U.S. Customary SystemU.S. Customary SystemUnit MultipliersUnit Multipliers

Lesson 23Lesson 23

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

The units of the denominate number, 4 The units of the denominate number, 4 feet are feet.feet are feet.

The Customary System is used as the The Customary System is used as the basic unit of measurement in the United basic unit of measurement in the United States.States.

The basic units of the Customary System The basic units of the Customary System are the inch, foot, yard, and mile.are the inch, foot, yard, and mile.

Length EquivalentsLength Equivalents

12 inches (in.) = 1 foot (ft.)12 inches (in.) = 1 foot (ft.)

3 feet (ft.) = 1 yard (yd.)3 feet (ft.) = 1 yard (yd.)

5280 feet (ft) = 1 mile (mi.)5280 feet (ft) = 1 mile (mi.)

Weight EquivalentsWeight Equivalents

The basic unit of weight are the ounce, The basic unit of weight are the ounce, pound, and ton.pound, and ton.

16 ounces (oz.) = 1 pound (lb.)16 ounces (oz.) = 1 pound (lb.)

2000 pounds (lbs.) = 1 ton 2000 pounds (lbs.) = 1 ton

Liquid EquivalentsLiquid Equivalents

8 fluid ounces (fl. oz.) = 1 cup ( c)8 fluid ounces (fl. oz.) = 1 cup ( c)

2 cup ( c) = 1 pint (pt)2 cup ( c) = 1 pint (pt)

2 pint (pt) = 1 quart (qt)2 pint (pt) = 1 quart (qt)

4 quarts (qt) = 1 gallon (gal)4 quarts (qt) = 1 gallon (gal)

Unit MultipliersUnit Multipliers

Unit Multipliers are fractions that have a Unit Multipliers are fractions that have a denominator with an equal value as its denominator with an equal value as its numerator.numerator.

For example, unit multipliers would For example, unit multipliers would include:include:

12 in. 12 in. 1 yd 1 yd 5280 ft5280 ft 1 ft. 3 ft. 1 mi. 1 ft. 3 ft. 1 mi.

We can use unit multipliers to convert one We can use unit multipliers to convert one unit of measurement to another.unit of measurement to another.

This will change the unit without changing This will change the unit without changing the value.the value.

For exampleFor example

To convert 5 feet to inches, we use the To convert 5 feet to inches, we use the unit multiplier that has the relationship unit multiplier that has the relationship between feet and inches.between feet and inches.

5 ft 5 ft x x 12 in 12 in = 60 in = 60 in

1 1 ft1 1 ft

ExampleExample

Use unit multipliers to convert 420 feet to Use unit multipliers to convert 420 feet to yardsyards

ExampleExample

Use unit multipliers to convert 72 inches to Use unit multipliers to convert 72 inches to feetfeet

Multiple Unit MultipliersMultiple Unit Multipliers

Convert 360 inches to yardsConvert 360 inches to yards

AnswerAnswer

We will first convert inches to feet and then We will first convert inches to feet and then the feet to yards.the feet to yards.

360 in. 360 in. xx 1 ft1 ft. . x x 1 yd1 yd = = 360360 = 10 yd = 10 yd

12 in. 3 ft. (12)(3)12 in. 3 ft. (12)(3)

ExampleExample

Convert 48 gallons to cupsConvert 48 gallons to cups

AnswerAnswer

48 gal 48 gal xx 4 qts.4 qts. xx 2 pt.2 pt. x x 2 cups2 cups = = (48)(4)(2)(2)(48)(4)(2)(2)

1 gal 1 qt. 1 pint 11 gal 1 qt. 1 pint 1

768 cups768 cups

Approximations Between System Approximations Between System LengthsLengths

1 inch 1 inch ≈ 2.5 centimeters≈ 2.5 centimeters

1 centimeter ≈ 0.4 inch1 centimeter ≈ 0.4 inch

1 yard ≈ 0.9 meter1 yard ≈ 0.9 meter

1 meter ≈ 1.1 yards1 meter ≈ 1.1 yards

1 mile ≈ 1.6 kilometers1 mile ≈ 1.6 kilometers

1 kilometer ≈ 0.6 mile1 kilometer ≈ 0.6 mile

Approximate Conversions Between Approximate Conversions Between System Units of Weight & MassSystem Units of Weight & Mass

1 ounce 1 ounce ≈ 28 grams≈ 28 grams

1 pound ≈ 0.45 kilogram1 pound ≈ 0.45 kilogram

1 kilogram ≈ 2.2 pounds1 kilogram ≈ 2.2 pounds

1 ton ≈ 0.9 metric ton1 ton ≈ 0.9 metric ton

1 metric ton ≈ 1.1 tons1 metric ton ≈ 1.1 tons

Approximate Conversions Between Approximate Conversions Between System Units of CapacitySystem Units of Capacity

1 quart 1 quart ≈ 0.95 liter≈ 0.95 liter

1 liter ≈ 1.05 quart1 liter ≈ 1.05 quart

ExamplesExamples

Which is longer: 40 centimeters or 1.5 Which is longer: 40 centimeters or 1.5 feet? How much longer?feet? How much longer?

A Rottweiler weighs 128 pounds. What is A Rottweiler weighs 128 pounds. What is the weight in kilograms?the weight in kilograms?

Approximately how many milliliters are Approximately how many milliliters are equal to 1 fluid ounce?equal to 1 fluid ounce?

Try It Yourself!Try It Yourself!

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

TemperatureTemperature

The unit of temperature in the U.S. The unit of temperature in the U.S. Customary System is degrees Fahrenheit.Customary System is degrees Fahrenheit.

The unit of temperature in the metric The unit of temperature in the metric system is degrees Celsius.system is degrees Celsius.

TemperatureTemperature

U.S. U.S. Customary Customary

SystemSystem

MetricMetric

SystemSystem

Water freezesWater freezes 32 32 ºFºF 0 0 ºCºC

Room Room temperaturetemperature

72 72 ºFºF 22.2 22.2 ºCºC

Normal human Normal human body temp.body temp.

98.6 98.6 ºFºF 37 37 ºCºC

Water boilsWater boils 212 212 ºFºF 100 100 ºCºC

TemperatureTemperature

To convert from degrees Celsius to degrees To convert from degrees Celsius to degrees Fahrenheit, use the following formula:Fahrenheit, use the following formula:

ºF = (9/5 · ºC) + 32ºF = (9/5 · ºC) + 32

To convert from degrees Fahrenheit to degrees To convert from degrees Fahrenheit to degrees Celsius use:Celsius use:

ºC = 5/9(ºF – 32)ºC = 5/9(ºF – 32)

Homework 1Homework 1

1. 160 fl. oz. = ________ qt1. 160 fl. oz. = ________ qt

2. 56 oz. = ________ lbs2. 56 oz. = ________ lbs

3. 72 yd = ________ in.3. 72 yd = ________ in.

4. 36,960 ft = _______ mi4. 36,960 ft = _______ mi

5. 5.5 T = ________ oz5. 5.5 T = ________ oz

6. 72 c = ________ qt 6. 72 c = ________ qt

Homework 2Homework 2

1. 2.5 m = _______ mm1. 2.5 m = _______ mm

2. 12 kg = _______ mg2. 12 kg = _______ mg

3. 3,400 L = _______ kL3. 3,400 L = _______ kL

4. 180 cm = _______ hm4. 180 cm = _______ hm

Homework 3Homework 3

1. 57 kg = ________ lbs1. 57 kg = ________ lbs

2. 121 qt = ________ L2. 121 qt = ________ L

3. 6 in = ________ cm3. 6 in = ________ cm

4. 7 fl oz = _______ mL4. 7 fl oz = _______ mL

5. Patrick weighs 147 pounds. How many 5. Patrick weighs 147 pounds. How many kilograms does Patrick weigh?kilograms does Patrick weigh?

Homework 4Homework 4

1. 38 1. 38 ºCºC = _______ = _______ºFºF

2. 68.4 ºF = _______ ºC2. 68.4 ºF = _______ ºC

3. 15 ºC = _______ ºF3. 15 ºC = _______ ºF

4. The melting point of zinc is 787 ºF. 4. The melting point of zinc is 787 ºF. What is the melting point of zinc in ºC?What is the melting point of zinc in ºC?

5. A recipe says that cookies should be 5. A recipe says that cookies should be baked at 180 ºC. What is the temperature baked at 180 ºC. What is the temperature in ºF?in ºF?