SI Units, Metric Conversions, Dimensional Analysis

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SI Units, Metric Conversions, Dimensional Analysis Powered By Docstoc
					              Drill – 9/23
1. How many seconds are in 9.7 hours?

2. How did you figure out that answer?
SI Units, Metric Conversions,
   & Dimensional Analysis
• A major theme of science
  is communication and
  collaboration. We need a
  single measurement
  system for everyone.
• Le Systeme International
  d’Unites - SI
                     SI UNITS
    Quantity         Unit Name   Abbreviation
     Length            Meter          m
     Mass             Kilogram       kg
      Time            Second          s
 Temperature           Kelvin         K
   Amount of           Mole          mol
   substance
 Electric current      Ampere         A

Luminous intensity    Candela         cd
• We use SI prefixes to represent quantities
  that are larger or smaller than the base
  units.
Prefix   Abbreviation   Conversion
giga     G              1 Gm = 109 m
mega     M              1 Mm = 106 m
kilo     k              1 km = 1000 m
hecto    h              1 hm = 100 m
deca     da             1 dam = 10 m
                        1 meter (1 m)
deci     d              1 m = 10 dm
centi    c              1 m = 100 cm
milli    m              1 m = 1000 mm
micro    μ              1 m = 106 μm
nano     n              1 m = 109 nm
       Dimensional Analysis
• Dimensional Analysis is a method used to
  make conversions. This method helps us
  organize information without becoming
  confused about what units are being
  cancelled or multiplied/divided.
                    Rules
1. You must use Dimensional Analysis to
   solve conversion problems
2. Always show all your work
3. Include units
4. Make sure your units cancel out
5. Everything on the top is multiplied
   Everything on bottom is divided from the top
        Conversion Factors
• A ratio (or fraction) derived from the
  equality between two different units that
  can be used to convert from one unit to
  the other.
• Conversion factors always equal one
  because the two values are equal to each
  other.
             Conversion Factors
4 quarters         1 dollar
              =1                =1
1 dollar           4 quarters



60 minutes         1 hour
              =1                =1
1 hour             60 minutes



1m                 100 cm
              =1                =1
100 cm             1m
Convert 62.0 inches to centimeters

• First we need to map out what we are
  doing.
           62.0 in  ___ cm
Convert 62.0 inches to centimeters
• Second we need to determine our
  conversion factor

How many centimeters are in one inch?
  2.54 cm = 1 in




   1 in              2.54 cm            Note: We could have also
             =1                =1       used that 1cm = .394 inch
   2.54 cm           1 in               but as a general rule, the
                                        larger unit gets the 1!
Convert 62.0 inches to centimeters

• Third, we multiply our given by the
  conversion factor…making sure to arrange
  the conversion factor so that the units
  CANCEL!

       62.0 in X 2.54 cm
                         = 157.48 cm
                 1 in

       Note: Units that are both on the top and the
       bottom cancel
Convert 62.0 inches to centimeters

• Lastly, we make sure that we reached our
  “destination” and that we have the correct
  number of significant figures.

          157.48 cm  157 cm


       Note: Conversions factors do not follow
       significant figure rules, they are not
       measured and do not show accuracy.
       Multiple Conversions
• When conversions require several steps,
  Dimensional Analysis is extremely useful.
  It helps organize information so we can
  think through problems step-by-step.
 How many feet are in 965 cm?
• 1. Map it out: 965 cm  ___ ft
• 2. Find conversion factors:
How many feet are in 965 cm?


965 cm        1 in         1 ft
         X             X           = 31.66  31.7 ft
             2.54 cm       12 in
You are cooking for a large group of
people. You must change the recipe to
accommodate all the guests. How many
gallons will 384 teaspoons of vanilla
extract occupy?
– 1 Tablespoon (T) = 3 teaspoons (t)
– 1 cup (c) = 16 Tablespoons
– 1 pint (pt) = 2 cups
– 1 quart (qt) = 2 pints
– 1 gallon (gal) = 4 quarts