.’s That would be the .0095 -- it only has 2 • For * or /, the answer has the same number of S.D.’s as the number in the problem with the fewest S.D.’s!! • 5.339 can only have 2 S.D.’s…it becomes • 5.3

  14. Rounding Off Nonsignificant Digits • If a calculator displays 12.846239 and only 3 significant digits are justified, use the rounding rules… • Beware of “Place-Holder Zeros” !!! Round off 151.1 to 2 sig digits? Round off 14652.83 to 3 sig digits?

  15. Rounding Off Nonsignificant Digits • If the first nonsignificant digit is less that 5, drop all nonsignificant digit • If the first nonsignificant digit is ≤5, increase the last significant digit by 1 and drop all nonsignificant digits. • If a calculation has 2 or more operations, retain the nonsignificant digits until the final operation.

  16. ALL DONE!!!

  17. This has been…. A Baron & Baron Production Special thanks to Mrs. Robin McNemar

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