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Prealgebra 2e

7.5 Systems of Measurement

Prealgebra 2e7.5 Systems of Measurement
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  1. Preface
  2. 1 Whole Numbers
    1. Introduction
    2. 1.1 Introduction to Whole Numbers
    3. 1.2 Add Whole Numbers
    4. 1.3 Subtract Whole Numbers
    5. 1.4 Multiply Whole Numbers
    6. 1.5 Divide Whole Numbers
    7. Key Terms
    8. Key Concepts
    9. Exercises
      1. Review Exercises
      2. Practice Test
  3. 2 The Language of Algebra
    1. Introduction to the Language of Algebra
    2. 2.1 Use the Language of Algebra
    3. 2.2 Evaluate, Simplify, and Translate Expressions
    4. 2.3 Solving Equations Using the Subtraction and Addition Properties of Equality
    5. 2.4 Find Multiples and Factors
    6. 2.5 Prime Factorization and the Least Common Multiple
    7. Key Terms
    8. Key Concepts
    9. Exercises
      1. Review Exercises
      2. Practice Test
  4. 3 Integers
    1. Introduction to Integers
    2. 3.1 Introduction to Integers
    3. 3.2 Add Integers
    4. 3.3 Subtract Integers
    5. 3.4 Multiply and Divide Integers
    6. 3.5 Solve Equations Using Integers; The Division Property of Equality
    7. Key Terms
    8. Key Concepts
    9. Exercises
      1. Review Exercises
      2. Practice Test
  5. 4 Fractions
    1. Introduction to Fractions
    2. 4.1 Visualize Fractions
    3. 4.2 Multiply and Divide Fractions
    4. 4.3 Multiply and Divide Mixed Numbers and Complex Fractions
    5. 4.4 Add and Subtract Fractions with Common Denominators
    6. 4.5 Add and Subtract Fractions with Different Denominators
    7. 4.6 Add and Subtract Mixed Numbers
    8. 4.7 Solve Equations with Fractions
    9. Key Terms
    10. Key Concepts
    11. Exercises
      1. Review Exercises
      2. Practice Test
  6. 5 Decimals
    1. Introduction to Decimals
    2. 5.1 Decimals
    3. 5.2 Decimal Operations
    4. 5.3 Decimals and Fractions
    5. 5.4 Solve Equations with Decimals
    6. 5.5 Averages and Probability
    7. 5.6 Ratios and Rate
    8. 5.7 Simplify and Use Square Roots
    9. Key Terms
    10. Key Concepts
    11. Exercises
      1. Review Exercises
      2. Practice Test
  7. 6 Percents
    1. Introduction to Percents
    2. 6.1 Understand Percent
    3. 6.2 Solve General Applications of Percent
    4. 6.3 Solve Sales Tax, Commission, and Discount Applications
    5. 6.4 Solve Simple Interest Applications
    6. 6.5 Solve Proportions and their Applications
    7. Key Terms
    8. Key Concepts
    9. Exercises
      1. Review Exercises
      2. Practice Test
  8. 7 The Properties of Real Numbers
    1. Introduction to the Properties of Real Numbers
    2. 7.1 Rational and Irrational Numbers
    3. 7.2 Commutative and Associative Properties
    4. 7.3 Distributive Property
    5. 7.4 Properties of Identity, Inverses, and Zero
    6. 7.5 Systems of Measurement
    7. Key Terms
    8. Key Concepts
    9. Exercises
      1. Review Exercises
      2. Practice Test
  9. 8 Solving Linear Equations
    1. Introduction to Solving Linear Equations
    2. 8.1 Solve Equations Using the Subtraction and Addition Properties of Equality
    3. 8.2 Solve Equations Using the Division and Multiplication Properties of Equality
    4. 8.3 Solve Equations with Variables and Constants on Both Sides
    5. 8.4 Solve Equations with Fraction or Decimal Coefficients
    6. Key Terms
    7. Key Concepts
    8. Exercises
      1. Review Exercises
      2. Practice Test
  10. 9 Math Models and Geometry
    1. Introduction
    2. 9.1 Use a Problem Solving Strategy
    3. 9.2 Solve Money Applications
    4. 9.3 Use Properties of Angles, Triangles, and the Pythagorean Theorem
    5. 9.4 Use Properties of Rectangles, Triangles, and Trapezoids
    6. 9.5 Solve Geometry Applications: Circles and Irregular Figures
    7. 9.6 Solve Geometry Applications: Volume and Surface Area
    8. 9.7 Solve a Formula for a Specific Variable
    9. Key Terms
    10. Key Concepts
    11. Exercises
      1. Review Exercises
      2. Practice Test
  11. 10 Polynomials
    1. Introduction to Polynomials
    2. 10.1 Add and Subtract Polynomials
    3. 10.2 Use Multiplication Properties of Exponents
    4. 10.3 Multiply Polynomials
    5. 10.4 Divide Monomials
    6. 10.5 Integer Exponents and Scientific Notation
    7. 10.6 Introduction to Factoring Polynomials
    8. Key Terms
    9. Key Concepts
    10. Exercises
      1. Review Exercises
      2. Practice Test
  12. 11 Graphs
    1. Graphs
    2. 11.1 Use the Rectangular Coordinate System
    3. 11.2 Graphing Linear Equations
    4. 11.3 Graphing with Intercepts
    5. 11.4 Understand Slope of a Line
    6. Key Terms
    7. Key Concepts
    8. Exercises
      1. Review Exercises
      2. Practice Test
  13. A | Cumulative Review
  14. B | Powers and Roots Tables
  15. C | Geometric Formulas
  16. Answer Key
    1. Chapter 1
    2. Chapter 2
    3. Chapter 3
    4. Chapter 4
    5. Chapter 5
    6. Chapter 6
    7. Chapter 7
    8. Chapter 8
    9. Chapter 9
    10. Chapter 10
    11. Chapter 11
  17. Index

Learning Objectives

By the end of this section, you will be able to:
  • Make unit conversions in the U.S. system
  • Use mixed units of measurement in the U.S. system
  • Make unit conversions in the metric system
  • Use mixed units of measurement in the metric system
  • Convert between the U.S. and the metric systems of measurement
  • Convert between Fahrenheit and Celsius temperatures
Be Prepared 7.13

Before you get started, take this readiness quiz.

Multiply: 4.29(1000).4.29(1000).
If you missed this problem, review Example 5.18.

Be Prepared 7.14

Simplify: 3054.3054.
If you missed this problem, review Example 4.20.

Be Prepared 7.15

Multiply: 715·2528.715·2528.
If you missed this problem, review Example 4.27.

In this section we will see how to convert among different types of units, such as feet to miles or kilograms to pounds. The basic idea in all of the unit conversions will be to use a form of 1,1, the multiplicative identity, to change the units but not the value of a quantity.

Make Unit Conversions in the U.S. System

There are two systems of measurement commonly used around the world. Most countries use the metric system. The United States uses a different system of measurement, usually called the U.S. system. We will look at the U.S. system first.

The U.S. system of measurement uses units of inch, foot, yard, and mile to measure length and pound and ton to measure weight. For capacity, the units used are cup, pint, quart and gallons. Both the U.S. system and the metric system measure time in seconds, minutes, or hours.

The equivalencies among the basic units of the U.S. system of measurement are listed in Table 7.2. The table also shows, in parentheses, the common abbreviations for each measurement.

U.S. System Units
Length Volume
11 foot (ft) = 1212 inches (in)
11 yard (yd) = 33 feet (ft)
11 mile (mi) = 52805280 feet (ft)
33 teaspoons (t) = 11 tablespoon (T)
1616 Tablespoons (T) = 11 cup (C)
11 cup (C) = 88 fluid ounces (fl oz)
11 pint (pt) = 22 cups (C)
11 quart (qt) = 22 pints (pt)
11 gallon (gal) = 44 quarts (qt)
Weight Time
11 pound (lb) = 1616 ounces (oz)
11 ton = 20002000 pounds (lb)
11 minute (min) = 6060 seconds (s)
11 hour (h) = 6060 minutes (min)
11 day = 2424 hours (h)
11 week (wk) = 77 days
11 year (yr) = 365365 days
Table 7.2

In many real-life applications, we need to convert between units of measurement. We will use the identity property of multiplication to do these conversions. We’ll restate the Identity Property of Multiplication here for easy reference.

For any real numbera,a·1=a1·a=aFor any real numbera,a·1=a1·a=a

To use the identity property of multiplication, we write 11 in a form that will help us convert the units. For example, suppose we want to convert inches to feet. We know that 11 foot is equal to 1212 inches, so we can write 11 as the fraction 1 ft12 in.1 ft12 in. When we multiply by this fraction, we do not change the value but just change the units.

But 12 in1 ft12 in1 ft also equals 1.1. How do we decide whether to multiply by 1 ft12 in1 ft12 in or 12 in1 ft?12 in1 ft? We choose the fraction that will make the units we want to convert from divide out. For example, suppose we wanted to convert 6060 inches to feet. If we choose the fraction that has inches in the denominator, we can eliminate the inches.

60in·1 ft12in=5 ft60in·1 ft12in=5 ft

On the other hand, if we wanted to convert 55 feet to inches, we would choose the fraction that has feet in the denominator.

5 ft·12 in1ft=60 in5 ft·12 in1ft=60 in

We treat the unit words like factors and ‘divide out’ common units like we do common factors.

How To

Make unit conversions.

  1. Step 1. Multiply the measurement to be converted by 1;1; write 11 as a fraction relating the units given and the units needed.
  2. Step 2. Multiply.
  3. Step 3. Simplify the fraction, performing the indicated operations and removing the common units.

Example 7.44

Mary Anne is 6666 inches tall. What is her height in feet?

Try It 7.87

Lexie is 3030 inches tall. Convert her height to feet.

Try It 7.88

Rene bought a hose that is 1818 yards long. Convert the length to feet.

When we use the Identity Property of Multiplication to convert units, we need to make sure the units we want to change from will divide out. Usually this means we want the conversion fraction to have those units in the denominator.

Example 7.45

Ndula, an elephant at the San Diego Safari Park, weighs almost 3.23.2 tons. Convert her weight to pounds.

A photograph of an adult elephant.
Figure 7.5 (credit: Guldo Da Rozze, Flickr)
Try It 7.89

Arnold’s SUV weighs about 4.34.3 tons. Convert the weight to pounds.

Try It 7.90

A cruise ship weighs 51,00051,000 tons. Convert the weight to pounds.

Sometimes to convert from one unit to another, we may need to use several other units in between, so we will need to multiply several fractions.

Example 7.46

Juliet is going with her family to their summer home. She will be away for 99 weeks. Convert the time to minutes.

Try It 7.91

The distance between Earth and the moon is about 250,000250,000 miles. Convert this length to yards.

Try It 7.92

A team of astronauts spends 1515 weeks in space. Convert the time to minutes.

Example 7.47

How many fluid ounces are in 11 gallon of milk?

A photograph of a milk display in a grocery store.
Figure 7.6 (credit: www.bluewaikiki.com, Flickr)
Try It 7.93

How many cups are in 11 gallon?

Try It 7.94

How many teaspoons are in 11 cup?

Use Mixed Units of Measurement in the U.S. System

Performing arithmetic operations on measurements with mixed units of measures requires care. Be sure to add or subtract like units.

Example 7.48

Charlie bought three steaks for a barbecue. Their weights were 1414 ounces, 11 pound 22 ounces, and 11 pound 66 ounces. How many total pounds of steak did he buy?

A photograph of meat being cooked on a charcoal grill.
Figure 7.7 (credit: Helen Penjam, Flickr)
Try It 7.95

Laura gave birth to triplets weighing 33 pounds 1212 ounces, 33 pounds 33 ounces, and 22 pounds 99 ounces. What was the total birth weight of the three babies?

Try It 7.96

Seymour cut two pieces of crown molding for his family room that were 88 feet 77 inches and 1212 feet 1111 inches. What was the total length of the molding?

Example 7.49

Anthony bought four planks of wood that were each 66 feet 44 inches long. If the four planks are placed end-to-end, what is the total length of the wood?

The image shows 4 planks of wood placed end-to-end horizontally. Each plank is labeled 6 feet 4 inches. A line starts at the left of the first plank and runs horizontally to the right of the fourth plank. The line is labeled with the letter l to represent length.
Try It 7.97

Henri wants to triple his spaghetti sauce recipe, which calls for 11 pound 88 ounces of ground turkey. How many pounds of ground turkey will he need?

Try It 7.98

Joellen wants to double a solution of 55 gallons 33 quarts. How many gallons of solution will she have in all?

Make Unit Conversions in the Metric System

In the metric system, units are related by powers of 10.10. The root words of their names reflect this relation. For example, the basic unit for measuring length is a meter. One kilometer is 10001000 meters; the prefix kilo- means thousand. One centimeter is 11001100 of a meter, because the prefix centi- means one one-hundredth (just like one cent is 11001100 of one dollar).

The equivalencies of measurements in the metric system are shown in Table 7.3. The common abbreviations for each measurement are given in parentheses.

Metric Measurements
Length Mass Volume/Capacity
11 kilometer (km) = 10001000 m
11 hectometer (hm) = 100100 m
11 dekameter (dam) = 1010 m
11 meter (m) = 11 m
11 decimeter (dm) = 0.10.1 m
11 centimeter (cm) = 0.010.01 m
11 millimeter (mm) = 0.0010.001 m
11 kilogram (kg) = 10001000 g
11 hectogram (hg) = 100100 g
11 dekagram (dag) = 1010 g
11 gram (g) = 11 g
11 decigram (dg) = 0.10.1 g
11 centigram (cg) = 0.010.01 g
11 milligram (mg) = 0.0010.001 g
11 kiloliter (kL) = 10001000 L
11 hectoliter (hL) = 100100 L
11 dekaliter (daL) = 1010 L
11 liter (L) = 11 L
11 deciliter (dL) = 0.10.1 L
11 centiliter (cL) = 0.010.01 L
11 milliliter (mL) = 0.0010.001 L
11 meter = 100100 centimeters
11 meter = 10001000 millimeters
11 gram = 100100 centigrams
11 gram = 10001000 milligrams
11 liter = 100100 centiliters
11 liter = 10001000 milliliters
Table 7.3

To make conversions in the metric system, we will use the same technique we did in the U.S. system. Using the identity property of multiplication, we will multiply by a conversion factor of one to get to the correct units.

Have you ever run a 5 k5 k or 10 k10 k race? The lengths of those races are measured in kilometers. The metric system is commonly used in the United States when talking about the length of a race.

Example 7.50

Nick ran a 10-kilometer10-kilometer race. How many meters did he run?

A photograph of 8 male runners in a track race.
Figure 7.8 (credit: William Warby, Flickr)
Try It 7.99

Sandy completed her first 5-km5-km race. How many meters did she run?

Try It 7.100

Herman bought a rug 2.52.5 meters in length. How many centimeters is the length?

Example 7.51

Eleanor’s newborn baby weighed 32003200 grams. How many kilograms did the baby weigh?

Try It 7.101

Kari’s newborn baby weighed 28002800 grams. How many kilograms did the baby weigh?

Try It 7.102

Anderson received a package that was marked 45004500 grams. How many kilograms did this package weigh?

Since the metric system is based on multiples of ten, conversions involve multiplying by multiples of ten. In Decimal Operations, we learned how to simplify these calculations by just moving the decimal.

To multiply by 10,100,or1000,10,100,or1000, we move the decimal to the right 1,2,or31,2,or3 places, respectively. To multiply by 0.1,0.01,or0.0010.1,0.01,or0.001 we move the decimal to the left 1,2,or31,2,or3 places respectively.

We can apply this pattern when we make measurement conversions in the metric system.

In Example 7.51, we changed 32003200 grams to kilograms by multiplying by 11000(or0.001).11000(or0.001). This is the same as moving the decimal 33 places to the left.

Multiplying 3200 by 1 over 1000 gives 3.2. Notice that the answer, 3.2, is similar to the original value, 3200, just with the decimal moved three places to the left.

Example 7.52

Convert:

  1. 350350 liters to kiloliters
  2. 4.14.1 liters to milliliters.
Try It 7.103

Convert: 7.257.25 L to kL 6.36.3 L to mL.

Try It 7.104

Convert: 350350 hL to L 4.14.1 L to cL.

Use Mixed Units of Measurement in the Metric System

Performing arithmetic operations on measurements with mixed units of measures in the metric system requires the same care we used in the U.S. system. But it may be easier because of the relation of the units to the powers of 10.10. We still must make sure to add or subtract like units.

Example 7.53

Ryland is 1.61.6 meters tall. His younger brother is 8585 centimeters tall. How much taller is Ryland than his younger brother?

Try It 7.105

Mariella is 1.581.58 meters tall. Her daughter is 7575 centimeters tall. How much taller is Mariella than her daughter? Write the answer in centimeters.

Try It 7.106

The fence around Hank’s yard is 22 meters high. Hank is 9696 centimeters tall. How much shorter than the fence is Hank? Write the answer in meters.

Example 7.54

Dena’s recipe for lentil soup calls for 150150 milliliters of olive oil. Dena wants to triple the recipe. How many liters of olive oil will she need?

Try It 7.107

A recipe for Alfredo sauce calls for 250250 milliliters of milk. Renata is making pasta with Alfredo sauce for a big party and needs to multiply the recipe amounts by 8.8. How many liters of milk will she need?

Try It 7.108

To make one pan of baklava, Dorothea needs 400400 grams of filo pastry. If Dorothea plans to make 66 pans of baklava, how many kilograms of filo pastry will she need?

Convert Between U.S. and Metric Systems of Measurement

Many measurements in the United States are made in metric units. A drink may come in 2-liter2-liter bottles, calcium may come in 500-mg500-mg capsules, and we may run a 5-K5-K race. To work easily in both systems, we need to be able to convert between the two systems.

Table 7.4 shows some of the most common conversions.

Conversion Factors Between U.S. and Metric Systems
Length Weight Volume
11 in = 2.542.54 cm
11 ft = 0.3050.305 m
11 yd = 0.9140.914 m
11 mi = 1.611.61 km


11 m = 3.283.28 ft
11 lb = 0.450.45 kg
11 oz = 2828 g




11 kg = 2.22.2 lb
11 qt = 0.950.95 L
11 fl oz = 3030 mL




11 L = 1.061.06 qt
Table 7.4

We make conversions between the systems just as we do within the systems—by multiplying by unit conversion factors.

Example 7.55

Lee’s water bottle holds 500500 mL of water. How many fluid ounces are in the bottle? Round to the nearest tenth of an ounce.

Try It 7.109

How many quarts of soda are in a 2-liter2-liter bottle?

Try It 7.110

How many liters are in 44 quarts of milk?

The conversion factors in Table 7.4 are not exact, but the approximations they give are close enough for everyday purposes. In Example 7.55, we rounded the number of fluid ounces to the nearest tenth.

Example 7.56

Soleil lives in Minnesota but often travels in Canada for work. While driving on a Canadian highway, she passes a sign that says the next rest stop is in 100100 kilometers. How many miles until the next rest stop? Round your answer to the nearest mile.

Try It 7.111

The height of Mount Kilimanjaro is 5,8955,895 meters. Convert the height to feet. Round to the nearest foot.

Try It 7.112

The flight distance from New York City to London is 5,5865,586 kilometers. Convert the distance to miles. Round to the nearest mile.

Convert Between Fahrenheit and Celsius Temperatures

Have you ever been in a foreign country and heard the weather forecast? If the forecast is for 22°C.22°C. What does that mean?

The U.S. and metric systems use different scales to measure temperature. The U.S. system uses degrees Fahrenheit, written °F.°F. The metric system uses degrees Celsius, written °C.°C. Figure 7.9 shows the relationship between the two systems.

On the left side of the figure is a thermometer marked in degrees Celsius. The bottom of the thermometer begins with negative 20 degrees Celsius and ranges up to 100 degrees Celsius. There are tick marks on the thermometer every 5 degrees with every 10 degrees labeled. On the right side is a thermometer marked in degrees Fahrenheit. The bottom of the thermometer begins with negative 10 degrees Fahrenheit and ranges up to 212 degrees Fahrenheit. There are tick marks on the thermometer every 2 degrees with every 10 degrees labeled. Between the thermometers there is an arrow pointing on the left to 0 degrees Celsius and on the right to 32 degrees Fahrenheit. This is the temperature at which water freezes. Another arrow points on the left to 37 degrees Celsius and on the right to 98.6 degrees Fahrenheit. This is normal body temperature. A third arrow points on the left to 100 degrees Celsius and on the right to 212 degrees Fahrenheit. This is the temperature at which water boils.
Figure 7.9 A temperature of 37°C37°C is equivalent to 98.6°F.98.6°F.

If we know the temperature in one system, we can use a formula to convert it to the other system.

Temperature Conversion

To convert from Fahrenheit temperature, F,F, to Celsius temperature, C,C, use the formula

C=59(F32)C=59(F32)

To convert from Celsius temperature, C,C, to Fahrenheit temperature, F,F, use the formula

F=95C+32F=95C+32

Example 7.57

Convert 50°F50°F into degrees Celsius.

Try It 7.113

Convert the Fahrenheit temperatures to degrees Celsius: 59°F.59°F.

Try It 7.114

Convert the Fahrenheit temperatures to degrees Celsius: 41°F.41°F.

Example 7.58

The weather forecast for Paris predicts a high of 20°C.20°C. Convert the temperature into degrees Fahrenheit.

Try It 7.115

Convert the Celsius temperatures to degrees Fahrenheit:

The temperature in Helsinki, Finland was 15°C.15°C.

Try It 7.116

Convert the Celsius temperatures to degrees Fahrenheit:

The temperature in Sydney, Australia was 10°C.10°C.

Section 7.5 Exercises

Practice Makes Perfect

Make Unit Conversions in the U.S. System

In the following exercises, convert the units.

214.

A park bench is 66 feet long. Convert the length to inches.

215.

A floor tile is 22 feet wide. Convert the width to inches.

216.

A ribbon is 1818 inches long. Convert the length to feet.

217.

Carson is 4545 inches tall. Convert his height to feet.

218.

Jon is 66 feet 44 inches tall. Convert his height to inches.

219.

Faye is 44 feet 1010 inches tall. Convert her height to inches.

220.

A football field is 160160 feet wide. Convert the width to yards.

221.

On a baseball diamond, the distance from home plate to first base is 3030 yards. Convert the distance to feet.

222.

Ulises lives 1.51.5 miles from school. Convert the distance to feet.

223.

Denver, Colorado, is 5,1835,183 feet above sea level. Convert the height to miles.

224.

A killer whale weighs 4.64.6 tons. Convert the weight to pounds.

225.

Blue whales can weigh as much as 150150 tons. Convert the weight to pounds.

226.

An empty bus weighs 35,00035,000 pounds. Convert the weight to tons.

227.

At take-off, an airplane weighs 220,000220,000 pounds. Convert the weight to tons.

228.

The voyage of the Mayflower took 22 months and 55 days. Convert the time to days (30 days = 1 month).

229.

Lynn’s cruise lasted 66 days and 1818 hours. Convert the time to hours.

230.

Rocco waited 112112 hours for his appointment. Convert the time to seconds.

231.

Misty’s surgery lasted 214214 hours. Convert the time to seconds.

232.

How many teaspoons are in a pint?

233.

How many tablespoons are in a gallon?

234.

JJ’s cat, Posy, weighs 1414 pounds. Convert her weight to ounces.

235.

April’s dog, Beans, weighs 88 pounds. Convert his weight to ounces.

236.

Baby Preston weighed 77 pounds 33 ounces at birth. Convert his weight to ounces.

237.

Baby Audrey weighed 66 pounds 1515 ounces at birth. Convert her weight to ounces.

238.

Crista will serve 2020 cups of juice at her son’s party. Convert the volume to gallons.

239.

Lance needs 500500 cups of water for the runners in a race. Convert the volume to gallons.

Use Mixed Units of Measurement in the U.S. System

In the following exercises, solve and write your answer in mixed units.

240.

Eli caught three fish. The weights of the fish were 22 pounds 44 ounces, 11 pound 1111 ounces, and 44 pounds 1414 ounces. What was the total weight of the three fish?

241.

Judy bought 11 pound 66 ounces of almonds, 22 pounds 33 ounces of walnuts, and 88 ounces of cashews. What was the total weight of the nuts?

242.

One day Anya kept track of the number of minutes she spent driving. She recorded trips of 45,10,8,65,20,and 35 minutes.45,10,8,65,20,and 35 minutes. How much time (in hours and minutes) did Anya spend driving?

243.

Last year Eric went on 66 business trips. The number of days of each was 5,2,8,12,6,and 3.5,2,8,12,6,and 3. How much time (in weeks and days) did Eric spend on business trips last year?

244.

Renee attached a 6-foot-6-inch6-foot-6-inch extension cord to her computer’s 3-foot-8-inch3-foot-8-inch power cord. What was the total length of the cords?

245.

Fawzi’s SUV is 66 feet 44 inches tall. If he puts a 2-foot-10-inch2-foot-10-inch box on top of his SUV, what is the total height of the SUV and the box?

246.

Leilani wants to make 88 placemats. For each placemat she needs 1818 inches of fabric. How many yards of fabric will she need for the 88 placemats?

247.

Mireille needs to cut 2424 inches of ribbon for each of the 1212 girls in her dance class. How many yards of ribbon will she need altogether?

Make Unit Conversions in the Metric System

In the following exercises, convert the units.

248.

Ghalib ran 55 kilometers. Convert the length to meters.

249.

Kitaka hiked 88 kilometers. Convert the length to meters.

250.

Estrella is 1.551.55 meters tall. Convert her height to centimeters.

251.

The width of the wading pool is 2.452.45 meters. Convert the width to centimeters.

252.

Mount Whitney is 3,0723,072 meters tall. Convert the height to kilometers.

253.

The depth of the Mariana Trench is 10,91110,911 meters. Convert the depth to kilometers.

254.

June’s multivitamin contains 1,5001,500 milligrams of calcium. Convert this to grams.

255.

A typical ruby-throated hummingbird weights 33 grams. Convert this to milligrams.

256.

One stick of butter contains 91.691.6 grams of fat. Convert this to milligrams.

257.

One serving of gourmet ice cream has 2525 grams of fat. Convert this to milligrams.

258.

The maximum mass of an airmail letter is 22 kilograms. Convert this to grams.

259.

Dimitri’s daughter weighed 3.83.8 kilograms at birth. Convert this to grams.

260.

A bottle of wine contained 750750 milliliters. Convert this to liters.

261.

A bottle of medicine contained 300300 milliliters. Convert this to liters.

Use Mixed Units of Measurement in the Metric System

In the following exercises, solve and write your answer in mixed units.

262.

Matthias is 1.81.8 meters tall. His son is 8989 centimeters tall. How much taller, in centimeters, is Matthias than his son?

263.

Stavros is 1.61.6 meters tall. His sister is 9595 centimeters tall. How much taller, in centimeters, is Stavros than his sister?

264.

A typical dove weighs 345345 grams. A typical duck weighs 1.21.2 kilograms. What is the difference, in grams, of the weights of a duck and a dove?

265.

Concetta had a 2-kilogram2-kilogram bag of flour. She used 180180 grams of flour to make biscotti. How many kilograms of flour are left in the bag?

266.

Harry mailed 55 packages that weighed 420420 grams each. What was the total weight of the packages in kilograms?

267.

One glass of orange juice provides 560560 milligrams of potassium. Linda drinks one glass of orange juice every morning. How many grams of potassium does Linda get from her orange juice in 3030 days?

268.

Jonas drinks 200200 milliliters of water 88 times a day. How many liters of water does Jonas drink in a day?

269.

One serving of whole grain sandwich bread provides 66 grams of protein. How many milligrams of protein are provided by 77 servings of whole grain sandwich bread?

Convert Between U.S. and Metric Systems

In the following exercises, make the unit conversions. Round to the nearest tenth.

270.

Bill is 7575 inches tall. Convert his height to centimeters.

271.

Frankie is 4242 inches tall. Convert his height to centimeters.

272.

Marcus passed a football 2424 yards. Convert the pass length to meters.

273.

Connie bought 99 yards of fabric to make drapes. Convert the fabric length to meters.

274.

Each American throws out an average of 1,6501,650 pounds of garbage per year. Convert this weight to kilograms (2.20 pounds = 1 kilogram).

275.

An average American will throw away 90,00090,000 pounds of trash over his or her lifetime. Convert this weight to kilograms (2.20 pounds = 1 kilogram).

276.

A 5K5K run is 55 kilometers long. Convert this length to miles.

277.

Kathryn is 1.61.6 meters tall. Convert her height to feet.

278.

Dawn’s suitcase weighed 2020 kilograms. Convert the weight to pounds.

279.

Jackson’s backpack weighs 1515 kilograms. Convert the weight to pounds.

280.

Ozzie put 1414 gallons of gas in his truck. Convert the volume to liters.

281.

Bernard bought 88 gallons of paint. Convert the volume to liters.

Convert between Fahrenheit and Celsius

In the following exercises, convert the Fahrenheit temperature to degrees Celsius. Round to the nearest tenth.

282.

86°F86°F

283.

77°F77°F

284.

104°F104°F

285.

14°F14°F

286.

72°F72°F

287.

4°F4°F

288.

0°F0°F

289.

120°F120°F

In the following exercises, convert the Celsius temperatures to degrees Fahrenheit. Round to the nearest tenth.

290.

5°C5°C

291.

25°C25°C

292.

−10°C−10°C

293.

−15°C−15°C

294.

22°C22°C

295.

8°C8°C

296.

43°C43°C

297.

16°C16°C

Everyday Math

298.

Nutrition Julian drinks one can of soda every day. Each can of soda contains 4040 grams of sugar. How many kilograms of sugar does Julian get from soda in 11 year?

299.

Reflectors The reflectors in each lane-marking stripe on a highway are spaced 1616 yards apart. How many reflectors are needed for a one-mile-long stretch of highway?

Writing Exercises

300.

Some people think that 65°65° to 75°75° Fahrenheit is the ideal temperature range.

  1. What is your ideal temperature range? Why do you think so?

  2. Convert your ideal temperatures from Fahrenheit to Celsius.

301.

Did you grow up using the U.S. customary or the metric system of measurement? Describe two examples in your life when you had to convert between systems of measurement. Which system do you think is easier to use? Explain.

Self Check

After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.

.

Overall, after looking at the checklist, do you think you are well-prepared for the next chapter? Why or why not?

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