Measurement, Error,

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Measurement, Error, Uncertainty

• Overview
• Units in chemistry
• Graphs
• Scientific notation Orders of Magnitude
• Error and Significant Figures

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Units

• Metric system SI Système Internationale
• Length
• meters (m)
• centimeters (cm) 100 cm 1 m
• Millimeters (mm) 1000 mm 1 m
• Kilometers (km) 1000 m 1 km
• Temperature
• Kelvin (K) oC 273.15

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Units

• Mass
• Grams (g)
• Milligrams (mg) 1000 mg 1 g
• Kilograms (kg) 1000 g 1 kg
• Volume
• Liters (L)
• Milliliters (mL) 1000 mL 1 L
• Time
• Sec (s)

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Problem 1

• Express the following in the units indicated
• 558 m in km
• 0.00894 g in mg
• 116,322 mL in L
• 0.00889 kg in g, in mg

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Problem 1

• 558 m in km
• 1000 m 1 km

1000 kmm 558 mx km
0.558 km
558. m
b) 0.00894 g in mg 1000 mg 1 g
8.94 mg
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Problem 1

• c) 116,322 mL in L
• 1000 mL 1 L
• 116,322 mL 116.322 L
• d) 0.00889 kg in g, in mg
• 1000 g 1 kg
• 0.00889 kg 8.89 g 0.00889 mg

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Graphs

• Reading graphs

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Reading Graphs
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Ozone Levels

• Problem 2
• What time of day are ozone levels at their
  lowest?
• What time of day are ozone levels at their
  highest?
• If levels gt 84 ppb are considered harmful, what
  percentage of the day has levels above harmful?

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Rationale for Graphing
Power of the visual depiction of data to
understand relationships
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Scientific Notation

• Used to express very large or very small numbers
• 55,800,000 km from earth to sun
• 5.58 x 107 km
• Mass of a H atom
• 0.00000000000000000000000168 g
• 1.68 x 1024 g

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Problem 3

• Put the following numbers into scientific
  notation
• 346,000,000,000
• 0.00049100
• 0.000000005664
• 340

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Problem 3

• 346,000,000,000 3.46 x 1011
• 0.00049100 4.9100 x 104
• 0.000000005664 5.664 x 109
• 340 3.4 x 102

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Significant Figures and Error

• E.g. Density calculation
• 22 g has volume of 19 mL
• Density 1.157894737 g/mL
• Not truthful value
• Precision vs. Accuracy

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Precision vs. Accuracy

• Precision depends upon the detection limit or
  sensitivity of the instrument used
• Accuracy Difference between the true value and
  the average of a series of measurements
• True values rarely known need multiple,
  repetitive measurements

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Precision vs. Accuracy
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Types of Error

• Every scientific measurement has error associated
  with it
• Error implies mistake uncertainty better way to
  look at it
• Random (indeterminate) error result from large
  number of minute variations in materials,
  conditions, equipment, etc. completely
  unavoidable. Can be (never eliminated) mitigated
  by improving precision, calibration
• Systematic (determinate) error result of
  inaccurate calibration, sampling or procedural
  bias, operator error, etc. Measurements are
  systematically low or high. Only error that we
  can eliminate

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Precision vs. Accuracy
bias
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Back to Significant Figures

• Place holders not significant
• Actual values or illustrating precision
  significant
• E.g.
• 45,600 vs. 45,600.0
• 0.0067 vs. 0.006700
• Scientific notation solves issue
• 2.34 x 104 compared to 2.3400 x 104

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Full Disclosure

• Significant figures crude approach
• Standard deviation (statistics) more appropriate
• Error values (error bars on graphs)
• 3.44 mL ? 0.04 mL implies range 3.40 3.48 mL
• If error were ? 0.1, could only report 3.4 ? 0.1

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Error Bars