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Dimensional Analysis Problem-solving method that uses the fact that any number or expression can be multiplied by one without changing its value A BIT DIFFERENT THAN USING PROPORTIONS! 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 Converting from English to Metric Units and Vice versa Use conversion factors that are exact by definition 1 inch = 2.54 cm 1 ounce = 28.35 g 1 quart = 0.946L or 946 mL 1 meter = 39.37 inches 1 kilogram = 2.2 pounds Metric second = English second 1L = 1.0567 quarts Conversion w/only 2 Units Conversions with several units: When it comes time to do the math, the first number can be overlooked perhaps because it is visually different and not in line with other values. An error of omission is less likely using the following non-fraction format: Conversion of Metric Units Using Dimensional Analysis • Depends on how many units are between the initial unit and the final unit Conversion chart from larger to smaller 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 Some Classroom Exercises • A child weighs seven pounds at birth. How many ounces is this? • An aspirin tablet contains 325 mg of active ingredient. How much is this in cg? • One-fourth teaspoon has a mass of 0.21 g. What is this mass in mg? Some Classroom Exercises • 32 grams is equal to ____________ kg • 23 meters is equal to ____________ mm