Unit Conversions: Study Guide Answers

Study Guide - Part 2 (One-Step Conversions)

Answers:

  1. \(8 \text{ ft} \times \frac{12 \text{ in}}{1 \text{ ft}} = 96 \text{ inches}\)
  2. \(144 \text{ in} \times \frac{1 \text{ ft}}{12 \text{ in}} = 12 \text{ feet}\)
  3. \(5 \text{ lb} \times \frac{16 \text{ oz}}{1 \text{ lb}} = 80 \text{ ounces}\)
  4. \(80 \text{ oz} \times \frac{1 \text{ lb}}{16 \text{ oz}} = 5 \text{ pounds}\)
  5. \(2.5 \text{ gal} \times \frac{4 \text{ qt}}{1 \text{ gal}} = 10 \text{ quarts}\)
  6. \(12 \text{ qt} \times \frac{1 \text{ gal}}{4 \text{ qt}} = 3 \text{ gallons}\)
  7. \(100 \text{ m} \times \frac{3.2808 \text{ ft}}{1 \text{ m}} = 328.08 \text{ feet}\)
  8. \(500 \text{ ft} \times \frac{1 \text{ m}}{3.2808 \text{ ft}} = 152.4 \text{ meters}\)
  9. \(3.5 \text{ kg} \times \frac{2.2046 \text{ lb}}{1 \text{ kg}} = 7.72 \text{ pounds}\)
  10. \(50 \text{ lb} \times \frac{1 \text{ kg}}{2.2046 \text{ lb}} = 22.7 \text{ kilograms}\)

Study Guide - Part 3 (Multi-Step Conversions)

Answers:

  1. \(2 \text{ mi} \times \frac{5280 \text{ ft}}{1 \text{ mi}} \times \frac{12 \text{ in}}{1 \text{ ft}} = 126{,}720 \text{ inches}\)
  2. \(50000 \text{ cm} \times \frac{1 \text{ in}}{2.54 \text{ cm}} \times \frac{1 \text{ ft}}{12 \text{ in}} \times \frac{1 \text{ mi}}{5280 \text{ ft}} = 0.311 \text{ miles}\)
  3. \(5 \text{ gal} \times \frac{4 \text{ qt}}{1 \text{ gal}} \times \frac{2 \text{ pt}}{1 \text{ qt}} \times \frac{2 \text{ cups}}{1 \text{ pt}} = 80 \text{ cups}\)
  4. \(128 \text{ fl oz} \times \frac{1 \text{ cup}}{8 \text{ fl oz}} \times \frac{1 \text{ pt}}{2 \text{ cups}} \times \frac{1 \text{ qt}}{2 \text{ pt}} \times \frac{1 \text{ gal}}{4 \text{ qt}} = 1 \text{ gallon}\)
  5. \(5 \text{ lb} \times \frac{16 \text{ oz}}{1 \text{ lb}} \times \frac{28.35 \text{ g}}{1 \text{ oz}} = 2268 \text{ grams}\)

Study Guide - Part 4 (Squared and Cubed Conversions)

Answers:

  1. \(3 \text{ ft}^2 \times \frac{12 \text{ in}}{1 \text{ ft}} \times \frac{12 \text{ in}}{1 \text{ ft}} = 3 \times 12 \times 12 \text{ in}^2 = \) \(432 \text{ in}^2\)
  2. \(500 \text{ in}^2 \times \frac{1 \text{ ft}}{12 \text{ in}} \times \frac{1 \text{ ft}}{12 \text{ in}} = 500 \times \frac{1}{12} \times \frac{1}{12} \text{ ft}^2 = \) \(3.47 \text{ ft}^2\)
  3. \(2 \text{ yd}^2 \times \frac{3 \text{ ft}}{1 \text{ yd}} \times \frac{3 \text{ ft}}{1 \text{ yd}} = 2 \times 3 \times 3 \text{ ft}^2 = \) \(18 \text{ ft}^2\)
  4. \(5 \text{ m}^2 \times \frac{100 \text{ cm}}{1 \text{ m}} \times \frac{100 \text{ cm}}{1 \text{ m}} = 5 \times 100 \times 100 \text{ cm}^2 = \) \(50{,}000 \text{ cm}^2\)
  5. \(1 \text{ mi}^2 \times \frac{5280 \text{ ft}}{1 \text{ mi}} \times \frac{5280 \text{ ft}}{1 \text{ mi}} = 1 \times 5280 \times 5280 \text{ ft}^2 = \) \(27{,}878{,}400 \text{ ft}^2\)
  6. \(4 \text{ ft}^3 \times \frac{12 \text{ in}}{1 \text{ ft}} \times \frac{12 \text{ in}}{1 \text{ ft}} \times \frac{12 \text{ in}}{1 \text{ ft}} = 4 \times 12 \times 12 \times 12 \text{ in}^3 = \) \(6912 \text{ in}^3\)
  7. \(10000 \text{ cm}^3 \times \frac{1 \text{ m}}{100 \text{ cm}} \times \frac{1 \text{ m}}{100 \text{ cm}} \times \frac{1 \text{ m}}{100 \text{ cm}} = 10000 \times \frac{1}{100} \times \frac{1}{100} \times \frac{1}{100} \text{ m}^3 = \) \(0.01 \text{ m}^3\)
  8. \(0.5 \text{ yd}^3 \times \frac{3 \text{ ft}}{1 \text{ yd}} \times \frac{3 \text{ ft}}{1 \text{ yd}} \times \frac{3 \text{ ft}}{1 \text{ yd}} = 0.5 \times 3 \times 3 \times 3 \text{ ft}^3 = \) \(13.5 \text{ ft}^3\)
  9. \(2.5 \text{ m}^3 \times \frac{100 \text{ cm}}{1 \text{ m}} \times \frac{100 \text{ cm}}{1 \text{ m}} \times \frac{100 \text{ cm}}{1 \text{ m}} = 2.5 \times 100 \times 100 \times 100 \text{ cm}^3 = \) \(2{,}500{,}000 \text{ cm}^3\)
  10. \(1 \text{ in}^3 \times \frac{2.54 \text{ cm}}{1 \text{ in}} \times \frac{2.54 \text{ cm}}{1 \text{ in}} \times \frac{2.54 \text{ cm}}{1 \text{ in}} = 1 \times 2.54 \times 2.54 \times 2.54 \text{ cm}^3 = \) \(16.39 \text{ cm}^3\)

Study Guide - Part 5 (Metric Conversions)

Answers:

  1. \(4.2 \text{ km} \times \frac{1000 \text{ m}}{1 \text{ km}} = 4200 \text{ m}\)
  2. \(850 \text{ cm} \times \frac{1 \text{ m}}{100 \text{ cm}} = 8.5 \text{ m}\)
  3. \(2500 \text{ mm} \times \frac{1 \text{ m}}{1000 \text{ mm}} = 2.5 \text{ m}\)
  4. \(6.8 \text{ kg} \times \frac{1000 \text{ g}}{1 \text{ kg}} = 6800 \text{ g}\)
  5. \(450 \text{ mg} \times \frac{1 \text{ g}}{1000 \text{ mg}} = 0.45 \text{ g}\)
  6. \(3.2 \text{ g} \times \frac{1000 \text{ mg}}{1 \text{ g}} = 3200 \text{ mg}\)
  7. \(2.5 \text{ L} \times \frac{1000 \text{ mL}}{1 \text{ L}} = 2500 \text{ mL}\)
  8. \(750 \text{ mL} \times \frac{1 \text{ L}}{1000 \text{ mL}} = 0.75 \text{ L}\)
  9. \(5.6 \text{ cm} \times \frac{10 \text{ mm}}{1 \text{ cm}} = 56 \text{ mm}\)
  10. \(8500 \text{ g} \times \frac{1 \text{ kg}}{1000 \text{ g}} = 8.5 \text{ kg}\)

Study Guide - Part 6 (Derived Units)

Answers:

  1. \(45 \frac{\text{mi}}{\text{hr}} \times \frac{5280 \text{ ft}}{1 \text{ mi}} \times \frac{1 \text{ hr}}{3600 \text{ s}} = 66 \frac{\text{ft}}{\text{s}}\)
  2. \(25 \frac{\text{m}}{\text{s}} \times \frac{3.2808 \text{ ft}}{1 \text{ m}} \times \frac{1 \text{ mi}}{5280 \text{ ft}} \times \frac{3600 \text{ s}}{1 \text{ hr}} = 55.9 \text{ mph}\)
  3. \(8.0 \frac{\text{g}}{\text{cm}^3} \times \frac{1 \text{ kg}}{1000 \text{ g}} \times \frac{1000 \text{ cm}^3}{1 \text{ L}} = 8.0 \frac{\text{kg}}{\text{L}}\)
  4. \(1.2 \frac{\text{kg}}{\text{L}} \times \frac{1000 \text{ g}}{1 \text{ kg}} \times \frac{1 \text{ L}}{1000 \text{ mL}} = 1.2 \frac{\text{g}}{\text{mL}}\)
  5. \(88 \frac{\text{ft}}{\text{s}} \times \frac{1 \text{ mi}}{5280 \text{ ft}} \times \frac{3600 \text{ s}}{1 \text{ hr}} = 60 \text{ mph}\)

Study Guide - Part 7 (Special Conversions)

Answers:

  1. \(350 \text{ cm}^3 \times \frac{1 \text{ mL}}{1 \text{ cm}^3} = 350 \text{ mL}\)
  2. \(2.5 \text{ L} \times \frac{1000 \text{ mL}}{1 \text{ L}} \times \frac{1 \text{ cm}^3}{1 \text{ mL}} = 2500 \text{ cm}^3\)
  3. \(500 \text{ mL water} \times \frac{1 \text{ g water}}{1 \text{ mL water}} = 500 \text{ g water}\)
  4. \(750 \text{ g water} \times \frac{1 \text{ mL water}}{1 \text{ g water}} = 750 \text{ mL}\)
  5. a) \(10 \text{ cm} \times 8 \text{ cm} \times 6 \text{ cm} = 480 \text{ cm}^3\)
    b) \(480 \text{ cm}^3 \times \frac{1 \text{ mL}}{1 \text{ cm}^3} = 480 \text{ mL}\)
    c) \(480 \text{ mL water} \times \frac{1 \text{ g water}}{1 \text{ mL water}} = 480 \text{ g water}\)