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BELLWORK 8/27/18

BELLWORK 8/27/18. Explain how volume is a derived unit. Why do we have to learn about Sig Figs?. Sig Figs tell you what place to round your answers to. Your final measurement (answer) can never be more precise than your starting measurement.

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BELLWORK 8/27/18

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  1. BELLWORK 8/27/18 • Explain how volume is a derived unit.

  2. Why do we have to learn about Sig Figs?

  3. Sig Figs tell you what place to round your answers to. • Your final measurement (answer) can never be more precise than your starting measurement. • To understand that idea, we will discuss accuracy vs. precision

  4. Accuracy & Precision Two important points in measurement

  5. THE BIG CONCEPT • Accuracy –indicates the closeness of the measurements to the true or accepted value. Beware of Parallax – the apparent shift in position when viewed at a different angle. 2. Precision - The closeness of the results to others obtained in exactly the same way.

  6. High Accuracy High Precision High Precision Low Accuracy Accuracy vs. Precision

  7. Master Archers

  8. Can you hit the bull's-eye? Three targets with three arrows each to shoot. Accurate and precise Precise but not accurate Neither accurate nor precise How do they compare? Can you define accuracy vs. precision?

  9. Example: Accuracy Who is more accurate when measuring a book that has a true length of 17.0 cm? Susan: 17.0 cm, 16.0 cm, 18.0 cm, 15.0 cm Amy: 15.5 cm, 15.0 cm, 15.2 cm, 15.3 cm

  10. Example - Precision • Which set is more precise? A. 18.2 , 18.4 , 18.3 B. 17.9 , 18.3 , 18.8 C. 16.8 , 17.2 , 19.4

  11. Recording Measurements 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.

  12. Known + Estimated Digits In 2.77 cm… • Known digits 2 and 7 are 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

  13. Always estimate ONE place past the smallest mark! 11.50mL

  14. Learning Check . l8. . . . I . . . . I9. . . . I . . . . I10. . cm What is the length of the line? 1) 9.31 cm 2) 9.32 cm 3) 9.33 cm How does your answer compare with your neighbor’s answer? Why or why not?

  15. Zero as a Measured Number . l3. . . . I . . . . I4 . . . . I . . . . I5. . cm What is the length of the line? First digit 5.?? cm Second digit 5.0? cm Last (estimated) digit is 5.00cm

  16. Precision and Instruments • Do all measuring devices have the same amount of precision?

  17. You indicate the precision of the equipment by recording its Uncertainty • Ex: The scale on the left has an uncertainty of (+/- .1g) • Ex: The scale on the right has an uncertainty of (+/- .01g)

  18. 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.

  19. ACCURACY AND PRECISION WORKSHEET

  20. BELLWORK - 8/29/18 • You measure the dimensions of the block and its displacement in a container of a known volume of water. You calculate the density of the block of aluminum to be 2.68 g/cm3. You look up the density of a block aluminum at room temperature and find it to be 2.70 g/cm3. Calculate the percent error of your measurement.

  21. ANSWER • Your value – Accepted value x 100 Accepted value • Y- A A • 2.68 g/cm3– 2.70 g/cm3 x 100 2.70 g/cm3 • 74%

  22. Significant Figures In Measurements

  23. 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.

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

  25. Rule #1 • Every nonzero digit is significant in a measurement. Examples: 24m = 2 3.56m = 3 7m = 1

  26. Rule #2 – Sandwiched 0’s • Zeros between non-zeros are significant Examples: 203,205 = 6 7003m = 4 40.9m = 3

  27. Rule #3 – Leading 0’s • Zeros appearing in front of non-zero digits are not significant • Act as placeholders Examples: 0.0000000056 = 2 0. 24m = 2 0.453m = 3

  28. Rule #4 – Trailing 0’s with Decimal Points • Zeros at the end of a number and to the right of a decimal point are significant. Examples: 1.0 = 2 43.00m = 4 1.010m = 4 1.50m = 3

  29. Performing Calculations with Significant Figures • Rule: When adding or subtracting measured numbers, the answer can have no more places after the decimal than the LEAST of the measured numbers. • Only count the Sig Figs that come after the decimal.

  30. Adding and Subtracting • 2.45cm + 1.2cm = 3.65cm, Round off to  3.7cm • 7.432cm + 2cm = 9.432 Round to  9.4cm

  31. Multiplication and Division • Rule: When multiplying or dividing, the result can have no more significant figures than the least reliable measurement. • Count all of the Sig figs in the entire number.

  32. Examples • 56.78 cm x 2.45cm = 139.111 cm2 Round to  139cm2 • 75.8cm x 9.6cm = ?

  33. 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

  34. 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

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

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