Converting between American and Metric Units

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Clothing Labels

EXAMPLE 1

470 Chapter 5 Ratio, Proportion, and Measurement

Objectives

S E C T I O N 5.5

1Use unit conversion factors to convert between American and metric units.

2Convert between Fahrenheit and Celsius temperatures.

This is the unit we want to introduce.

This is the unit we want to eliminate (the original unit).

It is often necessary to convert between American units and metric units. For example, we must convert units to answer the following questions.

•Which is higher: Pikes Peak (elevation 14,110 feet) or the Matterhorn (elevation 4,478 meters)?

•Does a 2-pound tub of butter weigh more than a 1-kilogram tub?

•Is a quart of soda pop more or less than a liter of soda pop?

In this section, we discuss how to answer such questions.

1Use unit conversion factors to convert between American and metric units.

The following table shows some conversions between American and metric units of length. In all but one case, the conversions are rounded approximations. An symbol is used to show this. The one exact conversion in the table is 1 inch = 2.54 centimeters.


1	2	3	4	5	6	7	8	9	10 11 12
				1 foot


1	2	3	4	5	6	7	8	9	10 11 12	13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36
											1 yard


			10				20		30	40	50	60	70	80	90	100

1 meter

Equivalent Lengths

American to metric	Metric to American

1 in. 2.54 cm	1 cm 0.39 in.

1 ft 0.30 m	1 m 3.28	ft

1 yd 0.91 m	1 m 1.09	yd
1 mi 1.61 km	1 km 0.62 mi

Self Check 1

CLOTHING LABELS Refer to the ﬁgure in Example 1. What is the inseam length, to the nearest inch?

Now Try Problem 13

Unit conversion factors can be formed from the facts in the table to make speciﬁc conversions between American and metric units of length.

The ﬁgure shows a label sewn into some pants made in Mexico that are for sale in the United States. Express the waist size to the nearest inch.

Strategy We will multiply 82 centimeters by a carefully chosen unit conversion factor.

WHY If we multiply by the proper unit conversion factor, we can eliminate the unwanted units of centimeters and convert to inches.

WAIST: 82 cm INSEAM: 76 cm RN-80811

SEE REVERSE FOR CARE

MADE IN

MEXICO

Solution

To convert from centimeters to inches, we must choose a unit conversion factor whose numerator contains the units we want to introduce (inches), and whose denominator contains the units we want to eliminate (centimeters). From the ﬁrst row of the Metric to American column of the table, we see that there is approximately 0.39 inch per centimeter. Thus, we will use the unit conversion factor:

							5.5 Converting between American and Metric Units	471
To perform the conversion, we multiply.
82 cm		82 cm		0.39 in.	Write 82 cm as a fraction: 82 cm 82 cm .
					Multiply by a form of 1:	0.39 in.	1
	1			1 cm
						1 cm	.
	82 cm		0.39 in.		Remove the common units of centimeters from the
	1			1 cm	numerator and denominator. The units of inches remain.

82 0.39 in.	Simplify.	0.39

31.98 in.	Do the multiplication.	82
		78
32 in.	Round to the nearest inch (ones column).
		3120
To the nearest inch, the waist size is 32 inches.		31.98

	EXAMPLE 2	Mountain Elevations Pikes Peak, one of the most	Self Check 2
			TRACK AND FIELD Which is
famous peaks in the Rocky Mountains, has an elevation of 14,110 feet. The
Matterhorn, in the Swiss Alps, rises to an elevation of 4,478 meters. Which			longer: a 500-meter race or a
mountain is higher?			550-yard race?

Strategy	We will convert the elevation of Pikes Peak, which given in feet, to	Now Try Problem 17

meters.

WHY Then we can compare the mountain’s elevations in the same units, meters.

Solution

To convert Pikes Peak elevation from feet to meters we must choose a unit conversion factor whose numerator contains the units we want to introduce (meters) and whose denominator contains the units we want to eliminate (feet). From the second row of the American to metric column of the table, we see that there is approximately 0.30 meter per foot. Thus, we will use the unit conversion factor:

To perform the conversion, we multiply.

14,110 ft	14,110 ft		0.30 m
	1		1 ft

14,110 ft 0.30 m

11 ft

14,110 0.30 m

4,233 m

Write 14,110 ft as a fraction: 14,110 ft 14,110 ft .

Multiply by a form of 1: 0.30 m.

1 ft

	1
Remove the common units of feet from	14,110
the numerator and denominator. The		0.30
units of meters remain.	000 00
Simplify.	4233 00
	4233.00
Do the multiplication.

Since the elevation of Pikes Peak is about 4,233 meters, we can conclude that the

Matterhorn, with an elevation of 4,478 meters, is higher.

We can convert between American units of weight and metric units of mass using the rounded approximations in the following table.

Equivalent Weights and Masses

American to metric	Metric to American

1 oz 28.35 g	1 g 0.035 oz	1 pound

1 lb 0.45 kg	1 kg 2.20 lb

1 kilogram

472	Chapter 5 Ratio, Proportion, and Measurement

Self Check 3

Convert 68 pounds to grams. Round to the nearest gram.

Now Try Problem 21

EXAMPLE 3 Convert 50 pounds to grams.

Strategy We will use a two-part multiplication process that converts 50 pounds to ounces, and then converts that result to grams.

WHY We must use a two-part process because the conversion table on page 471 does not contain a single unit conversion factor that converts from pounds to grams.

Self Check 4

BODY WEIGHT Who weighs more, a person who weighs 165 pounds or one who weighs 76 kilograms?

Now Try Problem 25

Solution

Since there are 16 ounces per pound, we can convert 50 pounds to ounces by multiplying by the unit conversion factor 161 lboz . Since there are approximately 28.35 g per ounce, we can convert that result to grams by multiplying by the unit conversion factor 28.1 35oz g .


50 lb		50 lb		16 oz		28.35 g
	1			1 lb		1 oz
	50 lb		16 oz		28.35 g
	1			1 lb		1oz

50 16 28.35 g

800 28.35 g

22,680 g

Write 50 lb as a fraction: 50 lb				50 lb	. Multiply
				1
by two forms of 1:	16 oz	and	28.35 g	.
	1 lb		1 oz

Remove the common units of pounds and ounces from the numerator and denominator. The units of grams remain.

Simplify.


Multiply: 50 16 800.	3	6 2		4
Multiply: 50 16 800.	16	28.35
Do the multiplication.	50		800
Do the multiplication.	800	22680.00
	800	22680.00

Thus, 50 pounds 22,680 grams.

EXAMPLE 4	Packaging Does a 2.5 pound tub of butter weigh more

than a 1.5-kilogram tub?

Strategy We will convert the weight of the 1.5-kilogram tub of butter to pounds.

WHY Then we can compare the weights of the tubs of butter in the same units, pounds.

Solution

To convert 1.5 kilograms to pounds we must choose a unit conversion factor whose numerator contains the units we want to introduce (pounds), and whose denominator contains the units we want to eliminate (kilograms). From the second row of the Metric to American column of the table, we see that there are approximately 2.20 pounds per kilogram. Thus, we will use the unit conversion factor:

2.20

This is the unit we want to introduce.

This is the unit we want to eliminate (the original unit).

To perform the conversion, we multiply.

1.5 kg

2.20 lb

Write 1.5 kg as a fraction: 1.5 kg 1.5 kg .

1 kg

Multiply by a form of 1: 2.20 lb .

1 kg

1.5 kg

2.20 lb

Remove the common units of kilograms from

2.20

the numerator and denominator. The units

1.5

1 kg

of pounds remain.

1100

1.5 2.20 lb

Simplify.

2200

3.300

3.3 lb

Do the multiplication.

Since a 1.5-kilogram tub of butter weighs about 3.3 pounds, the 1.5-kilogram tub weighs more.

Cleaning Supplies

EXAMPLE 5

5.5 Converting between American and Metric Units

473

We can convert between American and metric units of capacity using the rounded approximations in the following table.

Equivalent Capacities

American to metric	Metric to American

1 ﬂ oz 29.57 mL	1 L		33.81 ﬂ oz
1 pt 0.47 L	1	L	2.11 pt
1 qt 0.95 L	1	L	1.06 qt
1 gal 3.79 L	1	L	0.264 gal	1 liter	1 quart

THINK IT THROUGH

Studying in Other Countries

“Over the past decade, the number of U.S. students studying abroad has more than doubled.”

From The Open Doors 2008 Report

In 2006/2007, a record number of 241,791 college students received credit for study abroad. Since students traveling to other countries are almost certain to come into contact with the metric system of measurement, they need to have a basic understanding of metric units.

Suppose a student studying overseas needs to purchase the following school supplies. For each item in red, choose the appropriate metric units.

1. 8	1 in. 11 in. notebook paper:
	2
	216 meters 279 meters	216 centimeters 279 centimeters

216 millimeters 279 millimeters

2. A backpack that can hold 20 pounds of books:

9 kilograms

9 grams

9 milligrams

3. 34 ﬂuid ounce bottle of Liquid Paper correction ﬂuid:

22.5 hectoliters

2.5 liters

22.2 milliliters

A bottle of window cleaner contains 750 milliliters of solution. Convert this measure to quarts. Round to the nearest tenth.

Strategy We will use a two-part multiplication process that converts 750 milliliters to liters, and then converts that result to quarts.

WHY We must use a two-part process because the conversion table at the top of this page does not contain a single unit conversion factor that converts from milliliters to quarts.

Self Check 5

DRINKING WATER A student bought a 360-mL bottle of water. Convert this measure to quarts. Round to the nearest tenth.

Now Try Problem 29

Solution

Since there is 1 liter for every 1,000 mL, we can convert 750 milliliters to liters by

1 L

multiplying by the unit conversion factor 1,000 mL . Since there are approximately

474Chapter 5 Ratio, Proportion, and Measurement

1.06qt per liter, we can convert that result to quarts by multiplying by the unit conversion factor 1.061 Lqt .

750 mL	750 mL	1 L	1.06 qt
750 mL	1	1,000 mL	1 L
	750 mL	1 L	1.06 qt

	1	1,000 mL	1 L

750 1.06 qt

1,000

1,000795 qt

0.795 qt

0.8 qt

Write 750 mL as a fraction:
750 mL 750 mL		. Multiply by
1		1 L	and 1.06 qt .
two forms of 1:		1 L
two forms of 1:	1,000 mL
	1,000 mL			1 L
Remove the common units of
milliliters and liters from the
numerator and denominator.				750
numerator and denominator.				750
The units of quarts remain.					1.06
Multiply the fractions.				4500
Multiply the fractions.				0000
				0000
				75000
Multiply: 750 1.06 795.				795.00
Multiply: 750 1.06 795.				795.00

Divide 795 by 1,000 by moving the decimal point 3 places to the left.

Round to the nearest tenth.

The bottle contains approximately 0.8 qt of cleaning solution.

2 Convert between Fahrenheit and Celsius temperatures.

In the American system, we measure temperature using degrees Fahrenheit ( F). In the metric system, we measure temperature using degrees Celsius ( C). These two scales are shown on the thermometers on the right. From the ﬁgures, we can see that

• 212 F 100 C	Water boils
• 32 F 0 C	Water freezes
• 5 F 15 C	A cold winter day
• 95 F 35 C	A hot summer day

There are formulas that enable us to convert from degrees Fahrenheit to degrees Celsius and from degrees Celsius to degrees Fahrenheit.

Celsius scale		Fahrenheit scale
	100°C	212°F
100°C		Water	210°F
		boils	210°F
		boils	200°F
90°C			200°F
90°C			190°F
			190°F
80°C			180°F
80°C			170°F
			170°F
70°C			160°F
70°C
			150°F
60°C			140°F
			130°F
50°C			120°F
			120°F
40°C	37°C	98.6°F	110°F
40°C	37°C	98.6°F
		Normal	100°F
30°C		body	90°F
30°C	temperature		80°F
	temperature		80°F
20°C			70°F
20°C
			60°F
10°C			50°F
	0°C	Water 32°F	40°F
0°C	0°C	Water 32°F	30°F
0°C		freezes

			20°F
			20°F
–10°C			10°F
			10°F
–20°C			–0°F
–20°C			–10°F
			–10°F

Conversion Formulas for Temperature

If F is the temperature in degrees Fahrenheit and C is the corresponding temperature in degrees Celsius, then

C	5	1F 322	and F	9	C 32
	9			5

EXAMPLE 7

EXAMPLE 6

5.5 Converting between American and Metric Units

475

Bathing Warm bath water is 90 F. Express this temperature in degrees Celsius. Round to the nearest tenth of a degree.

Strategy We will substitute 90 for F in the formula C 59 (F 32).

WHY Then we can use the rule for the order of operations to evaluate the right side of the equation and ﬁnd the value of C, the temperature in degrees Celsius of the bath water.

Self Check 6

COFFEE Hot coffee is 110 F. Express this temperature in degrees Celsius. Round to the nearest tenth of a degree.

Now Try Problem 33

Solution

C	5	1F 322		This is the formula to ﬁnd degrees Celsius.				4
	5							4
								58
	9							58
	5							5
	5	190 322		Substitute 90 for F.				290
	9	190 322		Substitute 90 for F.
	5			Do the subtraction within the		32.22
	5			Do the subtraction within the
9 1582				parentheses ﬁrst: 90 32 58.

						9 290.00
						9 290.00
	5		58			27
	5		58	Write 58 as a fraction: 58	58	20
					58	20
		a b			1 .
	9		1				18
	290			Multiply the numerators.		20
	9			Multiply the denominators.					18
	9			Multiply the denominators.		20
32.222 . . .				Do the division.		20
32.222 . . .				Do the division.		18
32.2				Round to the nearest tenth.		2
32.2				Round to the nearest tenth.		2

To the nearest tenth of a degree, the temperature of the bath water is 32.2 C.

Dishwashers A dishwasher manufacturer recommends that dishes be rinsed in hot water with a temperature of 60 C. Express this temperature in degrees Fahrenheit.

Strategy We will substitute 60 for C in the formula F 95 C 32.

WHY Then we can use the rule for the order of operations to evaluate the right side of the equation and ﬁnd the value of F, the temperature in degrees Fahrenheit of the water.

Solution

	9
F	5 C 32	This is the formula to ﬁnd degrees Fahrenheit.

5 1602 32 Substitute 60 for C.

5405 32 Multiply: 95 (60) 95 1601 2 5405 .9

108 32	Do the division.
140	Do the addition.

The manufacturer recommends that dishes be rinsed in 140 F water.

60108

9 5 540

5405

ANSWERS TO SELF CHECKS

1.	30 in.	2.	the 550-yard race 3. 30, 845 g 4. the person who weighs 76 kg
5.	0.4 qt	6.	43.3°C 7. yes

Self Check 7

FEVERS To determine whether a baby has a fever, her mother takes her temperature with a Celsius thermometer. If the reading is 38.8 C, does the baby have a fever? (Hint: Normal body temperature is 98.6 F.)

Now Try Problem 37

476 Chapter 5 Ratio, Proportion, and Measurement


	S E C T I O N 5.5			STUDY SET
		VOCABULARY


	Fill in the blanks.
1.			In the American system, temperatures are measured
			in degrees		. In the metric system,
			temperatures are measured in degrees			.
2.			a. Inches and centimeters are units used to
			measure	.

b.Pounds and grams are used to measure (weight).

c.Gallons and liters are units used to measure

CONCEPTS

3.Which is longer:

a.A yard or a meter?

b.A foot or a meter?

c.An inch or a centimeter?

d.A mile or a kilometer?

4.Which is heavier:

a.An ounce or a gram?

b.A pound or a kilogram?

5.Which is the greater unit of capacity:

a.A pint or a liter?

b.A quart or a liter?

c.A gallon or a liter?

6.a. What formula is used for changing degrees Celsius to degrees Fahrenheit?

b.What formula is used for changing degrees Fahrenheit to degrees Celsius?

7.Write a unit conversion factor to convert

a.feet to meters

b.pounds to kilograms

c.gallons to liters

8.Write a unit conversion factor to convert

a.centimeters to inches

b.grams to ounces

c.liters to ﬂuid ounces

NOTATION

Complete each solution.

9. Convert 4,500 feet to meters.

4,500 ft	4,500ft
	1	1ft

	1,350

10. Convert 8 liters to gallons.

8 L	8 L		gal

	1	1 L

2.112

11. Convert 3 kilograms to ounces.

3 kg	3 kg	1,000 g		oz

	1	1 kg	1 g

3 0.035 oz

105

12.Convert 70°C to degrees Fahrenheit.


F	9		C 32
	5
	9	(		) 32


	5

158

Thus, 70°C 158

GUIDED PRACTICE

Perform each conversion. Round to the nearest inch.

See Example 1.

13.25 centimeters to inches

14.35 centimeters to inches

15.88 centimeters to inches

16.91 centimeters to inches

Perform each conversion. See Example 2.

17.8,400 feet to meters

18.7,300 feet to meters

19.25,115 feet to meters

20.36,242 feet to meters

Perform each conversion. See Example 3.

21.20 pounds to grams

22.30 pounds to grams

23.75 pounds to grams

24.95 pounds to grams

Perform each conversion. See Example 4.

25.6.5 kilograms to pounds

26.7.5 kilograms to pounds

27.300 kilograms to pounds

28.800 kilograms to pounds

Perform each conversion. Round to the nearest tenth.

See Example 5.

29.650 milliliters to quarts

30.450 milliliters to quarts

31.1,200 milliliters to quarts

32.1,500 milliliters to quarts

Express each temperature in degrees Celsius. Round to the nearest tenth of a degree. See Example 6.

33.	120°F	34.	110°F
35.	35°F	36.	45°F

Express each temperature in degrees Fahrenheit. See Example 7.

37.	75°C	38.	85°C
39.	10°C	40.	20°C

TRY IT YOURSELF

Perform each conversion. If necessary, round answers to the nearest tenth. Since most conversions are approximate, answers will vary slightly depending on the method used.

41.25 pounds to grams

42.7.5 ounces to grams

43.50°C to degrees Fahrenheit

44.36.2°C to degrees Fahrenheit

45.0.75 quarts to milliliters

46.3 pints to milliliters

47.0.5 kilograms to ounces

48.35 grams to pounds

49.3.75 meters to inches

50.2.4 kilometers to miles

51.3 ﬂuid ounces to liters

52.2.5 pints to liters

53.12 kilometers to feet

54.3,212 centimeters to feet

55.37 ounces to kilograms

56.10 pounds to kilograms

57.10°C to degrees Fahrenheit

58.22.5°C to degrees Fahrenheit

59.17 grams to ounces

60.100 kilograms to pounds

61.7.2 liters to ﬂuid ounces

62.5 liters to quarts

63.3 feet to centimeters

64.7.5 yards to meters

65.500 milliliters to quarts

66.2,000 milliliters to gallons

67.50°F to degrees Celsius

68.67.7°F to degrees Celsius

5.5 Converting between American and Metric Units

477

69.5,000 inches to meters

70.25 miles to kilometers

71.5°F to degrees Celsius

72.10°F to degrees Celsius

APPLICATIONS

Since most conversions are approximate, answers will vary slightly depending on the method used.

73.THE MIDDLE EAST The distance between Jerusalem and Bethlehem is 8 kilometers. To the nearest mile, give this distance in miles.

74.THE DEAD SEA The Dead Sea is 80 kilometers long. To the nearest mile, give this distance in miles.

75.CHEETAHS A cheetah can run 112 kilometers per hour. Express this speed in mph. Round to the nearest mile.

76.LIONS A lion can run 50 mph. Express this speed in kilometers per hour.

77.MOUNT WASHINGTON The highest peak of the White Mountains of New Hampshire is Mount Washington, at 6,288 feet. Give this height in kilometers. Round to the nearest tenth.

78.TRACK AND FIELD Track meets are held

on an oval track. One lap around the track is usually 400 meters. However, some older tracks in the United States are 440-yard ovals. Are these two types of tracks the same length? If not, which is longer?

79.HAIR GROWTH When hair is short, its rate of growth averages about 34 inch per month. How many centimeters is this a month? Round to the nearest

tenth of a centimeter.

80.WHALES An adult male killer whale can weigh as much as 12,000 pounds and be as long as 25 feet. Change these measurements to kilograms and meters.

81.WEIGHTLIFTING The table lists the personal best bench press records for two of the world’s best powerlifters. Change each metric weight to pounds. Round to the nearest pound.

		Bench
Name	Hometown	press

Liz Willet	Ferndale, Washington	187 kg
Brian Siders	Charleston, W. Virginia	350 kg

478Chapter 5 Ratio, Proportion, and Measurement

82.WORDS OF WISDOM Refer to the wall hanging. Convert the ﬁrst metric weight to ounces and the second to pounds. What famous saying results?

83.OUNCES AND FLUID OUNCES

a.There are 310 calories in 8 ounces of broiled chicken. Convert 8 ounces to grams.

b.There are 112 calories in a glass of fresh Valencia orange juice that holds 8 ﬂuid ounces. Convert

8 ﬂuid ounces to liters. Round to the nearest hundredth.

84.TRACK AND FIELD A shot-put weighs 7.264 kilograms. Convert this weight to pounds. Round to the nearest pound.

85.POSTAL REGULATIONS You can mail a package weighing up to 70 pounds via priority mail. Can you mail a package that weighs 32 kilograms by priority mail?

86.NUTRITION Refer to the nutrition label shown below for a packet of oatmeal. Change each circled weight to ounces.

Nutrition Facts

Serving Size: 1 Packet (46g)

Servings Per Container: 10

Amount Per Serving

Calories 170 Calories from Fat 20

		% Daily Value
Total fat 2g		3%
	Saturated fat 0.5g	2%
	Polyunsaturated Fat 0.5g
	Monounsaturated Fat 1g
Cholesterol 0mg		0%
Sodium 250mg		10%
Total carbohydrate 35g		12%
	Dietary fiber 3g	12%

	Soluble Fiber 1g
	Sugars 16g
Protein 4g

87.HOT SPRINGS The thermal springs in Hot Springs National Park in central Arkansas emit water as warm as 143°F. Change this temperature to degrees Celsius.

88.COOKING MEAT Meats must be cooked at temperatures high enough to kill harmful bacteria. According to the USDA and the FDA, the internal temperature for cooked roasts and steaks should be at least 145°F, and whole poultry should be 180°F. Convert these temperatures to degrees Celsius. Round up to the next degree.

89.TAKING A SHOWER When you take a shower, which water temperature would you choose: 15°C, 28°C, or 50°C?

90.DRINKING WATER To get a cold drink of water, which temperature would you choose: 2°C, 10°C, or 25°C?

91.SNOWY WEATHER At which temperatures might it snow: 5°C, 0°C, or 10°C?

92.AIR CONDITIONING At which outside temperature would you be likely to run the air conditioner: 15°, 20°C, or 30°C?

93.COMPARISON SHOPPING Which is the better buy: 3 quarts of root beer for $4.50 or 2 liters of root beer for $3.60?

94.COMPARISON SHOPPING Which is the better buy: 3 gallons of antifreeze for $10.35 or 12 liters of antifreeze for $10.50?

WRITING

95.Explain how to change kilometers to miles.

96.Explain how to change 50°C to degrees Fahrenheit.

97.The United States is the only industrialized country in the world that does not ofﬁcially use the metric system. Some people claim this is costing American businesses money. Do you think so? Why?

98.What is meant by the phrase a table of equivalent measures?

REVIEW

Perform each operation.


99.	3			4	100.	3		4
99.	5			3	100.	5		3
101.	3	4			102.	3		4

	5		3			5		3
103.	3.25			4.8	104.	3.25		4.8
	3.25			4.8		4.8
105.	3.25			4.8	106.	4.8	15.6

Chapter 5 Summary and Review

479

STUDY SKILLS CHECKLIST

Proportions and Unit Conversion Factors

Before taking the test on Chapter 5, make sure that you have a solid understanding of how to write proportions and how to choose unit conversion factors. Put a checkmark in the box if you can answer “yes” to the statement.

When writing a proportion, I know that the units of

When converting from one unit to another, I know

the numerators must be the same and the units of

that I must choose a unit conversion factor with

the denominators must be the same.

the following form:

This proportion is correctly written:

Unit I want to introduce

Ounces

150

Ounces

Unit I want to eliminate

Cost

2.75

For example, in the following conversion of 15

This proportion is incorrectly written:

pints to cups, the units of pints are eliminated and

the units of cups are introduced by choosing the

Ounces

2.75

Cost

2 c

unit conversion factor

Cost

Ounces

1 pt

15 pt

2 c

15 pt

30 c

1 pt

C H A P T E R 5 SUMMARY AND REVIEW

S E C T I O N 5.1 Ratios and Rates

DEFINITIONS AND CONCEPTS EXAMPLES

Ratios are often used to describe important relationships between two quantities.

A ratio is the quotient of two numbers or the quotient of two quantities that have the same units.

Ratios are written in three ways: as fractions, in words separated by the word to, and using a colon.

To write a ratio as a fraction, write the ﬁrst number (or quantity) mentioned as the numerator and the second number (or quantity) mentioned as the denominator. Then simplify the fraction, if possible.

The ratio 4 to 5 can be written as 45 .

The ratio 5 : 12 can be written as 125 .

Write the ratio 30 to 36 as a fraction in simplest form. The word to separates the numbers to be compared.

		1
30		5 6 To simplify, factor 30 and 36. Then remove the common

36		6 6 factor of 6 from the numerator and denominator.
		1
		5

		6

480		Chapter 5 Summary and Review


	To write a ratio in simplest form, remove any				Write the ratio 14 feet: 2 feet as a fraction in simplest form.
	common factors		of the	numerator and	A colon separates the quantities to be compared.
	denominator as well as any common units.				A colon separates the quantities to be compared.
	denominator as well as any common units.										1
											1									To simplify, factor 14. Then remove the common
						14 feet						2 7 feet								To simplify, factor 14. Then remove the common
						14 feet						2 7 feet								factor of 2 and the common units of feet from
						2 feet								2 feet						factor of 2 and the common units of feet from
						2 feet								2 feet						the numerator and denominator.
											1									the numerator and denominator.
												7								Since a ratio compares two numbers, we leave the
											1									result in fractional form. Do not simplify further.
	To simplify ratios involving decimals, multiply				Write the ratio 0.23 to 0.71 as a fraction in simplest form.
	the ratio by a form of 1 so that the numerator				To write this as a ratio of whole numbers, we need to move the decimal
	and	denominator	become	whole numbers.
	and	denominator	become	whole numbers.	points in the numerator and denominator two places to the right. This
	Then simplify, if possible.
	Then simplify, if possible.				will occur if they are both multiplied by 100.
					will occur if they are both multiplied by 100.
						0.23			0.23								100			Multiply the ratio by a form of 1.
					0.71			0.71									100
											1
									0.23 100											Multiply the numerators.
								0.71 100												Multiply the denominators.
									23											To ﬁnd the product of each decimal and 100, simply
									23											move the decimal point two places to the right.
								71												move the decimal point two places to the right.
								71												The resulting fraction is in simplest form.
																				The resulting fraction is in simplest form.
	To simplify ratios involving mixed numbers, use				Write the ratio 3										1			to 4	1	as a fraction in simplest form.
	To simplify ratios involving mixed numbers, use				Write the ratio 3										3			to 4	6	as a fraction in simplest form.
	the method for simplifying complex fractions														3				6
	the method for simplifying complex fractions				1			10
	from Section 3.7. Perform the division				1			10
	indicated by the main fraction bar.				3		3			3										Write 3	1	and 4	1	and as improper fractions.
																					1		1

					4		1			25										3		6
							1			25
								6
					6			6
								10								25				Write the division indicated by the main
								3							6					fraction bar using a symbol.
								10			6									Use the rule for dividing fractions: Multiply the
								3					25							ﬁrst fraction by the reciprocal of 256 , which is					6	.
								3					25							ﬁrst fraction by the reciprocal of 256 , which is					25	.
								10 6												Multiply the numerators.
								3 25												Multiply the denominators.
											1				1
								2 5 2 3												To simplify the fraction, factor 10, 6, and 25.
								3 5 5												Then remove the common factors 3 and 5.
								3 5 5												Then remove the common factors 3 and 5.
								1			1
								4												Multiply the remaining factors in the numerator.
								5												Multiply the remaining factors in the denominator.
	When a ratio compares two quantities, both				Write the ratio 5 inches to 2 feet as a fraction in simplest form.
	quantities must be measured in the same units.				Since inches are smaller than feet, compare in inches:
	When the units are different, it’s usually easier					5 inches to 24 inches Because 2 feet 24 inches.
	to write the ratio using the smaller unit of					5 inches to 24 inches Because 2 feet 24 inches.
	to write the ratio using the smaller unit of
	measurement.				Next, write the ratio in fraction form and simplify.
						5 inches										5				Remove the common units of inches.
						24 inches									24					Remove the common units of inches.

Write each rate as a fraction in simplest form.

Chapter 5 Summary and Review

481

When we compare two quantities that have

Write the rate 33 miles in 6 hours as a fraction in simplest form.

different

units

(and

neither unit

can

converted to the other), we call the comparison

33 miles

a rate.

33 miles in 6 hours can be written as

6 hours

To write a rate as a fraction, write the ﬁrst

quantity mentioned as the numerator and the

To simplify, factor 33 and 6. Then

second

quantity

mentioned

the

33 miles

3 11 miles

remove the common factor of 3 from

denominator, and then simplify,

possible.

6 hours

2 3 hours

the numerator and denominator.

Write the units as part of the fraction.

Words such as per, for, in, from, and on are used

11 miles

Write the units as part of the rate.

to separate the two quantities that are

2 hours

compared in a rate.

The rate can be written as 11 miles per 2 hours.

A unit rate is a rate in which the denominator

Write as a unit rate: 2,490 apples from 6 trees.

is 1.

To ﬁnd the unit rate, divide 2,490 by 6.

To write

a rate

a unit rate,

divide

the

415

numerator of the rate by the denominator.

6 2,490

A slash mark / is often used to write a unit rate.

415 apples

apples

The unit rate is

1 tree

. This rate can also be expressed as: 415 tree ,

415 apples per tree, or 415 apples/tree.

A unit price is a rate that tells how much is paid

Which is the better buy for shampoo?

for one unit (or one item). It is the quotient of

12 ounces for $3.84

16 ounces for $4.64

price to the number of units.

price

To ﬁnd the unit price of a bottle of shampoo, write the quotient of its

Unit price

price and its weight, and then perform the indicated division. Before

number of units

dividing, convert each price from dollars to cents so that the unit price

Comparison shopping can be made easier by

can be expressed in cents per ounce.

ﬁnding unit prices. The best buy is the item that

$3.84

384¢

$4.64

464¢

has the lowest unit price.

12 oz

16 oz

32¢ per oz

29¢ per oz

One ounce of shampoo for 29¢ is better than one ounce for 32¢. Thus,

the 16-ounce bottle is the better buy.

REVIEW EXERCISES

Write each ratio as a fraction in simplest form.

1.	7 to 25				2.	15 16				13.	64 centimeters in 12 years
1.	7 to 25				2.	15 16				14.	$15 for 25 minutes
										14.	$15 for 25 minutes
3.	24 to 36				4.	21 14				Write each rate as a unit rate.
										Write each rate as a unit rate.
5.	4 inches to 12 inches				6.	63 meters to 72 meters				15.	600 tickets in 20 minutes
										16.	45 inches every 3 turns
7.	0.28 to 0.35				8.	5.1 1.7				17.	195 feet in 6 rolls
										17.	195 feet in 6 rolls
	1			2		1			1	18.	48 calories in 15 pieces
9.	2		to 2		10.	4		3
9.	2	3	to 2	3	10.	4	6	3	3
11.	15 minutes : 3 hours				12.	8 ounces to 2 pounds

482	Chapter 5 Summary and Review

Find the unit price of each item.

19.5 pairs cost $11.45.

20.$3 billion in a 12-month span

21.AIRCRAFT Speciﬁcations for a Boeing B-52 Stratofortress are shown below. What is the ratio of the airplane’s wingspan to its length?

Crew: 6

Length: 160 ft Wingspan: 185 ft

Maximum takeoff weight: 488,000 lb

Maximum speed:

595 mph

Maximum altitude: more than 50,000 ft

Range: 7,500 mi

22.PAY RATES Find the hourly rate of pay

for a student who earned $333.25 for working 43 hours.

23.CROWD CONTROL After a concert is over, it takes 48 minutes for a crowd of 54,000 people to exit a stadium. Find the unit rate of people exiting the stadium.

24.COMPARISON SHOPPING Mixed nuts come packaged in a 12-ounce can, which sells for $4.95, or an 8-ounce can, which sells for $3.25. Which is the better buy?

S E C T I O N 5.2 Proportions

DEFINITIONS AND CONCEPTS

A proportion is a statement that two ratios or two rates are equal.

Each of the four numbers in a proportion is called a term. The ﬁrst and fourth terms are called the extremes, and the second and third terms are called the means.

Since a proportion is an equation, a proportion can be true or false. A proportion is true if its ratios (or rates) are equivalent and false if its ratios (or rates) are not equivalent.

One way to determine whether a proportion is true or false is to use the fraction simplifying skills of Chapter 3.

The two products found by multiplying diagonally in a proportion are called cross products.

Another way to determine whether a proportion is true or false involves the cross products. If the cross products are equal, the proportion is true. If the cross products are not equal, the proportion is false.

EXAMPLES

Write each statement as a proportion.

6 is to 10 as 3 is to 5				The word “to” is used to separate the numbers
⎪ ⎬ ⎪ ⎭		⎪ ⎬ ⎪ ⎭		to be compared in a ratio (or rate).
6		3		to be compared in a ratio (or rate).

10
10		5
$300 is to 500 minutes as $3 is to 5 minutes
⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎩				⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎩
	$300					$3
	500 minutes					5 minutes
	500 minutes					5 minutes
First term (extreme)					Third term (mean)
			1	3
			1	3

			2	6
Second term (mean)					Fourth term (extreme)
Determine whether the proportion							3	15	is true or false.
Determine whether the proportion								27	is true or false.
					5			27

Method 1 Simplify any ratios in the proportion that are not in simplest form. Then compare them to determine whether they are equal.

Since the ratios on the left and right sides of the proportion are not equal, the proportion is false.

Method 2 Check to see whether the cross products are equal.

Cross products


3 27 81			5 15 75
	3	15
	3	15
	5	27

Since the cross products are not equal, the proportion is not true.

Chapter 5

Summary and Review

483

When two pairs of numbers form a proportion,

Determine whether 0.7, 0.3 and 2.1, 0.9 are proportional.

we say that they are proportional.

Write two ratios and form a proportion. Then ﬁnd the cross products.

0.7

2.1

0.7 0.9 0.63

0.3 2.1 0.63

0.3

0.9

Since the cross products are equal, the numbers are proportional.

Solving a proportion to ﬁnd an unknown term:

Solve the proportion:

37.5

1. Set the cross products equal to each other

to form an equation.

This is the proportion to solve.

37.5 x

2. Isolate the variable on one side of the

Set the cross products equal to each

equation by dividing both sides by the

5 x 37.5 2

other to form an equation.

number that is multiplied by that variable.

To simplify the right side of the

3. Check by substituting the result into the

5 x 75

equation, multiply: 37.5 2 75.

original proportion and ﬁnding the cross

5 x

products.

To undo the multiplication by 5 and

isolate x, divide both sides by 5.

To simplify the left side, remove the

x 15

common factor of 5. To simplify the

right side, do the division: 75 5 15.

Thus, x is 15. Check this result in the original proportion by ﬁnding the

cross products.

Proportions can be used to solve application

PEANUT BUTTER It takes 360 peanuts to make 8 ounces of peanut

problems. It is easy to spot problems that can

butter. How many peanuts does it take to make 12 ounces? (Source:

be solved using a proportion. You will be given

National Peanut Board)

a ratio (or rate) and asked to ﬁnd the missing

Analyze

part of another ratio (or rate).

• We can express the fact that it takes 360 peanuts to make

It is helpful to follow the ﬁve-step problem-

8 ounces of peanut butter as a rate:

360 peanuts .

solving strategy seen earlier in the text to solve

8 ounces

• How many peanuts does it take to make 12 ounces?

proportion problems.

Form We will let the variable p represent the unknown number of

peanuts.

360 peanuts is to 8 ounces as p peanuts is to 12 ounces.

Number of peanuts

360

Number of peanuts

Ounces of peanuts

Solve To ﬁnd the number of peanuts needed, solve the proportion

for p.

360 12 8 p

Set the cross products equal to each

other to form an equation.

4,320

8 p

To simplify the left side of the equation,

multiply: 360 12 4,320.

4,320

8 p

To undo the multiplication by 8 and

isolate p, divide both sides by 8.

To simplify the left side, do the division:

540

4,320 8 540. To simplify the right side,

remove the common factor of 8.

State It takes 540 peanuts to make 12 ounces of peanut butter.

Check 16 ounces of peanut butter would require twice as many

peanuts

ounces:

2 360 peanuts

720 peanuts. It

seems

reasonable that 12 ounces would require 540 peanuts.

484	Chapter 5 Summary and Review

REVIEW EXERCISES

25.Write each statement as a proportion.

a.20 is to 30 as 2 is to 3.

b.6 buses replace 100 cars as 36 buses replace

600 cars.

26.Complete the cross products.

27			9
	2	6
	2	6

	9	27

Determine whether each proportion is true or false by simplifying.

8		3	4		10
27.			28.
	12	7		18	45

Determine whether each proportion is true or false by ﬁnding cross products.

29.	9	2		30.	17		51
29.	27	6		30.	7		21
					1	1			1
31.	3.5		1.2	32.	1	2		4
31.	9.3	3		32.	3	1		1		1
					3	3		1		7
						3				7

Determine whether the numbers are proportional.

33.	5, 9 and 20, 36								34.	7, 13 and 29, 54
Solve each proportion.
35.	12			3					36.	4			2

	18				x					x			8
37.	4.8						x		38.	0.08					0.04
37.	6.6					9.9			38.		x			0.06
	9							1		4							2
	1			3										2
39.	1		11	3				3	40.	5				2			3

			x					3		1						x
				2						1
				2				4		1		20
		2
41.	3						x		42.	x				5,000
41.	1			0.25					42.	300				1,500

	2

43.TRUCKS A Dodge Ram pickup truck can go 35 miles on 2 gallons of gas. How far can it go on 11 gallons?

44.QUALITY CONTROL In a manufacturing process, 12 parts out of 66 were found to be defective. How many defective parts will be expected in a run of 1,650 parts?

45.SCALE DRAWINGS The illustration below

shows an architect’s drawing1 of a2 kitchen using a scale of 18 inch to 1 foot 18 1 0 . On the drawing, the length of the kitchen is 112 inches. How long

is the actual kitchen? (The symbol means inch and means foot.)

ELEVATION B-B

1" SCALE: –8 to 1'0"

46.DOGS The American Kennel Club website gives

the ideal length to height proportions for a German

Shepherd as 10 : 812 . What is the ideal length of a German Shepherd that is 2512 inches high at the shoulder?

Height

Length

Chapter 5 Summary and Review

485

S E C T I O N 5.3

American Units of Measurement

DEFINITIONS AND CONCEPTS

EXAMPLES

The American system of measurement uses the

1 ft = 12 in.

1 yd = 3 ft

units of inch, foot, yard, and mile to measure

1 yd = 36 in.

1 mi = 5,280 ft

length.

Since the black tick marks between 0 and 1 on the ruler create sixteen

A ruler is one of the most common tools for

equal spaces, the ruler is scaled in sixteenths.

measuring lengths. Most rulers are 12 inches

long. Each inch is divided into halves of an

in.

inch, quarters of an inch, eighths of an inch, and

––

–

1– in.

– in.

sixteenths of an inch.

16 spaces

To convert from one unit of length to another,

Convert 4 yards to inches.

we use unit conversion factors. They are called

To convert from yards to inches, we select a unit conversion factor that

unit conversion factors because their value is 1.

introduces the units of inches and eliminates the units of yards. Since

Multiplying a measurement by a unit

there are 36 inches per yard, we will use:

conversion factor does not change the measure;

in.

This is the unit we want to introduce.

it only changes the units of the measure.

This is the unit we want to eliminate (the original unit).

A list of unit conversion factors for American

To perform the conversion, we multiply.

units of length is given on page 445.

4 yd

36 in.

Write 4 yd as a fraction.

1 yd

36 in.

Then multiply by a form of 1: 1 yd

4 yd

36 in.

Remove the common units of yards from

the numerator and denominator. The

1 yd

units of inches remain.

4 36 in.

Simplify.

144 in.

Do the multiplication.

Thus, 4 yards = 144 inches.

The American system of measurement uses the

1 lb = 16 oz

1 ton = 2,000 lb

units of ounce, pound, and ton to measure

weight.

A list of unit conversion factors for American

Convert 9,000 pounds to tons.

units of weight is given on page 447.

To convert from pounds to tons, we select a unit conversion factor that

introduces the units of tons and eliminates the units of pounds. Since

there is 1 ton for every 2,000 pounds, we will use:

ton

This is the unit we want to introduce.

2,000

This is the unit we want to eliminate (the original unit).

486

Chapter 5 Summary and Review

To perform the conversion, we multiply.

9,000 lb

1 ton

Write 9,000 lb as a fraction. Then

1 ton

2,000 lb

multiply by a form of 1:

2,000 lb

Remove the common units of pounds

9,000 lb

1 ton

from the numerator and denominator.

2,000 lb

The units of tons remains.

9,000

ton

Multiply the fractions.

2,000

There are two ways to complete the solution. First, we can remove any

common factors of the numerator and denominator to simplify the

fraction. Then we can write the result as a mixed number.

9,000

9 1,000

tons

tons 4

tons

2,000

2 1,000

A second approach is to divide the numerator by the denominator and

express the result as a decimal.

9,000

tons

4.5 tons

2,000

tons (or 4.5 tons).

Thus, 9,000 pounds is equal to 4

The American system of measurement uses the

1 c = 8 ﬂ oz

1 pt = 2 c

units of ounce, cup, pint, quart, and gallon to

1 qt = 2 pt

1 gal = 4 qt

measure capacity.

A list of unit conversion factors for American

Convert 5 gallons to pints.

units of capacity is given on page 449.

There is not a single unit conversion factor that converts from gallons

Some conversions require the use of two (or

to pints. We must use two unit conversion factors.

more) unit conversion factors.

Since there are 4 quarts per gallon, we can convert 5 gallons to quarts

by multiplying by the unit conversion factor

4 qt

. Since there are 2 pints

1 gal

per quart, we can convert that result to pints by multiplying by the unit

conversion factor

2 pt .

1 qt

5 gal

4 qt

2 pt

1 gal

1 qt

5 gal

4 qt

2 pt

Remove the common units of gallons

and quarts in the numerator and

1 gal

1 qt

denominator. The units of pints remain.

40 pt

Do the multiplication: 5 4 2 40.

Thus, 5 gallons 40 pints.

The American (and metric) system of

1 min = 60 sec

1 hr = 60 min

1 day = 24 hr

measurement use the units of seconds, minutes,

hours, and days to measure time.

A list of unit conversion factors for units of time is given on page 450.

Chapter 5 Summary and Review

487

Convert 240 minutes to hours.

To convert from minutes to hours, we select a unit conversion factor that introduces the units of hours and eliminates the units of minutes. Since there is 1 hour for every 60 minutes, we will use:

To perform the conversion, we multiply.

240 min	240 min		1 hr
	1		60 min
	240 min		1 hr
	1		60 min
	240	hr
	60

4 hr

Write 240 min as a fraction. Then

1 hr multiply by a form of 1: 60 min .

Remove the common units of minutes from the numerator and denominator. The units of hours remain.

Multiply the fractions.

Do the division.

Thus, 240 minutes is equal to 4 hours.

REVIEW EXERCISES

47.a. Refer to the ruler below. Each inch is divided into how many equal parts?

b.Determine which measurements the arrows point to on the ruler.

Inches

48.Use a ruler to measure the length of the computer mouse.

49.Write two unit conversion factors using the fact that 1 mile 5,280 ft.

50.Consider the work shown below.

100 min		60 sec
1		1 min

a. What units can be removed? b. What units remain?

Perform each conversion.

51.5 yards to feet

52.6 yards to inches

53.66 inches to feet

54.9,240 feet to miles

55.412 feet to inches

56.1 mile to yards

57.32 ounces to pounds

58.17.2 pounds to ounces

59.3 tons to ounces

60.4,500 pounds to tons

61.5 pints to ﬂuid ounces

62.8 cups to gallons

63.17 quarts to cups

64.176 ﬂuid ounces to quarts

65.5 gallons to pints

66.3.5 gallons to cups

67.20 minutes to seconds

68.900 seconds to minutes

69.200 hours to days

70.6 hours to minutes

71.4.5 days to hours

72.1 day to seconds

488		Chapter 5 Summary and Review


	73. Convert 210 yards to miles. Give the exact answer		2009.ImagingElementalcopyrightImage	Shutterstock.comfromlicenseunderUsed	75.	SKYSCRAPERS The Sears Tower in Chicago is
		and a decimal approximation, rounded to the	2009.ImagingElementalcopyrightImage	Shutterstock.comfromlicenseunderUsed		1,454 feet high. Express this height in yards.
		and a decimal approximation, rounded to the				1,454 feet high. Express this height in yards.
		nearest hundredth.			76.	BOTTLING A magnum is a 2-quart bottle of wine.
					76.	BOTTLING A magnum is a 2-quart bottle of wine.
	74.	TRUCKING Large				How many magnums will be needed to hold 50
		concrete trucks can				gallons of wine?
		carry roughly 40,500
		pounds of concrete.
		Express this weight in
		tons.

S E C T I O N 5.4

Metric Units of Measurement

DEFINITIONS AND CONCEPTS

EXAMPLES

The basic metric unit of measurement is the

kilo means thousands

deci means tenths

meter, which is abbreviated m.

hecto means hundreds

centi means hundredths

Longer and shorter metric units are created by

deka means tens

milli means thousandths

adding preﬁxes to the front of the basic unit,

meter.

Common metric units of length are the

1 km 1,000 m

1 m 10 dm

kilometer, hectometer, dekameter, decimeter,

1 hm 100 m

1 m 100 cm

centimeter, and millimeter. Abbreviations are

1 dam 10 m

1 m 1,000 mm

often used when writing these units. See the

table on page 456.

A metric ruler can be used for measuring

2 cm

43 mm

65 mm

lengths. On most metric rulers, each centimeter

is divided into 10 millimeters.

10 mm 1

Centimeters

To convert from one metric unit of length to

Convert 4 meters to centimeters.

another, we use unit conversion factors.

To convert from meters to centimeters, we select a unit conversion

factor that introduces the units of centimeters and eliminates the units

of meters. Since there are 100 centimeters per meter, we will use:

100

This is the unit we want to introduce.

This is the unit we want to eliminate (the original unit).

To perform the conversion, we multiply.

4 m

100 cm

Write 4 m as a fraction.

100 cm

1 m

Then multiply by a form of 1:

1 m .

4 m

100 cm Remove the common units of meters from

the numerator and denominator. The units

1 m

of cm remain.

400 cm

Multiply the fractions and simplify.

Thus, 4 meters = 400 centimeters.

The mass of an object is a measure of the amount of material in the object.

Common metric units of mass are the kilogram, hectogram, dekagram, decigram, centigram and milligram. Abbreviations are often used when writing these units. See the table on page 461.

Converting from one metric unit to another can be done using unit conversion factors or a conversion chart.

In a conversion chart, the units are listed from largest to smallest, reading left to right. We count the places and note the direction as we move from the original units to the conversion units.

Common metric units of capacity are the kiloliter, hectoliter, dekaliter, deciliter, centiliter and milliliter. Abbreviations are often used when writing these units. See the table on page 464.

Converting from one metric unit to another can be done using unit conversion factors or a conversion chart.

	Chapter 5 Summary and Review		489
1 kg 1,000 g	1 g 10 dg
1 hg 100 g	1 g	100 cg
1 dag 10 g	1 g	1,000 mg

Convert 820 grams to kilograms.

To use a conversion chart, locate the original units of grams and move to the conversion units of kilograms.

largest								smallest
	kg	hg	dag	g	dg	cg	mg
unit								unit

To go from grams to kilograms, we must move 3 places to the left.

If we write 820 grams as 820.0 grams, we can convert to kilograms by moving the decimal point 3 places to the left.

820.0 grams = 0.820 0 kilograms = 0.82 kilograms

The unit conversion factor method gives the same result:

820 g	820 g		1 kg
	1		1,000 g

1,000820 kg

0.82 kg

Thus, 820 grams 0.82 kilograms.

1 kL 1,000 L	1 L 10 dL
1 hL 100 L	1 L 100 cL
1 daL 10 L	1 L 1,000 mL

Convert 0.7 kiloliters to milliliters.

To use a conversion chart, locate the original units of kiloliters and move to the conversion units of milliliters.

kL hL daL	L	dL cL mL

To go from kiloliters to milliliters, we must move 6 places to the right.

We can convert to milliliters by moving the decimal point 6 places to the right.

0.7 kiloliters = 0 700000. milliliters = 700,000 milliliters

490	Chapter 5 Summary and Review


	Another metric unit of capacity is the cubic	The unit conversion factor method gives the same result:
	centimeter, written cm3, or, more simply, cc.The		0.7 kL	1,000 L			1,000 mL
		0.7 kL	0.7 kL	1,000 L			1,000 mL
		0.7 kL	1			1 kL	1 L
		0.7 1,000 1,000 mL
		700,000 mL
		Thus, 0.7 kiloliters 700,000 milliliters.
	units of cubic centimeters are used frequently	1 milliliter = 1 cm3 = 1 cc
	in medicine.	5 milliliters = 5 cm			3	= 5 cc
		5 milliliters = 5 cm				= 5 cc
		0.6 milliliters = 0.6 cm3 = 0.6 cc

REVIEW EXERCISES

77.a. Refer to the metric ruler below. Each centimeter is divided into how many equal parts? What is the length of one of those parts?

b.Determine which measurements the arrows point to on the ruler.

Centimeters

78.Use a metric ruler to measure the length of the computer mouse to the nearest centimeter.

79.Write two unit conversion factors using the given fact.

a.1 km 1,000 m

b.1 g 100 cg

80.Use the chart to determine how many decimal places and in which direction to move the decimal point when converting from centimeters to kilometers.

km hm dam m dm cm mm

Perform each conversion.

81.475 centimeters to meters

82.8 meters to millimeters

83.165.7 kilometers to meters

84.6,789 centimeters to decimeters

85.5,000 centigrams to kilograms

86.800 centigrams to grams

87.5,425 grams to kilograms

88.5,425 grams to milligrams

89.150 centiliters to liters

90.3,250 liters to kiloliters

91.400 milliliters to centiliters

92.1 hectoliter to deciliters

93.THE BRAIN The adult human brain weighs about 1,350 g. Convert the weight to kilograms.

94.TEST TUBES A rack holds one dozen 20-mL test tubes. Find the total capacity of the test tubes in the rack in liters.

95.TYLENOL A bottle of Extra-Strength Tylenol contains 100 caplets of 500 milligrams each. How many grams of Tylenol are in the bottle?

96.SURGERY A dextrose

solution is being administered to a patient intravenously as shown to

	the right. How many	Dextrose
	the right. How many	1 L
	milliliters of solution does	1 L
	milliliters of solution does
	the IV bag hold?

Chapter 5 Summary and Review

491

S E C T I O N 5.5 Converting between American and Metric Units

DEFINITIONS AND CONCEPTS

EXAMPLES

We convert between American and metric

American to metric

Metric to American

units of length using the facts on the right. In all

1 in. 2.54 cm

1 cm 0.39 in.

but one case, the conversions are rounded

1 ft 0.30 m

1 m 3.28 ft

approximations.

1 yd 0.91 m

1 m 1.09 yd

1 mi 1.61 km

1 km 0.62 mi

Unit conversion factors can be formed from the

Convert 15 inches to centimeters.

facts in the tables on the right to make speciﬁc

To convert from inches to centimeters, we select a unit conversion

conversions between American and metric

factor that introduces the units of centimeters and eliminates the units

units of length.

of inches. Since there are 2.54 centimeters for every inch, we will use:

2.54

This is the unit we want to introduce.

in.

This is the unit we want to eliminate (the original unit).

To perform the conversion, we multiply.

15 in.

2.54 cm

Write 15 in. as a fraction.

2.54 cm

1 in.

Then multiply by a form of 1:

1 in. .

15 in.

2.54 cm

Remove the common units of inches

from the numerator and denominator.

1 in.

The units of cm remain.

15 2.54 cm

Simplify.

38.1 cm

Do the multiplication.

Thus, 15 inches = 38.1 centimeters.

We convert between American and metric

American to metric

Metric to American

units of mass (weight) using the facts on

1 oz 28.35 g

1 g 0.035 oz

the right. The conversions are rounded

1 lb 0.45 kg

1 kg 2.20 lb

approximations.

Unit conversion factors can be formed from the

Convert 6 kilograms to ounces.

facts in the tables on the right to make speciﬁc

There is not a

single unit conversion factor that converts from

conversions between American and metric

kilograms to ounces. We must use two unit conversion factors. One to

units of mass (weight).

convert kilograms to grams, and another to convert that result to

ounces.

6 kg

1,000 g

0.035 oz

1 kg

1 g

6 kg

1,000 g

0.035 oz

Remove the common units of

kilograms and grams in the

1 kg

1 g

numerator and denominator.

The units of oz remain.

6 1,000 0.035 oz

Simplify.

6 35 oz

Multiply the last two factors:

1,000 0.035 35.

210 oz

Do the multiplication.

Thus, 6 kilograms 210 ounces.

492

Chapter 5 Summary and Review

We convert between American and metric

American to metric

Metric to American

units of capacity using the facts on the right.

1 fl oz

29.57 mL

1 L 33.81 fl oz

The conversions are rounded approximations.

1 pt 0.47 L

1 L 2.11 pt

1 qt 0.95 L

1 L 1.06 qt

1 gal 3.79 L

1 L 0.264 gal

Unit conversion factors can be formed from the

Convert 5 ﬂuid ounces to milliliters. Round to the nearest tenth.

facts in the tables on the right to make speciﬁc

To convert from ﬂuid ounces to milliliters, we select a unit conversion

conversions between

American and metric

factor that introduces the units of milliliters and eliminates the units of

units of capacity.

ﬂuid ounces. Since there are 29.57 milliliters for every ﬂuid ounce, we

will use:

29.57

This is the unit we want to introduce.

fl oz

This is the unit we want to eliminate (the original unit).

To perform the conversion, we multiply.

5 fl oz

29.57 mL

Write 5 ﬂ oz as a fraction. Then multiply

1 fl oz

by a form of 1:

29.57 mL

1 fl oz .

5 fl oz

29.57 mL

Remove the common units of ﬂuid

ounces from the numerator and

1 fl oz

denominator. The units of mL remain.

5 29.57 mL

Simplify.

147.85 mL

Do the multiplication.

147.9 mL

Round to the nearest tenth.

Thus, 5 ﬂuid ounces 147.9 milliliters.

In the American system, we measure

Convert 92°F to degrees Celsius. Round to the nearest tenth of a

temperature using degrees Fahrenheit (°F). In

degree.

the metric system, we measure temperature

using degrees Celsius (°C).

(F 32)

C 9

This is the formula to ﬁnd degrees Celsius.

If F is the temperature in degrees Fahrenheit

and

C is the corresponding temperature in

(92 32)

Substitute 92 for F.

degrees Celsius, then

(60)

Do the subtraction within the parentheses ﬁrst.

(F 32)

and F

C 32

Write 60 as a fraction.

300

Multiply the numerators: 5 60 300.

Multiply the denominators.

33.333 . . .

Do the division.

33.3

Round to the nearest tenth.

Thus, 92°F 33.3°C.

REVIEW EXERCISES

97.SWIMMING Olympic-size swimming pools are 50 meters long. Express this distance in feet.

98.HIGH-RISE BUILDINGS The Sears Tower is 443 meters high, and the Empire State Building is 1,250 feet high. Which building is taller?

99.WESTERN SETTLERS The Oregon Trail was an overland route pioneers used from the 1840s through the 1870s to reach the Oregon Territory. It stretched 1,930 miles from Independence, Missouri, to Oregon City, Oregon. Find this distance to the nearest kilometer.

100.AIR JORDAN Michael Jordan is 78 inches tall (6 feet, 6 inches). Express his height in centimeters. Round to the nearest centimeter.

Perform each conversion. Since most conversions are approximate, answers will vary slightly depending on the method used.

101.30 ounces to grams

102.15 kilograms to pounds

Chapter 5 Summary and Review

493

103.50 pounds to grams

104.2,000 pounds to kilograms

105.POLAR BEARS At birth, polar bear cubs weigh less than human babies—about 910 grams. Convert this to pounds.

106.BOTTLED WATER LaCroix bottled water can be purchased in bottles containing 17 ﬂuid ounces. Mountain Valley water can be purchased in half-liter bottles. Which bottle contains more water?

107.CRUDE OIL There are 42 gallons in a barrel of crude oil. How many liters of crude oil is that?

108.Convert 105°C to degrees Fahrenheit.

109.Convert 77°F to degrees Celsius.

110.RECREATION Which water temperature is appropriate for swimming: 10°C, 30°C, 50°C, or 70°C?

494

C H A P T E R 5 TEST

1.Fill in the blanks.

a.A is the quotient of two numbers or the quotient of two quantities that have the same units.

b.A is the quotient of two quantities that have different units.

is a statement that two ratios (or

rates) are equal.

The

products for the proportion 3

are

3 16 and 8 6.

Deci means

, centi means

, and

milli means

The meter, the gram, and the liter are basic units

of measurement in the

system.

In the American system, temperatures are

measured in degrees

. In the metric

system, temperatures are measured in degrees

2.PIANOS A piano keyboard is made up of a total of eighty-eight keys, as shown below. What is the ratio of the number of black keys to white keys?

Middle C

Write each ratio as a fraction in simplest form.

3.6 feet to 8 feet

4.8 ounces to 3 pounds

5.0.26 : 0.65

6.313 to 389

7.Write the rate 54 feet in 36 seconds as a fraction in simplest form.

8.COMPARISON SHOPPING A 2-pound can

of coffee sells for $3.38, and a 5-pound can of the same brand of coffee sells for $8.50. Which is the better buy?

9.UTILITY COSTS A household used 675 kilowatt-hours of electricity during a

30-day month. Find the rate of electric usage in kilowatt-hours per day.

10.Write the following statement as a proportion: 15 billboards to 50 miles as 3 billboards to

10 miles.

11. Determine whether each proportion is true. a. 2533 23 b. 2.23.5 1.762.8

12. Are the numbers 7, 15 and 35, 75 proportional?

Solve each proportion.
13.	x			35			14.	15.3		3

	3			7					x	12.4
	2		2
	2				x			25		50
15.		9			x		16.	25		50
15.		4			1		16.	1			x
					1
		3			1	2		10

17.SHOPPING If 13 ounces of tea costs $2.79, how much would you expect to pay for 16 ounces of tea?

18.BAKING A recipe calls for 123 cup of sugar and 5 cups of ﬂour. How much sugar should be used

with 6 cups of ﬂour?

19.a. Refer to the ruler below. Each inch is divided into how many equal parts?

b.Determine which measurements the arrows point to on the ruler.

Inches

20.Fill in the blanks. In general, a unit conversion factor is a fraction with the following form:

Unit that we want to			Numerator
			Denominator

Unit that we want to
Unit that we want to

21.Convert 180 inches to feet.

22.TOOLS If a 25-foot tape measure is completely extended, how many yards does it stretch? Write your answer as a mixed number.

23.Convert 1034 pounds to ounces.

24.AUTOMOBILES A car weighs 1.6 tons. Find its weight in pounds.

25.CONTAINERS How many ﬂuid ounces are in a 1-gallon carton of milk?

26.LITERATURE An excellent work of early science ﬁction is the book Around the World in 80 Days

by Jules Verne (1828–1905). Convert 80 days to minutes.

27.a. A quart and a liter of fruit punch are shown below. Which is the 1-liter carton: The one on the left side or the right side?

		Open
	FRUIT PUNCH	Open
	FRUIT PUNCH	FRUIT PUNCH
	Vitamin C added	FRUIT PUNCH
		Vitamin C added

	Fruit	Fruit
	Punch
		Punch

b.The ﬁgures below show the relative lengths of a yardstick and a meterstick. Which one represents the meterstick: the longer one or the shorter one?


1	2	3	4	5	6	7	8	9	10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36


			10				20		30	40	50	60	70	80	90	100

c.One ounce and one gram weights are placed on a balance, as shown below. On which side is the gram: the left side or the right side?

28.Determine which measurements the arrows point to on the metric ruler shown below.

Centimeters

Chapter 5 Test

495

29.SPEED SKATING American Bonnie Blair won gold medals in the women’s 500-meter speed skating competitions at the 1988, 1992, and 1994 Winter Olympic Games. Convert the race length to kilometers.

30.How many centimeters are in 5 meters?

31.Convert 8,000 centigrams to kilograms.

32.Convert 70 liters to milliliters.

33.PRESCRIPTIONS A bottle contains 50 tablets, each containing 150 mg of medicine. How many grams of medicine does the bottle contain?

34.TRACK Which is the longer distance: a 100-yard race or an 80-meter race?

35.BODY WEIGHT Which person is heavier: Jim, who weighs 160 pounds, or Ricardo, who weighs 71 kilograms?

36.Convert 810 milliliters to quarts. Round to the nearest tenth.

37.Convert 16.5 inches to centimeters. Round to the nearest centimeter.

38.COOKING MEAT The USDA recommends that turkey be cooked to a temperature of 83°C. Change

this to degrees Fahrenheit. To be safe, round up to the next degree. (Hint: F 95 C 32.)

39.What is a scale drawing? Give an example.

40.Explain the beneﬁts of the metric system of measurement as compared to the American system.

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29.	27	6		30.	7		21
					1	1			1
31.	3.5		1.2	32.	1	2		4
31.	9.3	3		32.	3	1		1		1
					3	3		1		7
						3				7

29.	9	2		30.	17		51
29.	27	6		30.	7		21
					1	1			1
31.	3.5		1.2	32.	1	2		4
31.	9.3	3		32.	3	1		1		1
					3	3		1		7
						3				7

29.	9	2		30.	17		51
29.	27	6		30.	7		21
					1	1			1
31.	3.5		1.2	32.	1	2		4
31.	9.3	3		32.	3	1		1		1
					3	3		1		7
						3				7