1.11E: Exercises
- Page ID
- 30357
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Practice Makes Perfect
Make Unit Conversions in the U.S. System
In the following exercises, convert the units.
A park bench is 6 feet long. Convert the length to inches.
- Answer
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72 inches
A floor tile is 2 feet wide. Convert the width to inches.
A ribbon is 18 inches long. Convert the length to feet.
- Answer
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1.5 feet
Carson is 45 inches tall. Convert his height to feet.
A football field is 160 feet wide. Convert the width to yards.
- Answer
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53\(\frac{1}{3}\) yards
On a baseball diamond, the distance from home plate to first base is 30 yards. Convert the distance to feet.
On a baseball diamond, the distance from home plate to first base is 30 yards. Convert the distance to feet.
- Answer
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7,920 feet
Denver, Colorado, is 5,183 feet above sea level. Convert the height to miles.
A killer whale weighs 4.6 tons. Convert the weight to pounds.
- Answer
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9,200 pounds
Blue whales can weigh as much as 150 tons. Convert the weight to pounds.
An empty bus weighs 35,000 pounds. Convert the weight to tons.
- Answer
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17\(\frac{1}{2}\) tons
At take-off, an airplane weighs 220,000 pounds. Convert the weight to tons.
Rocco waited 1\(\frac{1}{2}\) hours for his appointment. Convert the time to seconds.
- Answer
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5,400 s
Misty's surgery lasted 2\(\frac{1}{4}\) hours. Convert the time to seconds.
How many teaspoons are in a pint?
- Answer
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96 teaspoons
How many tablespoons are in a gallon?
JJ’s cat, Posy, weighs 14 pounds. Convert her weight to ounces.
- Answer
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224 ounces
April’s dog, Beans, weighs 8 pounds. Convert his weight to ounces.
Crista will serve 20 cups of juice at her son’s party. Convert the volume to gallons.
- Answer
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1\(\frac{1}{4}\) gallons
Lance needs 50 cups of water for the runners in a race. Convert the volume to gallons.
Jon is 6 feet 4 inches tall. Convert his height to inches.
- Answer
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26 in.
Faye is 4 feet 10 inches tall. Convert her height to inches.
The voyage of the Mayflower took 2 months and 5 days. Convert the time to days.
- Answer
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65 days
Lynn’s cruise lasted 6 days and 18 hours. Convert the time to hours.
Baby Preston weighed 7 pounds 3 ounces at birth. Convert his weight to ounces.
- Answer
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115 ounces
Baby Audrey weighted 6 pounds 15 ounces at birth. Convert her weight to ounces.
Use Mixed Units of Measurement in the U.S. System
In the following exercises, solve.
Eli caught three fish. The weights of the fish were 2 pounds 4 ounces, 1 pound 11 ounces, and 4 pounds 14 ounces. What was the total weight of the three fish?
- Answer
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8 lbs. 13 oz.
Judy bought 1 pound 6 ounces of almonds, 2 pounds 3 ounces of walnuts, and 8 ounces of cashews. How many pounds of nuts did Judy buy?
One day Anya kept track of the number of minutes she spent driving. She recorded 45, 10, 8, 65, 20, and 35. How many hours did Anya spend driving?
- Answer
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3.05 hours
Last year Eric went on 6 business trips. The number of days of each was 5, 2, 8, 12, 6, and 3. How many weeks did Eric spend on business trips last year?
Renee attached a 6 feet 6 inch extension cord to her computer’s 3 feet 8 inch power cord. What was the total length of the cords?
- Answer
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10 ft. 2 in.
Fawzi’s SUV is 6 feet 4 inches tall. If he puts a 2 feet 10 inch box on top of his SUV, what is the total height of the SUV and the box?
Leilani wants to make 8 placemats. For each placemat she needs 18 inches of fabric. How many yards of fabric will she need for the 8 placemats?
- Answer
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4 yards
Mireille needs to cut 24 inches of ribbon for each of the 12 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.
Ghalib ran 5 kilometers. Convert the length to meters.
- Answer
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5,000 meters
Kitaka hiked 8 kilometers. Convert the length to meters.
Estrella is 1.55 meters tall. Convert her height to centimeters.
- Answer
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155 centimeters
The width of the wading pool is 2.45 meters. Convert the width to centimeters.
Mount Whitney is 3,072 meters tall. Convert the height to kilometers.
- Answer
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3.072 kilometers
The depth of the Mariana Trench is 10,911 meters. Convert the depth to kilometers.
June’s multivitamin contains 1,500 milligrams of calcium. Convert this to grams.
- Answer
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1.5 grams
A typical ruby-throated hummingbird weights 3 grams. Convert this to milligrams.
One stick of butter contains 91.6 grams of fat. Convert this to milligrams.
- Answer
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91,600 milligrams
One serving of gourmet ice cream has 25 grams of fat. Convert this to milligrams.
The maximum mass of an airmail letter is 2 kilograms. Convert this to grams.
- Answer
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2,000 grams
Dimitri’s daughter weighed 3.8 kilograms at birth. Convert this to grams.
A bottle of wine contained 750 milliliters. Convert this to liters.
- Answer
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0.75 liters
A bottle of medicine contained 300 milliliters. Convert this to liters.
Use Mixed Units of Measurement in the Metric System
In the following exercises, solve.
Matthias is 1.8 meters tall. His son is 89 centimeters tall. How much taller is Matthias than his son?
- Answer
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91 centimeters
Stavros is 1.6 meters tall. His sister is 95 centimeters tall. How much taller is Stavros than his sister?
A typical dove weighs 345 grams. A typical duck weighs 1.2 kilograms. What is the difference, in grams, of the weights of a duck and a dove?
- Answer
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855 grams
Concetta had a 2-kilogram bag of flour. She used 180 grams of flour to make biscotti. How many kilograms of flour are left in the bag?
Harry mailed 5 packages that weighed 420 grams each. What was the total weight of the packages in kilograms?
- Answer
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2.1 kilograms
One glass of orange juice provides 560 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 30 days?
Jonas drinks 200 milliliters of water 8 times a day. How many liters of water does Jonas drink in a day?
- Answer
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1.6 liters
One serving of whole grain sandwich bread provides 6 grams of protein. How many milligrams of protein are provided by 7 servings of whole grain sandwich bread?
Convert Between the U.S. and the Metric Systems of Measurement
In the following exercises, make the unit conversions. Round to the nearest tenth.
Bill is 75 inches tall. Convert his height to centimeters.
- Answer
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190.5 centimeters
Frankie is 42 inches tall. Convert his height to centimeters.
Marcus passed a football 24 yards. Convert the pass length to meters
- Answer
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21.9 meters
Connie bought 9 yards of fabric to make drapes. Convert the fabric length to meters.
Each American throws out an average of 1,650 pounds of garbage per year. Convert this weight to kilograms.
- Answer
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742.5 kilograms
An average American will throw away 90,000 pounds of trash over his or her lifetime. Convert this weight to kilograms.
A 5K run is 5 kilometers long. Convert this length to miles.
- Answer
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3.1 miles
Kathryn is 1.6 meters tall. Convert her height to feet.
Dawn’s suitcase weighed 20 kilograms. Convert the weight to pounds.
- Answer
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44 pounds
Jackson’s backpack weighed 15 kilograms. Convert the weight to pounds.
Ozzie put 14 gallons of gas in his truck. Convert the volume to liters.
- Answer
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53.2 liters
Bernard bought 8 gallons of paint. Convert the volume to liters.
Convert between Fahrenheit and Celsius Temperatures
In the following exercises, convert the Fahrenheit temperatures to degrees Celsius. Round to the nearest tenth.
86° Fahrenheit
- Answer
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30°C
77° Fahrenheit
104° Fahrenheit
- Answer
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40°C
14° Fahrenheit
72° Fahrenheit
- Answer
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22.2°C
4° Fahrenheit
0° Fahrenheit
- Answer
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−17.8°C
120° Fahrenheit
In the following exercises, convert the Celsius temperatures to degrees Fahrenheit. Round to the nearest tenth.
5° Celsius
- Answer
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41°F
25° Celsius
−10° Celsius
- Answer
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14°F
−15° Celsius
22° Celsius
- Answer
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71.6°F
8° Celsius
43° Celsius
- Answer
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109.4°F
16° Celsius
Everyday Math
Nutrition Julian drinks one can of soda every day. Each can of soda contains 40 grams of sugar. How many kilograms of sugar does Julian get from soda in 1 year?
- Answer
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14.6 kilograms
Reflectors The reflectors in each lane-marking stripe on a highway are spaced 16 yards apart. How many reflectors are needed for a one mile long lane-marking stripe?
Writing Exercises
Some people think that 65° to 75° Fahrenheit is the ideal temperature range.
- What is your ideal temperature range? Why do you think so?
- Convert your ideal temperatures from Fahrenheit to Celsius.
- Answer
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Answers may vary.
- Did you grow up using the U.S. or the metric system of measurement?
- Describe two examples in your life when you had to convert between the two systems of measurement.
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?