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Understanding Significant Digits in Measurements

Learn the importance of significant digits in measurements. Discover how to estimate precision and handle calculations accurately using SD rules. Improve your math skills with clear examples and rounding tips.

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Understanding Significant Digits in Measurements

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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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