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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 1 dozen eggs 12 eggs or 12 eggs 1 dozen eggs Doing Problems 1. Read problem completely 2. Determine the measured qty. in the problem and the units 3. Determine units being requested 4. Determine conversion factor that will allow you to change to the new unit We will look at converting: 1. English units 2. English units to Metric Units 3. Metric units Converting from English to English, • 75 cookies is equivalent to how many dozen cookies? ? dozen = 75 cookies 1 dozen X 12 cookies = 6.25 dozen Series of unit factors – 2 possible formats Converting English Units Converting English Units to Metric Units • How many centimeters are in 6.00 inches? ? cm = 6.00 inches X 2.54 cm 1 inch = 15.24 cm = 15.2 cm Conversion of Metric Units 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 10-4 103 102 101 meter (m) 10-1 10-2 10-3 10-5 10-6 Steps: 1. 2. Given quantity w/its unit Set up conversion factor a. b. c. d. e. 3. 4. 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 1 cg 10 mg = = 32.5cg of active ingredient 325 = 32.5 cg 10 • Convert 50.0 mL to liters? 50.0mL 1 cL 1 10 mL 1 dL 1 L = 50 10 cL 10 dL 1000 = 0.0500L