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C: 22 September 2011

This lesson focuses on differentiating between accurate and precise measurements, determining significant figures, and practicing problems. It includes notes, examples, and clicker practice problems. Homework assignment included.

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C: 22 September 2011

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  1. C: 22 September 2011 • Take Out Homework: W eek 3 #1-5 and Lab Report • Objective: You will be able to: • differentiate between accurate and precise measurements • determine the number of significant figures in any value • Do now: Calculate the mass of a pure copper penny (density = 8.92 g/cm3) with a volume of 0.20 cm3.

  2. Agenda • Do now • Track objective mastery • Go over homework • Accuracy vs. precision notes and examples • Practice problems • Significant figures rules and examples • Clicker practice problems Homework: Week 3 Homework #6-10: Fri.

  3. Track Objective Mastery • Objective 8 (Density) Exit Ticket • Unit 1 Pretest B Objectives 5-12 • Where have you improved most?!

  4. Density Exit Ticket II. b. Calculate the volume of a piece of gold (density = 19.32 g/cm3) that has a mass of 5.00 grams.

  5. Expectations • During notes and example problems: silently write them into your notebook • Raise your hand to ask questions or make comments

  6. Reading a graduated cylinder

  7. Precision and Accuracy • precision: how close a series of measurements are to each other. • accuracy: how close a series of measurements are to the actual or true value.

  8. Volume of a sample of water(Actual volume: 5 mL) • 2.0 mL, 2.1 mL, 1.9 mL • 4.0 mL, 5.0 mL, 6.0 mL • 1.2 mL, 5.5 mL, 10.6 mL • 4.9 mL, 5.0 mL, 5.0 mL

  9. Mass of copper cylinder (g) Three students made multiple weighings of a copper cylinder, each using a different balance. The correct mass of the cylinder had previously been determined to be 47.32 grams. Comment on the accuracy and precision of each student’s measurements.

  10. Comment on the accuracy and precision of these basketball free-throw shooters: • a. 99 of 100 shots are made • b. 99 of 100 shots hit the front of the rim and bounce off • c. 33 of 100 shots are made, the rest miss. SWBAT determine the precision and accuracy of data.

  11. On Your Own • How are accuracy and precision similar? • How are accuracy and precision different? • Give an example of a data set that is very precise but not accurate. (Hint: You’ll have to write down the “real” answer, too.)

  12. Percent Error: a measurement of how accurate your data are • So, if the actual value is 5.0 grams, but your average mass was 4.6 grams, what is your percent error? • What if your average volume was 25.0 mL, but the actual value is 23.9?

  13. An engineer was responsible for calculating amount of water that overflowed from a dam. He measured all of the water runoff going into the reservoir (1.2 million cubic feet per year), the rainfall (860 cubic feet per year), and the capacity of the reservoir (3.8 million cubic feet). He did some fancy calculations. He reported to his boss that the overflow from the dam would be 350,246.2544330 cubic feet per year. • What’s wrong here?

  14. Significant Figures • How to determine how accurate a number is • How to determine how much to round an answer

  15. I. Significant Figuresaka: Significant Digits • A. Nonzero integers count as significant figures • Ex. Any number that is NOT zero (1, 2, 3, 4, 5, 6, 7, 8, 9) • 345 • 597.2 • 145.456 SWBAT identify and round a number to the correct number of significant figures.

  16. Zeros • B. Leading zeros that come before all the nonzero digits do NOT count as significant figures • Ex: 0.0025 has two sig. fig. The zeros are “leading” and do not count. • 0.23 • 0.0004 • 0.03564 SWBAT identify and round a number to the correct number of significant figures.

  17. C. Captive zeros are between nonzero digits and DO count as sig. fig. • Ex: 1.008 has four sig. fig. The zeros are captive and DO count. • 10,004 • 1.000006 • 1,000,000,000,000,567 SWBAT identify and round a number to the correct number of significant figures.

  18. D. Trailing zeros are to the right end of the number and DO count as sig. fig. if the number contains a decimal point. • Ex.: 100 has only one sig. fig. because the trailing zeros DO NOT have a decimal point. • Example: 1.00 has three sig. fig. because the trailing zeros DO have a decimal point. SWBAT identify and round a number to the correct number of significant figures.

  19. More practice: Trailing zeros • 1.000000 • 3,000,000 • 3.00000 • 30.00 • 300 • 300.

  20. E. Exact numbers • Any number found by counting has an infinite number of significant figures. • Ex: I have 3 apples. The 3 has an infinite number of significant figures. • 50 people • 100 baseballs SWBAT identify and round a number to the correct number of significant figures.

  21. Which are exact numbers? • The elevation of Breckenridge, Colorado is 9600 feet. • There are 12 eggs in a dozen. • One yard is equal to 0.9144 meters. • The attendance at a football game was 52,806 people. • The budget deficit of the US government in 1990 was $269 billion. • The beaker held 25.6 mL of water. SWBAT identify and round a number to the correct number of significant figures.

  22. Clicker Use • Always pick up and use only your assigned clicker: You are responsible for it! • Remain silent while the question is being read and while you answer – only answer for yourself! • Never laugh at, mock or ridicule the proportion of students answering incorrectly. • Listen carefully as the answer is explained.

  23. How many significant figures? 256 • 1 • 2 • 3 • 4 SWBAT identify and round a number to the correct number of significant figures.

  24. How many significant figures? 647.9 • 1 • 2 • 3 • 4 SWBAT identify and round a number to the correct number of significant figures.

  25. How many significant figures? 647.0 • 1 • 2 • 3 • 4 SWBAT identify and round a number to the correct number of significant figures.

  26. How many significant figures? 321.00 • 2 • 3 • 4 • 5 SWBAT identify and round a number to the correct number of significant figures.

  27. How many significant figures? 4005 • 1 • 2 • 3 • 4 SWBAT identify and round a number to the correct number of significant figures.

  28. How many significant figures? nine • 1 • 2 • 3 • infinite SWBAT identify and round a number to the correct number of significant figures.

  29. How many significant figures? 200. • 1 • 2 • 3 • 4 SWBAT identify and round a number to the correct number of significant figures.

  30. How many significant figures? 200.0 • 1 • 2 • 3 • 4 SWBAT identify and round a number to the correct number of significant figures.

  31. How many significant figures? 0.009009 • 2 • 4 • 6 • 7 SWBAT identify and round a number to the correct number of significant figures.

  32. How many significant figures? -500 • 1 • 2 • 3 • 4 SWBAT identify and round a number to the correct number of significant figures.

  33. How many significant figures? -500. • 1 • 2 • 3 • 4 SWBAT identify and round a number to the correct number of significant figures.

  34. How many significant figures? 1.3x1032 • 1 • 2 • 3 • 4 SWBAT identify and round a number to the correct number of significant figures.

  35. How many significant figures? • A student’s extraction procedure yields 0.0105 g of caffeine. • A chemist records a mass of 0.050080 g in an analysis. • In an experiment, a span of time is determined to be 8.050 x 10-3 s. • Rewrite 8.050 x 10-3 so it has three significant figures. SWBAT identify and round a number to the correct number of significant figures.

  36. Assignment • In your lab notebook, find the density stations from yesterday. • Next to each value you measured, write the number of significant figures in a circle. • Ex: 12.35 cm 4

  37. Exit Ticket

  38. Homework • Week 3 Homework #6-10: Fri.

  39. C: 23 September 2011 Rounding Take Out Homework: Week 3 Homework #1-10 • Objective: You will be able to: • round values to the correct number of significant figures • Do now: How many significant figures? • a. 0.00045 • b. 0.00040 • c. 0.0004050

  40. Agenda • Do now • Go over homework • Accuracy/Precision, Sig. Fig. “Exit” Ticket • Rounding Notes and Examples • Practice Problems • Exit Ticket Homework: Week 3 Homework #11-14: Mon.

  41. “Exit” Ticket • Precision/Accuracy • Sig. Fig.

  42. Rounding • The answer to a calculation can not be any more accurate than the least accurate value in that calculation. • When multiplying or dividing, round to the least number of significant figures given in the problem.

  43. Example 1 • An iron block with side lengths 10.5 cm by 22.6 cm by 2.5 cm has a mass of 4655 grams. Calculate the density of iron.

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