Chapter 2.5: Writing Conversion Factors

2.5 Writing Conversion Factors

  • Equalities
    • Use two different units to describe the same quantity.
    • Can be between units of the metric system, U.S. units, or both.
    • Examples:
      • 1 m=1000 mm1 \text{ m} = 1000 \text{ mm}
      • 1 lb=16 oz1 \text{ lb} = 16 \text{ oz}
      • 2.20 lb=1 kg2.20 \text{ lb} = 1 \text{ kg}
  • Equalities on Food Labels
    • Packaged foods often list contents in both metric and U.S. units.
    • These indicate the same amount of a substance in two different units.
  • Equalities and Significant Figures
    • Equalities between two metric units or two U.S. system units are definitions. Their numbers are exact and do not affect significant figures (SFs).
      • 1 g=1000 mg1 \text{ g} = 1000 \text{ mg}
      • 1 ft=12 in.1 \text{ ft} = 12 \text{ in.}
      • 1 min=60 s1 \text{ min} = 60 \text{ s}
    • When an equality involves both a metric and a U.S. unit, one number is obtained by measurement and counts toward SFs.
      • 454 g=1 lb454 \text{ g} = 1 \text{ lb}
      • 946 mL=1 qt946 \text{ mL} = 1 \text{ qt}
      • 39.4 in.=1 m39.4 \text{ in.} = 1 \text{ m}
    • Exception: 1 in.=2.54 cm1 \text{ in.} = 2.54 \text{ cm} is an exact relationship, so 2.54 is an exact number.
  • Writing Conversion Factors
    • Any equality can be written as fractions called conversion factors. Always include units.
    • For example, the equality 1 h=60 min1 \text{ h} = 60 \text{ min} can be written as 60 min1 h\frac{60 \text{ min}}{1 \text{ h}} and 1 h60 min\frac{1 \text{ h}}{60 \text{ min}}.
    • The word "per" means "divide."
  • Common Equalities (Table 2.8)
    • Length:
      • 1 km=1000 m1 \text{ km} = 1000 \text{ m}
      • 1 m=1000 mm1 \text{ m} = 1000 \text{ mm}
      • 1 cm=10 mm1 \text{ cm} = 10 \text{ mm}
      • 1 ft=12 in.1 \text{ ft} = 12 \text{ in.}
      • 1 yd=3 ft1 \text{ yd} = 3 \text{ ft}
      • 1 mi=5280 ft1 \text{ mi} = 5280 \text{ ft}
      • 2.54 cm=1 in. (exact)2.54 \text{ cm} = 1 \text{ in.} \text{ (exact)}
      • 1 m=39.4 in.1 \text{ m} = 39.4 \text{ in.}
      • 1 km=0.621 mi1 \text{ km} = 0.621 \text{ mi}
    • Volume:
      • 1 L=1000 mL1 \text{ L} = 1000 \text{ mL}
      • 1 dL=100 mL1 \text{ dL} = 100 \text{ mL}
      • 1 mL=1 cc (cubic centimeter)1 \text{ mL} = 1 \text{ cc (cubic centimeter)}
      • 1 qt=4 cups1 \text{ qt} = 4 \text{ cups}
      • 1 qt=2 pt1 \text{ qt} = 2 \text{ pt}
      • 1 gal=4 qt1 \text{ gal} = 4 \text{ qt}
      • 946 mL=1 qt946 \text{ mL} = 1 \text{ qt}
      • 1 L=1.06 qt1 \text{ L} = 1.06 \text{ qt}
      • 473 mL=1 pt473 \text{ mL} = 1 \text{ pt}
      • 5 mL=1 tsp (teaspoon)5 \text{ mL} = 1 \text{ tsp (teaspoon)}
      • 15 mL=1 tbsp (tablespoon)15 \text{ mL} = 1 \text{ tbsp (tablespoon)}
    • Mass:
      • 1 kg=1000 g1 \text{ kg} = 1000 \text{ g}
      • 1 g=1000 mg1 \text{ g} = 1000 \text{ mg}
      • 1 mg=1000 mcg1 \text{ mg} = 1000 \text{ mcg}
      • 1 lb=16 oz1 \text{ lb} = 16 \text{ oz}
      • 1 kg=2.20 lb1 \text{ kg} = 2.20 \text{ lb}
      • 454 g=1 lb454 \text{ g} = 1 \text{ lb}
    • Time:
      • 1 h=60 min1 \text{ h} = 60 \text{ min}
      • 1 min=60 s1 \text{ min} = 60 \text{ s}
  • Metric Conversion Factors
    • Examples:
      • Metric conversion factors.
      • Metric–U.S. system conversion factors.
  • Equalities and Conversion Factors Stated Within a Problem
    • An equality may be stated within a problem and only applies to that problem.
    • Example: "The car travels at 85 km/h."
      • Equality: 85 km=1 h85 \text{ km} = 1 \text{ h}
      • Conversion Factors: 85 km1 h\frac{85 \text{ km}}{1 \text{ h}}, 1 h85 km\frac{1 \text{ h}}{85 \text{ km}}
      • Significant Figures: 85 km is measured (two SFs); 1 h is exact.
  • Conversion Factors From Dosage Problems
    • Example: "One tablet contains 500 mg of vitamin C"
      • Equality: 1 tablet=500 mg of vitamin C1 \text{ tablet} = 500 \text{ mg of vitamin C}
      • Conversion Factors: 500 mg vitamin C1 tablet\frac{500 \text{ mg vitamin C}}{1 \text{ tablet}}, 1 tablet500 mg vitamin C\frac{1 \text{ tablet}}{500 \text{ mg vitamin C}}
      • Significant Figures: 500 mg is measured (one SF); 1 tablet is exact.
  • Conversion Factors From a Percent
    • A percent (%) is a conversion factor expressing the numerical relationship of parts of a unit to 100 parts of the whole.
    • Example: "A person has 18% body fat by mass."
      • Equality: 18 kg of body fat=100 kg of body mass18 \text{ kg of body fat} = 100 \text{ kg of body mass}
      • Conversion Factors: 18 kg of body fat100 kg of body mass\frac{18 \text{ kg of body fat}}{100 \text{ kg of body mass}}, 100 kg of body mass18 kg of body fat\frac{100 \text{ kg of body mass}}{18 \text{ kg of body fat}}
      • Significant Figures: 18 kg is measured (two SFs); 100 kg is exact.
  • Conversion Factors From Dosage Problems (Medications)
    • Example: "Keflex (cephalexin) is available in 250-mg capsules."
      • Equality: 1 capsule=250 mg of Keflex1 \text{ capsule} = 250 \text{ mg of Keflex}
      • Conversion Factors: 250 mg of Keflex1 capsule\frac{250 \text{ mg of Keflex}}{1 \text{ capsule}}, 1 capsule250 mg of Keflex\frac{1 \text{ capsule}}{250 \text{ mg of Keflex}}
      • Significant Figures: 250 mg is measured (two SFs); 1 capsule is exact.