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Significant Figures

Significant Figures. In Measurements. Significant Figures At the conclusion of our time together, you should be able to:. Explain what significant figures are in a measurement Determine the number of significant figures in any measurement. Significant Figures.

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Significant Figures

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  1. Significant Figures In Measurements

  2. Significant FiguresAt the conclusion of our time together, you should be able to: Explain what significant figures are in a measurement Determine the number of significant figures in any measurement

  3. Significant Figures The significant figures in a measurement include all of the digits that are known, plus one last digit that is estimated. The numbers reported in a measurement are limited by the measuring tool.

  4. How many sig figs are there in a given measurement?

  5. Measurement and Significant Figures Every experimental measurement has a degree of uncertainty. The volume, V, at right is certain in the 10’s place, 10mL<V<20mL The 1’s digit is also certain, 17mL<V<18mL A best guess is needed for the tenths place.

  6. To indicate the precision of a measurement, the value recorded should use all the digits known with certainty, plus one additional estimated digit that usually is considered uncertain by plus or minus 1. No further insignificant digits should be recorded. The total number of digits used to express such a measurement is called the number of significant figures. All but one of the significant figures are known with certainty. The last significant figure is only the best possible estimate.

  7. Below are two measurements of the mass of the same object. The same quantity is being described at two different levels of precision or certainty.

  8. Reading a Meterstick . l2. . . . I . . . . I3 . . . .I . . . . I4. . cm First digit (known) = 2 2.?? cm Second digit (known) = 0.7 2.7? cm Third digit (estimated) between 0.05- 0.08 Length reported =2.77 cm or 2.76 cm or 2.78 cm

  9. Known + Estimated Digits In 2.77 cm… • Known digits2and7are 100% certain • The third digit 7 is estimated (uncertain) • In the reported length, all three digits (2.77 cm) are significant including the estimated one

  10. Learning Check . l8. . . . I . . . . I9. . . . I . . . . I10. . cm What is the length of the line? 1) 9.6 cm 2) 9.62 cm 3) 9.63 cm How does your answer compare with your neighbor’s answer? Why or why not?

  11. Zero as a Measured Number . l3. . . . I . . . . I4 . . . . I . . . . I5. . cm What is the length of the line? First digit5.?? cm Second digit5.0? cm Last (estimated) digit is 5.00 cm

  12. Always estimate ONE place past the smallest mark! 11.5 mL

  13. So how many sig figs are there in a given measurement? 52.8 mL

  14. How to Determine Significant Figures in a Problem Use the following rules:

  15. Rule #1 • Every nonzero digit is significant Examples: 24 = 2 3.56 = 3 7 = 1

  16. Rule #2 – Sandwiched 0’s • Zeros between non-zeros are significant Examples: 7003 = 4 40.9 = 3

  17. Rule #3 – Leading 0’s • Zeros appearing in front of non-zero digits are not significant • Act as placeholders • Can’t be dropped, show magnitude Examples: 0.00024 = 2 0.453 = 3

  18. Rule #4 – Trailing 0’s with DP • Zeros at the end of a number and to the right of a decimal point are significant. Examples: 43.00 = 4 1.010 = 4 1.50 = 3

  19. Rule #5 – Trailing 0’s without DP • Zeros at the end of a number and to the left of a decimal point aren’t significant Examples: 300 = 1 27,300 = 3

  20. Easier Way to do Sig Figs!! • Pacific/Atlantic P A If a decimal point is present, start on the Pacific (P) side and draw an arrow through the number until you hit a non-zero digit. Count all numbers without an arrow through them. If a decimal is absent, start on the Atlantic (A) side and draw an arrow through the number until you hit a non-zero digit.

  21. Examples: 123.003 grams decimal present, start on “P” side, draw arrow, count digits without an arrow through it. Answer = 6 10,100 centimeters Decimal absent, start on “A” side, draw an arrow, count digits without an arrow through it. Answer = 3

  22. Learning Check A. Which answer(s) contain 3 significant figures? 1) 0.4760 2) 0.00476 3) 4760 B. All the zeros are significant in 1) 0.00307 2) 25.300 3) 2.050 x 103 C. 534,675 rounded to 3 significant figures is 1) 535 2) 535,000 3) 5.35 x 105

  23. Learning Check In which set(s) do both numbers contain the samenumber of significant figures? 1) 22.0 and 22.00 2) 400.0 and 40 3) 0.000015 and 150,000

  24. Significant Figures and Numbers Some numbers are exact: There are 60 seconds in 1 minute 25 cents in 1 quarter 12 eggs in one dozen There is no uncertainty in any of these numbers. In other words there are 12.0000000000000000000000000000000000 eggs in 1 dozen (add as many zeros as you like)

  25. Counting Numbers Counting numbers have infinite sig figs. Ex: 3 apples

  26. Significant FiguresLets’ see if you can: Explain what significant figures are in a measurement Determine the number of significant figures in any measurement

  27. State the number of significant figures in each of the following: A. 0.030 m 1 2 3 B. 4.050 L 2 3 4 C. 0.0008 g 1 2 4 D. 3.00 m 1 2 3 E. 2,080,000 bees 3 5 7 Learning Check

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