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U.S. Customary System Unit Multipliers Lesson 23

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When we attach words to numbers, we call the combination a denominate number where the words are the units. The units of the denominate number, 4 feet are feet.

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The Customary System is used as the basic unit of measurement in the United States. The basic units of the Customary System are the inch, foot, yard, and mile.

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Length Equivalents 12 inches (in.) = 1 foot (ft.) 3 feet (ft.) = 1 yard (yd.) 5280 feet (ft) = 1 mile (mi.)

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Weight Equivalents The basic unit of weight are the ounce, pound, and ton. 16 ounces (oz.) = 1 pound (lb.) 2000 pounds (lbs.) = 1 ton

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Liquid Equivalents 8 fluid ounces (fl. oz.) = 1 cup ( c) 2 cup ( c) = 1 pint (pt) 2 pint (pt) = 1 quart (qt) 4 quarts (qt) = 1 gallon (gal)

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Unit Multipliers Unit Multipliers are fractions that have a denominator with an equal value as its numerator. For example, unit multipliers would include: 12 in. 1 yd 5280 ft 12 in. 1 yd 5280 ft 1 ft. 3 ft. 1 mi. 1 ft. 3 ft. 1 mi.

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We can use unit multipliers to convert one unit of measurement to another. This will change the unit without changing the value.

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For example To convert 5 feet to inches, we use the unit multiplier that has the relationship between feet and inches. 5 ft x 12 in = 60 in 5 ft x 12 in = 60 in 1 1 ft 1 1 ft

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Example Use unit multipliers to convert 420 feet to yards

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Example Use unit multipliers to convert 72 inches to feet

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Multiple Unit Multipliers Convert 360 inches to yards

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Answer We will first convert inches to feet and then the feet to yards. 360 in. x 1 ft. x 1 yd = 360 = 10 yd 12 in. 3 ft. (12)(3) 12 in. 3 ft. (12)(3)

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Example Convert 48 gallons to cups

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Answer 48 gal x 4 qts. x 2 pt. x 2 cups = (48)(4)(2)(2) 1 gal 1 qt. 1 pint 1 1 gal 1 qt. 1 pint 1 768 cups 768 cups

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Approximations Between System Lengths 1 inch ≈ 2.5 centimeters 1 centimeter ≈ 0.4 inch 1 yard ≈ 0.9 meter 1 meter ≈ 1.1 yards 1 mile ≈ 1.6 kilometers 1 kilometer ≈ 0.6 mile

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Approximate Conversions Between System Units of Weight & Mass 1 ounce ≈ 28 grams 1 pound ≈ 0.45 kilogram 1 kilogram ≈ 2.2 pounds 1 ton ≈ 0.9 metric ton 1 metric ton ≈ 1.1 tons

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Approximate Conversions Between System Units of Capacity 1 quart ≈ 0.95 liter 1 liter ≈ 1.05 quart

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Examples Which is longer: 40 centimeters or 1.5 feet? How much longer? A Rottweiler weighs 128 pounds. What is the weight in kilograms? Approximately how many milliliters are equal to 1 fluid ounce?

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Try It Yourself! A football player has a mass of 125 kilograms. Approximately what is the player’s weight in pounds?

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Temperature The unit of temperature in the U.S. Customary System is degrees Fahrenheit. The unit of temperature in the metric system is degrees Celsius.

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Temperature U.S. Customary System MetricSystem Water freezes 32 ºF 0 ºC Room temperature 72 ºF 22.2 ºC Normal human body temp. 98.6 ºF 37 ºC Water boils 212 ºF 100 ºC

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Temperature To convert from degrees Celsius to degrees Fahrenheit, use the following formula: ºF = (9/5 · ºC) + 32 To convert from degrees Fahrenheit to degrees Celsius use: ºC = 5/9(ºF – 32) ºC = 5/9(ºF – 32)

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Homework 1 1. 160 fl. oz. = ________ qt 2. 56 oz. = ________ lbs 3. 72 yd = ________ in. 4. 36,960 ft = _______ mi 5. 5.5 T = ________ oz 6. 72 c = ________ qt

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Homework 2 1. 2.5 m = _______ mm 2. 12 kg = _______ mg 3. 3,400 L = _______ kL 4. 180 cm = _______ hm

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Homework 3 1. 57 kg = ________ lbs 2. 121 qt = ________ L 3. 6 in = ________ cm 4. 7 fl oz = _______ mL 5. Patrick weighs 147 pounds. How many kilograms does Patrick weigh?

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Homework 4 1. 38 ºC = _______ºF 2. 68.4 ºF = _______ ºC 3. 15 ºC = _______ ºF 4. The melting point of zinc is 787 ºF. What is the melting point of zinc in ºC? 5. A recipe says that cookies should be baked at 180 ºC. What is the temperature in ºF?

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