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Using Conversion Factors in Unit Analysis (Dimensional Analysis) Problem-solving method that uses the fact that any number or expression can be multiplied by one without changing its value

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Title: Using Conversion Factors in Unit Analysis (Dimensional Analysis) Problem-solving method that uses the fact that any number or expression can be multiplied by one without changing its value


1
Using Conversion Factors in Unit
Analysis(Dimensional Analysis)Problem-solving
method that uses the fact that any number or
expression can be multiplied by one without
changing its value
1 dozen eggs or 12 eggs
12 eggs or 1 dozen eggs
2
Doing Problems
  • Read problem completely
  • Determine the measured qty. in the problem and
    the units
  • Determine units being requested
  • Determine conversion factor that will allow you
    to change to the new unit

3
We will look at converting1. English
units 2. English units to Metric Units3.
Metric units
4
Converting from English to English,
  • 75 cookies is equivalent to how many dozen
    cookies?

? dozen 75 cookies X 1 dozen 6.25 dozen
? dozen 75 cookies X 12 cookies 6.25 dozen
5
Series of unit factors 2 possible formats

6
Converting English Units
7
Converting English Units to Metric Units
  • How many centimeters are in 6.00 inches?

? cm 6.00 inches X 2.54 cm 15.24 cm
? cm 6.00 inches X 1 inch 15.24 cm
15.2 cm
8
Conversion of Metric Units
9
Remember the order of the units!
kilo hecto deca Base Unit deci centi milli micro
k h da gram (g) d c m µ
1000 100 10 liter (L) 0.1 0.01 0.001 0.000001
103 102 101 meter (m) 10-1 10-2 10-3 10-4 10-5 10-6
10
Steps
  • Given quantity w/its unit
  • Set up conversion factor
  • Place given unit as the denominator of the
    conversion factor
  • Place desired unit as the numerator
  • Place a 1 in front of the large unit
  • Place a 10 in front of the smaller unit
  • Repeat b-d until reaching the final answer
  • Cancel Units only the desired unit should be
    left
  • Solve the problem

An aspirin tablet contains 325 mg of active
ingredient. How much is this in cg?
325 mg 1 cg 325 32.5 cg
1 10 mg 10
32.5cg of active ingredient
11
  • Convert 50.0 mL to liters?
  • 50.0mL 1 cL 1 dL 1 L 50
  • 1 10 mL 10 cL 10 dL 1000
  • 0.0500L
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