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Using the Factor Label Method • Easier way to write very large and very small numbers • 983,000,000 = 9.83 x 10 8 • 0.00000983 = 9.83 x 10 -6 • Takes advantage of the fact that: • Multiplying by 10, moves the decimal point one place to the right • 9.83 x 10 = 98.3 • Dividing by 10, moves the decimal point one place to the right • 9.83 = 0.983 10 • 34,000,000 = 3.4 x 10 7 • 7.29 x 10 5 = 729,000 • 0.3254 = 3.254 x 10 -1 • 5.6 x 10 -3 = 0.005600 IMPORTANT: MEMORIZE THESE 1 meter = 100 centimeters 1 gram = 1000 miligrams 1 gram = 0.001 kilograms 1 kilogram = 1000 grams • Changing one unit of measurement to another • Converting hours to minutes, for example OR… • Miles to kilometers • Meters to feet • Liters to milliliters • Etc… • Step 1: Start with what you start with • Turn it into a fraction by placing your known measurement over “1” • Step 2: multiply by a conversion factor Whoa! HOLD ON…..!! 𝟏𝒌𝒎 𝟏 • Multiplication – ok to multiply by “1” 𝟏𝒉𝒓 𝟏𝒉𝒓 𝒙𝟏= 𝟏 𝟏 𝟏𝒉𝒓 𝒙 𝟏 𝟒 𝟒 𝟏𝒉𝒓 𝟏 𝟔𝟎 𝒎𝒊𝒏 𝟏 𝒉𝒓 𝒙 𝟏𝒉𝒓 = 𝟏 𝟔𝟎 𝒎𝒊𝒏 = 𝟏 • Step 1: Start with what you start with • Turn it into a fraction by placing your known measurement over “1” • Step 2: multiply by a conversion factor • Numerator to denominator – keep the same units so they cancel • Step 3: Multiply the fraction • Step 4: Simplify 𝟏𝒌𝒎 𝟏 𝟏𝟎𝟎𝟎𝒎 × 𝟏𝒌𝒎 𝟏𝟎𝟎𝟎𝒎 = 𝟏 = 1000m • Step 1: Start with what you start with • Turn it into a fraction by placing your known measurement over “1” • Step 2: multiply by a conversion factor • Numerator to denominator – keep the same units so they cancel • Step 3: Multiply the fraction • Step 4: Simplify 𝟓𝒌𝒎 𝟏 X 𝟏 𝒎𝒊 𝟏. 𝟔𝟏 𝒌𝒎 = 𝟓 𝒎𝒊 𝟏. 𝟔𝟏 = 3.11 mi • Start with what you start with and set it over “1”. • Find your conversion factor and insert it so that the original units cancel. • Notice that the kg in my conversion factor is in the denominator to cancel! • Cancel the units, and then multiply the top of the tracks and then divide by the bottom of the tracks. 3 kg 1000 g 3000 g 1 1 kg • Start with what you start with and set it over “1”. • Find your conversion factor and insert it so that the original units cancel. • Notice that the kg in my conversion factor is in the denominator to cancel! • Cancel the units, and then multiply the top of the tracks and then divide by the bottom of the tracks. 15.2 cm 1m 0.152 m 1 100 cm • Start with what you start with and set it over “1”. • Find your conversion factor and insert it so that the original units cancel. • If you don’t have one conversion factor that gets you to the units you need, see what steps you can take to get there. 𝟒𝟑𝟎𝟎 𝒎 𝟏 𝒌𝒎 x 𝟏 𝟏𝟎𝟎𝟎 𝒎 x 𝟏 𝒎𝒊 𝟏. 𝟔𝟏 𝒌𝒎 = 2.8 miles • Double decker problem • Same procedure – just take on deck at a time… • Step 1: Start with what you start with • It’s already a fraction! (“per” means divide!) • Step 2: multiply by a conversion factor • Pick the numerator or denominator – either one; they both get done anyway… • Numerator to denominator – keep the same units so they cancel • Step 3: Multiply the fractions • Step 4: Simplify 𝟔𝟎 𝒎𝒊 𝟏. 𝟔𝟏 𝒌𝒎 X X 𝟏 𝒉𝒓 𝟏 𝒎𝒊 𝟏 𝒉𝒓 𝟔𝟎 𝒎𝒊𝒏 X 𝟗𝟔. 𝟔 𝒌𝒎 𝟎. 𝟎𝟐𝟕 𝒌𝒎 𝟏 𝒎𝒊𝒏 = = 𝟑𝟔𝟎𝟎 𝒔𝒆𝒄 𝒔𝒆𝒄 𝟔𝟎 𝒔𝒆𝒄
