How to Factor Label 1 Factor Label 1.1 What is a conversion factor? • Start with true statement 1 in. = 2.54 cm • Let’s multiply by one 1 in. = 2.54 cm × 1 in. • Reorganize 1 in. 2.54 cm 1 in. = 1 in. • Simplify 1 1= 1 in. 2.54 cm 1 in. ←− conversion factor Def : a conversion factor is always equal to one Note: Units cancel out just like numbers and algebraic symbols Examples: 1.2 cm2 = cm cm mL · g = mL g How to Factor Label by Example Problem: Convert 30 cm to inches. 1. Start with given 30 cm 2. Multiply by conversion factor 2,3 30.0 cm × 3. Cancel units × 30.0 cm 1 in. cm 2.54 4. Solve 4 × 30.0 cm 1 in. = 11.8 in. 2.54 cm 5. Box answer × 30.0 cm 1 in. = 11.8 in. cm 2.54 1 in. 2.54 cm • When converting units using the factor label method, the rules you applied for significant figures still apply. You must always provide the correct number of significant figures as well as the correct unit. 1 It is a good exercise to work out solved examples with a pencil and paper to really understand every step. As we saw earlier, we can do this because this is the same as multiplying by 1. 3 You insert the conversion factor into the equation so that undesired units cancel out leaving only the desired ones. It is acceptable and often times necessary to inverse the conversion factor. Again, you can do this because the conversation factor is equal to 1. 4 Your answer will be in inches because inches is the only unit left after cancellation. 2 1 Length and Displacement Conversion Worksheet Memorize: Conversion factors in bold print are exact and thus have an infinite number of significant figures. mi. = 1.609 km in. = 2.54 cm mi. = 5 280 ft. yd. = 36 in. ft. = 12 in. yd. = 3 ft. Directions Convert the following using the factor label method and box your final answer. Your answer must contain the correct number of significant figure and the proper unit. No unit should be written out; use symbol only. 1 235 feet to inches 2 47.0 miles to feet 3 12 feet to centimeters 4 5.00 kilometers to miles 5 1.00 millimeter to inches 6 70¯0 inches to micrometers 7 100. miles to meters 8 1.0 angstrom to inches 2 9 4.56×106 miles to gigameters 10 0.531 miles to megameters 11 2.0 exometers to miles 12 15.0 femtometers to inches 13 4.22 light years to miles 14 902 micrometers to inches 15 0.020 miles to decimeters 16 4.04×104 attometers to inches 17 7¯00 meters to yards 18 10.0 feet to nanometers 3 Mass and Weight Conversion Worksheet Memorize: lb. = 453.6 g ton = 2 000 lb. lb. = 16 oz. kg = 9.8 N 1 slug = 32.2 lb. 2 Conversion factors in bold print are exact and thus have an infinite number of significant figures. Directions Convert the following using the factor label method and box your final answer. Your answer must contain the correct number of significant figure and the proper unit. No unit should be written out; use symbol only. 19 5.00 pounds to kilograms 20 1.00 ounce to pounds 21 3.02 grams to ounces 22 60¯0 micrograms to pounds 23 2.000 tons to metric tons 24 5.21×107 femtograms to pounds 25 9.1093897×10−27 kilograms to ounces 1 2 Varies with distance above or below the earth’s surface. Varies with distance above or below the earth’s surface. 4 26 100. newtons to pounds 27 145 pounds to slugs 28 12.000 atomic mass units to grams 29 60.0 kilograms to newtons 30 1.00797 grams to atomic mass units 31 0.045 decagrams to pounds 32 6.02×10−3 ton to newtons 33 2.20 slugs to teragrams 34 18.01 ounces to pounds 35 mass of the earth in kilograms to pounds 36 0.0310 newtons to grams 5 Volume Conversion Worksheet Memorize: L = 1.057 qt. ft.3 = 28.32 L gal. = 4 qt. 2 pt. = qt. 2 cups = pt. cup = 8 fluid oz. 1 cm3 = mL m3 = kL ft.3 = (12 in.)3 in.3 = (2.54 cm)3 Conversion factors in bold print are exact and thus have an infinite number of significant figures. Directions Convert the following using the factor label method and box your final answer. Your answer must contain the correct number of significant figure and the proper unit. No unit should be written out; use symbol only. 37 5.00 pounds to kilograms 38 22 cubic centimeters to liters 39 54.5 gallons to cups 40 1¯00 milliliters to cubic feet 41 1.9×1020 attoliters to pints 42 40.0 liters to cubic feet 43 0.0250 decaliters to cubic inches 1 A fluid ounce is a volume. An ounce is a weight. 6 44 700 cubic feet to microliters 45 60.0 cubic inches to cubic yards 46 45.0 cubic feet to milliliters 47 4.0 pt. to cubic centimeters 48 11.34 grams per milliliter to pounds per cubic inch 49 1.00 grams per milliliter to pounds per cubic foot 50 50¯0 tons per year to ounces per millisecond 51 60 miles per hour to kilometers per hour 52 25 meters per second to miles per hour 53 10. meters per second per second to feet per second per second 54 9.80 meters per second per second to feet per hour per second 7 Assorted Unit Conversion Worksheet Directions Convert the following using the factor label method and box your final answer. Your answer must contain the correct number of significant figure and the proper unit. No unit should be written out; use symbol only. 55 18.0 km to mi. (Ans. 11.2 mi.) 56 45 mi. to cm 57 650 g to lb. 58 42 tons to kg 59 16 L to qt. 60 100. gal to mL 61 75 km/h to m · s−1 62 194 kg/yr. to lb./day 63 815 in.2 to ft.2 (Ans. 7.2×106 cm) (Ans. 1.4 lb.) (Ans. 3.8×104 kg) (Ans. 17 qt.) (Ans. 3.77×105 mL) Ans. 21 m · s−1 ) (Ans. 1.16 lb./day) (Ans. 5.66 ft.2 ) 8 64 32 yd.3 to in.3 (Ans. 1.5×106 in.3 ) 65 16 ft.3 to cm2 (Ans. 1.5×104 cm2 ) 66 200 cm3 to mL 67 6.3×109 TL to gal. (Ans. 1.7×1021 gal.) 68 6.5×104 cm to km. (Ans. 0.65 km) 69 15 EL to aL 70 (Ans. 200 mL) (Ans. 1.5×1037 aL) From here on out do not provide answers and use all sorts of units. (Continue using Mrs. Crapps sheets. 71 72 73 74 9 75 76 77 78 79 80 81 82 83 84 85 10 86 87 88 89 90 91 92 93 94 95 96 11