Chapter 2Measurement

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Chapter 2Measurement Problem Solving

• Dr. Ellen Wilson
• CHE-1000-58793
• Fall 2007

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The English System
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The English System
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The Metric System
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The Metric System
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SI Units

• International System of units
• Examples
• meter (m), kilogram (kg)
• second (s), Kelvin (K)
• joule (j)
• Prefixes in powers of ten

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Metric System Prefixes

• from Table 2.2, p. 24

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Examples
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Derived Units

• Volume is a derived unit
• the amount of space occupied
• Units are liter (L), milliliter (mL) or cubic
  centimeter (cc)
• Density
• d mass ? volume
• Typically has units of g/mL

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Scientific Notation uses decimals and exponents
to express very large or very small numbers

• 3, 019, 348, 704
• Or
• 3.019348704 x 109

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Examples

• Express in scientific notation
• 6,364,262,000 (est. population of the world)
• 11,051,000 (est. population of China)
• 0.000000001 s (the time for light to travel 1 ft)
• 0.143 s (time for light to travel around the
  world)

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Examples

• Express in decimal notation
• 450 x 109 m (wavelength of blue light)
• 5x109 yrs (approx age of the Earth)

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Accuracy and Precision
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Precise or Accurate?
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Using Significant Figures reflects precision by
estimating the last digit
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Rules of Significant Figures

• All nonzero digits are significant
• 345 6.98 7,894
• Zeros between numbers are significant
• 3045 6.908 78,094
• Zeros after a decimal are significant
• 345.0 6.9080 78,094.00
• Leading zeros are not significant
• 0.00345 0.06980 0.07894

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Rules of Significant Figures

• What about zeros at the end of a number but
  before/without a decimal point?
• Unable to determine
• Avoid this by using scientific notation
• Example
• 350 3.5x102 3.50x102

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Counting Significant Figures

• Examples

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Exact Numbers
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Rounding Significant Figures

• If the number dropped is 4 or less
• 2.33 2.34 both round to 2.3
• If the number dropped is 5 or more
• 2.37 2.35 both round to 2.4
• Round only the final answer in a series of
  calculations

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Rounding Significant Figures

• Examples

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Significant Figures

• in Calculations
• Rules for multiplication/division
• Rules for addition/subtraction
• Rules for combined equations

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Significant Figures

• Rules for multiplication/division
• The result has the same number of significant
  figures as the factor with the fewest significant
  figures
• The answer cant be more precise
• than the question

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Significant Figures

• Rules for multiplication/division
• Examples

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Significant Figures

• Rules for addition/subtraction
• The result has the same number of decimal places
  as the number with the fewest decimal places
• The answer cant be more precise
• than the question

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Significant Figures

• Rules for addition/subtraction
• Examples

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Significant Figures

• Rules for both /- and x/?
• Do the functions in parenthesis 1st, note the
  number of significant digits
• Perform the remainder of calculations
• Round the final answer

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Significant Figures

• Multiplication and division
• Answer is based on
• the number with the
• fewest sig figs

• Addition and subtraction
• Answer is based on
• the number with the
• fewest decimal points

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Significant Figures

• Examples

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We will report ALL mathematical answers in this
class to the correct number of significant
figures for the rest of the semester
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Conversion between Units

• This is called dimensional analysis
• Follow the units to the desired answer

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Simple Conversions involve only one step
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A Sort of Simple Conversion
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Units Raised to a Power

• Square the number, square the units!
• Example

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Density as a conversion factor

• Will convert between mass and volume
• Example

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Density

• Ratio of mass to volume
• Unit of density contains mass/volume
• g/L
• mg/mL