131 1-31-2011

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significant figures

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131 1-31-2011

  1. 1. review<br />35 mm = _______ dm _____ mm _____ km<br />0.25 dm3 = _____ cL = ______ cc<br />Bromine heptafluoride _____<br />N2 S3 ________________________<br />Na2S<br />6500000 = ________<br />0.00344 = __________<br />3.6 X 10-3 x 6.1 X 10-6 = _____________<br />3.6 X 10-3 / 6.1 X 10-6 = _____________<br />
  2. 2. review<br />35 mm = 0.35 dm = 35000mm = 0.000035km<br />0.25 dm3 (L) = 25cL = 250 cc (mL) <br />Bromine heptafluoride__BrF7___<br />N2 S3 dinitrogentrisulfide<br />Na2S sodium sulfide<br />6500000 = 6.5 X 106<br />0.00344 = 3.44 X 10-3<br />3.6 X 10-3 x 6.1 X 10-6 = 21.96 X 10-9 = 2.2 X 10-8<br />3.6 X 10-3 / 6.1 X 10-6 = 0.59 X 103 = 5.9 X 102<br />
  3. 3. Measurements are estimates<br />Exact numbers <br />Counted -- I have 3 sons<br />Defined -- 4 qt in 1 gal<br />Measured<br />“exactness” limited by measuring device, object and user<br />
  4. 4. Significant figures<br />Measured and exact number<br />Exact:<br />Counted <br />13,000 people attended the conference<br />49 citizens attended the council meeting<br />Defined<br />12 in = 1 ft, 2.54 cm = 1 in <br />1 kg = 2.2 lb NOT defined – remember weight changes!!!<br />Measurements<br />All are estimates – depend on precision of device<br />
  5. 5. 16 oz = 1 lb, exact -- defined<br />2.54 cm = 1 in, exaact -- defined<br />454 g = 1 lb, measured<br />1.6 km = 1 mi not exact (rounded off for convenience)<br />Actual exact number:<br />1 mi X 5280ft/mi X 12 in/ft X 2.54 cm/in = 160934 cm<br /> or 1.609344 km this would be the EXACT conversion<br />Exact or measured??<br />
  6. 6. Your reading might be 3.5 cm<br />Measuring<br />Estimate an<br />Additional digit<br />If possible<br />If lines are very<br />Close together<br />May not be<br />Practical!!!<br />Your reading might be 4.55 – but on<br />A real meter stick, you probably cannot<br />Read between the mm lines<br />Your reading should be 3.0 cm<br />This means you think the real<br />Value is between 2.9 and 3.1<br />Not between 2 and 4!!<br />
  7. 7. Counting Significant Figures<br />Number of Significant Figures<br /> 38.15 cm<br /> 5.6 ft <br /> 65.6 lb <br /> 122.55 m <br />Complete: All non-zero digits in a measured number are (significant or not significant).<br />Answers: 4,2,3,5<br />
  8. 8. Leading Zeros<br />Number of Significant Figures<br /> 0.008 mm <br /> 0.0156 oz <br /> 0.0042 lb <br /> 0.000262 mL<br />Complete: Leading zeros in decimal numbers are (significant or not significant).<br />Answers: 1,3,2,3<br />
  9. 9. Sandwiched Zeros<br />Number of Significant Figures<br />50.8 mm<br /> 2001 min <br /> 0.702 lb <br /> 0.00405 m <br />Complete: Zeros between nonzero numbers are (significant or not significant).<br />Answers: 3,4,3,3<br />
  10. 10. Trailing Zeros<br />Number of Significant Figures<br />25,000 in. <br />200 yr <br /> 48,600 gal <br /> 25,005,000 g <br />Complete: Trailing zeros in numbers without decimals are (significant or not significant) if they are serving as place holders.<br />Answers: 2,1,3,5<br />
  11. 11. review<br />35 mm = _______ dm _____ mm _____ km<br />0.25 dm3 = _____ cL = ______ cc<br />Bromine heptafluoride _____<br />N2 S3 ________________________<br />Na2S<br />6500000 = ________<br />0.00344 = __________<br />3.6 X 10-3 x 6.1 X 10-6 = _____________<br />3.6 X 10-3 / 6.1 X 10-6 = _____________<br />
  12. 12. review<br />35 mm = 0.35 dm = 35000mm = 0.000035km<br />0.25 dm3 (L) = 25cL = 250 cc (mL) <br />Bromine heptafluoride__BrF7___<br />N2 S3 dinitrogentrisulfide<br />Na2S sodium sulfide<br />6500000 = 6.5 X 106<br />0.00344 = 3.44 X 10-3<br />3.6 X 10-3 x 6.1 X 10-6 = 21.96 X 10-9 = 2.2 X 10-8<br />3.6 X 10-3 / 6.1 X 10-6 = 0.59 X 103 = 5.9 X 102<br />
  13. 13. Measurements are estimates<br />Exact numbers <br />Counted -- I have 3 sons<br />Defined -- 4 qt in 1 gal<br />Measured<br />“exactness” limited by measuring device, object and user<br />
  14. 14. Significant figures<br />Measured and exact number<br />Exact:<br />Counted <br />13,000 people attended the conference<br />49 citizens attended the council meeting<br />Defined<br />12 in = 1 ft, 2.54 cm = 1 in <br />1 kg = 2.2 lb NOT defined – remember weight changes!!!<br />Measurements<br />All are estimates – depend on precision of device<br />
  15. 15. 16 oz = 1 lb, exact -- defined<br />2.54 cm = 1 in, exaact -- defined<br />454 g = 1 lb, measured<br />1.6 km = 1 mi not exact (rounded off for convenience)<br />Actual exact number:<br />1 mi X 5280ft/mi X 12 in/ft X 2.54 cm/in = 160934 cm<br /> or 1.609344 km this would be the EXACT conversion<br />Exact or measured??<br />
  16. 16. Your reading might be 3.5 cm<br />Measuring<br />Estimate an<br />Additional digit<br />If possible<br />If lines are very<br />Close together<br />May not be<br />Practical!!!<br />Your reading might be 4.55 – but on<br />A real meter stick, you probably cannot<br />Read between the mm lines<br />Your reading should be 3.0 cm<br />This means you think the real<br />Value is between 2.9 and 3.1<br />Not between 2 and 4!!<br />
  17. 17. Counting Significant Figures<br />Number of Significant Figures<br /> 38.15 cm<br /> 5.6 ft <br /> 65.6 lb <br /> 122.55 m <br />Complete: All non-zero digits in a measured number are (significant or not significant).<br />Answers: 4,2,3,5<br />
  18. 18. Leading Zeros<br />Number of Significant Figures<br /> 0.008 mm <br /> 0.0156 oz <br /> 0.0042 lb <br /> 0.000262 mL<br />Complete: Leading zeros in decimal numbers are (significant or not significant).<br />Answers: 1,3,2,3<br />
  19. 19. Sandwiched Zeros<br />Number of Significant Figures<br />50.8 mm<br /> 2001 min <br /> 0.702 lb <br /> 0.00405 m <br />Complete: Zeros between nonzero numbers are (significant or not significant).<br />Answers: 3,4,3,3<br />
  20. 20. Trailing Zeros<br />Number of Significant Figures<br />25,000 in. <br />200 yr <br /> 48,600 gal <br /> 25,005,000 g <br />Complete: Trailing zeros in numbers without decimals are (significant or not significant) if they are serving as place holders.<br />Answers: 2,1,3,5<br />
  21. 21. HW<br />Quiz Wed: metrics, sci not, naming<br />HW problems: CH 1: 9-16-24, 61, 62<br />53 a,c (c volume displacement), 54 (density)<br />Next class: classification of matter, chem and physical properties, (Ch3 sec 1 and Ch 5 sec 3) start conversion factors (Ch 1: sec 6,7,8)<br />Check out mastering chemistry for problems!!<br />
  22. 22. Learning Check<br />A. Which answers contain 3 significant figures?<br />0.4760 2) 0.00476 3) 4760 <br />B. All the zeros are significant in <br />1) 0.00307 2) 25.300 3) 2.050 x 103<br />C. 534,675 rounded to 3 significant figures is<br />1) 535 2) 535,000 3) 5.35 x 105<br />Answers: a: 2/3; b: 2/3; c: 2/3<br />
  23. 23. Learning Check<br />In which set(s) do both numbers contain the same number of significant figures? <br />1) 22.0 and 22.00 <br /> 2) 400.0 and 40 <br /> 3) 0.000015 and 150,000<br />Answer: #3<br />
  24. 24. Learning Check<br />State the number of significant figures in each of the following: <br /> A. 0.030 m1 2 3<br /> B. 4.050 L 2 3 4<br /> C. 0.0008 g 1 2 4<br /> D. 3.00 m 1 2 3<br /> E. 2,080,000 bees 3 5 7<br /> 29 people attended the conference ???EXACT<br />Answers: a 2 b 4 c 1 d 3 e 3 <br />
  25. 25. Significant Numbers in Calculations<br /><ul><li>Help you decide where to round a number from your calculator
  26. 26. A calculated answer cannot be more precise than the measuring tool.
  27. 27. A calculated answer must match the least precise measurement.
  28. 28. Significant figures are needed for final answers from</li></ul> 1) adding or subtracting<br /> 2) multiplying or dividing<br />
  29. 29. Adding and Subtracting<br /> The answer has the same number of decimal places as the measurement with the fewest decimal places.<br />25.2 gone decimal place<br />+ 1.34 gtwo decimal places<br /> 26.54 answer 26.5 one decimal place<br />
  30. 30. Learning Check<br />In each calculation, round the answer to the correct number of significant figures.<br /> A. 235.05 + 19.6 + 2.1 = <br /> 1) 256.75 2) 256.8 3) 257<br /> B. 58.925 - 18.2 =<br /> 1) 40.725 2) 40.73 3) 40.7<br />Answers: a 2, b 3<br />Write vertically – calculators do not determine sig fig (84+ apps)<br />
  31. 31. Multiplying and Dividing<br /> Round (or add zeros) to the calculated answer until you have the same number of significant figures as the measurement with the fewest significant figures.<br />Or report in sci notation<br />
  32. 32. Learning Check ? # sig fig?<br /> A. 2.19 X 4.2 = <br />1) 9 2) 9.2 3) 9.198<br /> B. 4.311 ÷ 0.07 = <br />1)61.582) 62 3) 60 <br /> C. 2.54 X 0.0028 = <br /> 0.0105 X 0.060 <br />1) 11.3 2) 11 3) 0.041<br />Answers: a 2, b 3, c 2<br />

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