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131 1-31-2011
 

131 1-31-2011

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significant figures

significant figures

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    131 1-31-2011 131 1-31-2011 Presentation Transcript

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