Problem Set: Decimals

Writing and Identifying Characteristics of Decimals

Name Decimals

In the following exercises, name each decimal.

$5.5$
Show Solution

five and five tenths
$7.8$
$5.01$
Show Solution

five and one hundredth
$14.02$
$8.71$
Show Solution

eight and seventy-one hundredths
$2.64$
$0.002$
Show Solution

two thousandths
$0.005$
$0.381$
Show Solution

three hundred eighty-one thousandths
$0.479$
$-17.9$
Show Solution

negative seventeen and nine tenths
$-31.4$

Write Decimals

In the following exercises, translate the name into a decimal number.

Eight and three hundredths
Show Solution

8.03
Nine and seven hundredths
Twenty-nine and eighty-one hundredths
Show Solution

29.81
Sixty-one and seventy-four hundredths
Seven tenths
Show Solution

0.7
Six tenths
One thousandth
Show Solution

0.001
Nine thousandths
Twenty-nine thousandths
Show Solution

0.029
Thirty-five thousandths
Negative eleven and nine ten-thousandths
Show Solution

−11.0009
Negative fifty-nine and two ten-thousandths
Thirteen and three hundred ninety-five ten thousandths
Show Solution

13.0395
Thirty and two hundred seventy-nine thousandths

Convert Decimals to Fractions or Mixed Numbers

In the following exercises, convert each decimal to a fraction or mixed number.

$1.99$
Show Solution

$1\Large\frac{99}{100}$
$5.83$
$15.7$
Show Solution

$15\Large\frac{7}{10}$
$18.1$
$0.239$
Show Solution

$\Large\frac{239}{1000}$
$0.373$
$0.13$
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$\Large\frac{13}{100}$
$0.19$
$0.011$
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$\Large\frac{11}{1000}$
$0.049$
$-0.00007$
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$-\Large\frac{7}{100000}$
$-0.00003$
$6.4$
Show Solution

$6\Large\frac{2}{5}$
$5.2$
$7.05$
Show Solution

$7\Large\frac{1}{20}$
$9.04$
$4.006$
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$4\Large\frac{3}{500}$
$2.008$
$10.25$
Show Solution

$10\Large\frac{1}{4}$
$12.75$
$1.324$
Show Solution

$1\Large\frac{81}{250}$
$2.482$
$14.125$
Show Solution

$14\Large\frac{1}{8}$
$20.375$

Locate Decimals on the Number Line

In the following exercises, locate each number on a number line.

$0.8$
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$0.3$
$-0.2$
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$-0.9$
$3.1$
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$2.7$
$-2.5$
Show Solution
$-1.6$

Order Decimals

In the following exercises, order each of the following pairs of numbers, using $<\text{or}>$ ;.

$0.9\text{__}0.6$
Show Solution

>
$0.7\text{__}0.8$
$0.37\text{__}0.63$
Show Solution

<
$0.86\text{__}0.69$
$0.6\text{__}0.59$
Show Solution

>
$0.27\text{__}0.3$
$0.91\text{__}0.901$
Show Solution

>
$0.415\text{__}0.41$
$-0.5\text{__} - 0.3$
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<
$-0.1\text{__} - 0.4$
$-0.62\text{__} - 0.619$
Show Solution

<
$-7.31\text{__} - 7.3$

Round Decimals

In the following exercises, round each number to the nearest tenth.

$0.67$
Show Solution

0.7
$0.49$
$2.84$
Show Solution

2.8
$4.63$

In the following exercises, round each number to the nearest hundredth.

$0.845$
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0.85
$0.761$
$5.7932$
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5.79
$3.6284$
$0.299$
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0.30
$0.697$
$4.098$
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4.10
$7.096$

In the following exercises, round each number to the nearest ⓐ hundredth ⓑ tenth ⓒ whole number.

$5.781$
Show Solution

ⓐ 5.78 ⓑ 5.8 ⓒ 6
$1.638$
$63.479$
Show Solution

ⓐ 63.48 ⓑ 63.5 ⓒ 63
$84.281$

Exercises

Everyday Math

Salary Increase

Danny got a raise and now makes ${$58,965.95}$ a year. Round this number to the nearest:
ⓐ dollar
ⓑ thousand dollars
ⓒ ten thousand dollars.

Show Solution

New Car Purchase

Selena’s new car cost ${$23,795.95}$ . Round this number to the nearest:

dollar
thousand dollars
ten thousand dollars.

Sales Tax

Hyo Jin lives in San Diego. She bought a refrigerator for ${$1624.99}$ and when the clerk calculated the sales tax it came out to exactly ${$142.186625}$ . Round the sales tax to the nearest ⓐ penny ⓑ dollar.

Show Solution

Sales Tax

Jennifer bought a ${$1,038.99}$ dining room set for her home in Cincinnati. She calculated the sales tax to be exactly ${$67.53435}$ . Round the sales tax to the nearest ⓐ penny ⓑ dollar.

Writing Exercises

How does your knowledge of money help you learn about decimals

Explain how you write “three and nine hundredths” as a decimal.

Jim ran a $100-meter$ race in $\text{12.32 seconds}$ . Tim ran the same race in $\text{12.3 seconds}$ . Who had the faster time, Jim or Tim? How do you know?

Show Solution

Gerry saw a sign advertising postcards marked for sale at “10 for 0.99¢”What is wrong with the advertised price?

Operations on Decimals

Add and Subtract Decimals

In the following exercises, add or subtract.

$16.92+7.56$
Show Solution

24.48
$18.37+9.36$
$256.37 - 85.49$
Show Solution

170.88
$248.25 - 91.29$
$21.76 - 30.99$
Show Solution

−9.23
$15.35 - 20.88$
$37.5+12.23$
Show Solution

49.73
$38.6+13.67$
$-16.53 - 24.38$
Show Solution

−40.91
$-19.47 - 32.58$
$-38.69+31.47$
Show Solution

−7.22
$-29.83+19.76$
$-4.2+\left(-9.3\right)$
Show Solution

−13.5
$-8.6+\left(-8.6\right)$
$100 - 64.2$
Show Solution

35.8
$100 - 65.83$
$72.5 - 100$
Show Solution

−27.5
$86.2 - 100$
$15+0.73$
Show Solution

15.73
$27+0.87$
$2.51+40$
Show Solution

42.51
$9.38+60$
$91.75-\left(-10.462\right)$
Show Solution

102.212
$94.69-\left(-12.678\right)$
$55.01 - 3.7$
Show Solution

51.31
$59.08 - 4.6$
$2.51 - 7.4$
Show Solution

−4.89
$3.84 - 6.1$

Multiply Decimals

In the following exercises, multiply.

$\left(0.3\right)\left(0.4\right)$
Show Solution

0.12
$\left(0.6\right)\left(0.7\right)$
$\left(0.24\right)\left(0.6\right)$
Show Solution

0.144
$\left(0.81\right)\left(0.3\right)$
$\left(5.9\right)\left(7.12\right)$
Show Solution

42.008
$\left(2.3\right)\left(9.41\right)$
$\left(8.52\right)\left(3.14\right)$
Show Solution

26.7528
$\left(5.32\right)\left(4.86\right)$
$\text{(-4.3)(2.71)}$
Show Solution

−11.653
$\left(-8.5\right)\left(1.69\right)$
$\text{(-5.18)(-65.23)}$
Show Solution

337.8914
$\left(-9.16\right)\left(-68.34\right)$
$\left(0.09\right)\left(24.78\right)$
Show Solution

2.2302
$\left(0.04\right)\left(36.89\right)$
$\left(0.06\right)\left(21.75\right)$
Show Solution

1.305
$\left(0.08\right)\left(52.45\right)$
$\left(9.24\right)\left(10\right)$
Show Solution

92.4
$\left(6.531\right)\left(10\right)$
$\left(55.2\right)\left(1,000\right)$
Show Solution

55,200
$\left(99.4\right)\left(1,000\right)$

Divide Decimals

In the following exercises, divide.

$0.15\div 5$
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0.03
$0.27\div 3$
$4.75\div 25$
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0.19
$12.04\div 43$
${$8.49}\div 12$
Show Solution

$0.71
${$16.99}\div 9$
${$117.25}\div 48$
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$2.44
${$109.24}\div 36$
$0.6\div 0.2$
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3
$0.8\div 0.4$
$1.44\div \left(-0.3\right)$
Show Solution

−4.8
$1.25\div \left(-0.5\right)$
$-1.75\div \left(-0.05\right)$
Show Solution

35
$-1.15\div \left(-0.05\right)$
$5.2\div 2.5$
Show Solution

2.08
$6.5\div 3.25$
$12\div 0.08$
Show Solution

150
$5\div 0.04$
$11\div 0.55$
Show Solution

20
$14\div 0.35$

Mixed Practice

In the following exercises, simplify.

$6\left(12.4 - 9.2\right)$
Show Solution

19.2
$3\left(15.7 - 8.6\right)$
$24\left(0.5\right)+{\left(0.3\right)}^{2}$
Show Solution

12.09
$35\left(0.2\right)+{\left(0.9\right)}^{2}$
$1.15\left(26.83+1.61\right)$
Show Solution

32.706
$1.18\left(46.22+3.71\right)$
${$45}+0.08\left({$45}\right)$
Show Solution

$48.60
${$63}+0.18\left({$63}\right)$
$18\div \left(0.75+0.15\right)$
Show Solution

20
$27\div \left(0.55+0.35\right)$
$\left(1.43+0.27\right)\div \left(0.9 - 0.05\right)$
Show Solution

2
$\left(1.5 - 0.06\right)\div \left(0.12+0.24\right)$
$\left[{$75.42}+0.18\left({$75.42}\right)\right]\div 5$
Show Solution

$17.80
$\left[{$56.31}+0.22\left({$56.31}\right)\right]\div 4$

Use Decimals in Money Applications

In the following exercises, use the strategy for applications to solve.

Spending money

Brenda got ${$40}$ from the ATM. She spent ${$15.11}$ on a pair of earrings. How much money did she have left?

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Spending money

Marissa found ${$20}$ in her pocket. She spent ${$4.82}$ on a smoothie. How much of the ${$20}$ did she have left?

Shopping

Adam bought a t-shirt for ${$18.49}$ and a book for ${$8.92}$ The sales tax was ${$1.65}$ . How much did Adam spend?

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Restaurant

Roberto’s restaurant bill was ${$20.45}$ for the entrée and ${$3.15}$ for the drink. He left a ${$4.40}$ tip. How much did Roberto spend?

Coupon

Emily bought a box of cereal that cost ${$4.29}$ . She had a coupon for ${$0.55}$ off, and the store doubled the coupon. How much did she pay for the box of cereal?

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Coupon

Diana bought a can of coffee that cost ${$7.99}$ . She had a coupon for ${$0.75}$ off, and the store doubled the coupon. How much did she pay for the can of coffee?

Diet

Leo took part in a diet program. He weighed $190$ pounds at the start of the program. During the first week, he lost $4.3$ pounds. During the second week, he had lost $2.8$ pounds. The third week, he gained $0.7$ pounds. The fourth week, he lost $1.9$ pounds. What did Leo weigh at the end of the fourth week?

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Snowpack

On April $1$ , the snowpack at the ski resort was $4$ meters deep, but the next few days were very warm. By April $5$ , the snow depth was $1.6$ meters less. On April $8$ , it snowed and added $2.1$ meters of snow. What was the total depth of the snow?

Coffee

Noriko bought $4$ coffees for herself and her co-workers. Each coffee was ${$3.75}$ . How much did she pay for all the coffees?

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Subway Fare

Arianna spends ${$4.50}$ per day on subway fare. Last week she rode the subway $6$ days. How much did she spend for the subway fares?

Income

Mayra earns ${$9.25}$ per hour. Last week she worked $32$ hours. How much did she earn?

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Income

Peter earns ${$8.75}$ per hour. Last week he worked $19$ hours. How much did he earn?

Hourly Wage

Alan got his first paycheck from his new job. He worked $30$ hours and earned ${$382.50}$ . How much does he earn per hour?

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Hourly Wage

Maria got her first paycheck from her new job. She worked $25$ hours and earned ${$362.50}$ . How much does she earn per hour?

Restaurant

Jeannette and her friends love to order mud pie at their favorite restaurant. They always share just one piece of pie among themselves. With tax and tip, the total cost is $\$6.00$ . How much does each girl pay if the total number sharing the mud pie is

$2?$
Show Solution

$3
$3?$
Show Solution

$2
$4?$
Show Solution

$1.50
$5?$
Show Solution

$1.20
$6?$
Show Solution

$1

Pizza

Alex and his friends go out for pizza and video games once a week. They share the cost of a $\$15.60$ pizza equally. How much does each person pay if the total number sharing the pizza is

$2?$
$3?$
$4?$
$5?$
$6?$

Fast Food

At their favorite fast food restaurant, the Carlson family orders $4$ burgers that cost ${$3.29}$ each and $2$ orders of fries at ${$2.74}$ each. What is the total cost of the order?

Show Solution

Home Goods

Chelsea needs towels to take with her to college. She buys $2$ bath towels that cost ${$9.99}$ each and $6$ washcloths that cost ${$2.99}$ each. What is the total cost for the bath towels and washcloths?

Zoo

The Lewis and Chousmith families are planning to go to the zoo together. Adult tickets cost ${$29.95}$ and children’s tickets cost ${$19.95}$ . What will the total cost be for $4$ adults and $7$ children?

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Ice Skating

Jasmine wants to have her birthday party at the local ice skating rink. It will cost ${$8.25}$ per child and ${$12.95}$ per adult. What will the total cost be for $12$ children and $3$ adults?

Everyday Math

Paycheck

Annie has two jobs. She gets paid ${$14.04}$ per hour for tutoring at City College and ${$8.75}$ per hour at a coffee shop. Last week she tutored for $8$ hours and worked at the coffee shop for $15$ hours.

How much did she earn?
Show Solution

$243.57
If she had worked all $23$ hours as a tutor instead of working both jobs, how much more would she have earned?
Show Solution

$79.35

Paycheck Jake has two jobs. He gets paid $\$7.95$ per hour at the college cafeteria and $\$20.25$ at the art gallery. Last week he worked $12$ hours at the cafeteria and $5$ hours at the art gallery.

How much did he earn?
If he had worked all $17$ hours at the art gallery instead of working both jobs, how much more would he have earned?

Writing Exercises

In the 2010 winter Olympics, two skiers took the silver and bronze medals in the Men’s Super-G ski event. The silver medalist’s time was $1$ minute $30.62$ seconds and bronze medalist’s time was $1$ minute $30.65$ seconds. Whose time was faster? Find the difference in their times and then write the name of that decimal.

Show Solution

Find the quotient of $0.12\div 0.04$ and explain in words all the steps taken.

Exploring The Relationship Between Decimals and Fractions

Convert Fractions to Decimals

In the following exercises, convert each fraction to a decimal.

$\Large\frac{2}{5}$
Show Solution

0.4
$\Large\frac{4}{5}$
$-\Large\frac{3}{8}$
Show Solution

−0.375
$-\Large\frac{5}{8}$
$\Large\frac{17}{20}$
Show Solution

0.85
$\Large\frac{13}{20}$
$\Large\frac{11}{4}$
Show Solution

2.75
$\Large\frac{17}{4}$
$-\Large\frac{310}{25}$
Show Solution

−12.4
$-\Large\frac{284}{25}$
$\Large\frac{5}{9}$
Show Solution

$0.\stackrel{-}{5}$
$\Large\frac{2}{9}$
$\Large\frac{15}{11}$
Show Solution

$1.\stackrel{\text{-}}{36}$
$\Large\frac{18}{11}$
$\Large\frac{15}{111}$
Show Solution

$0.\stackrel{\text{-}}{135}$
$\Large\frac{25}{111}$

Convert Fractions to Decimals and Simplify

In the following exercises, simplify the expression.

$\Large\frac{1}{2}\normalsize+6.5$
Show Solution

7
$\Large\frac{1}{4}\normalsize+10.75$
$2.4+\Large\frac{5}{8}$
Show Solution

3.025
$3.9+\Large\frac{9}{20}$
$9.73+\Large\frac{17}{20}$
Show Solution

10.58
$6.29+\Large\frac{21}{40}$

Order Decimals and Fractions

In the following exercises, order each pair of numbers, using $<$ ; or $\text{>.}$

$\Large\frac{1}{8}\normalsize\text{___}0.8$
Show Solution

<
$\Large\frac{1}{4}\normalsize\text{___}0.4$
$\Large\frac{2}{5}\normalsize\text{___}0.25$
Show Solution

>
$\Large\frac{3}{5}\normalsize\text{___}0.35$
$\text {0.725___}\Large\frac{3}{4}$
Show Solution

<
$\text {0.92___}\Large\frac{7}{8}$
$\text {0.66___}\Large\frac{2}{3}$
Show Solution

<
$\text {0.83___}\Large\frac{5}{6}$
$\text {-0.75___}-\Large\frac{4}{5}$
Show Solution

>
$\text {-0.44___}-\Large\frac{9}{20}$
$-\Large\frac{3}{4}\normalsize\text{___} - 0.925$
Show Solution

>
$-\Large\frac{2}{3}\normalsize\text{___} - 0.632$

Order Decimals and Fractions

In the following exercises, write each set of numbers in order from least to greatest.

$\Large\frac{3}{5}\normalsize ,\Large\frac{9}{16}\normalsize,0.55$
Show Solution

$0.55,\Large\frac{9}{16}\normalsize ,\Large\frac{3}{5}$
$\Large\frac{3}{8}\normalsize ,\Large\frac{7}{20}\normalsize ,0.36$
$0.702,\Large\frac{13}{20}\normalsize ,\Large\frac{5}{8}$
Show Solution

$\Large\frac{5}{8}\normalsize ,\Large\frac{13}{20}\normalsize ,0.702$
$0.15,\Large\frac{3}{16}\normalsize ,\Large\frac{1}{5}$
$-0.3,-\Large\frac{1}{3}\normalsize ,-\Large\frac{7}{20}$
Show Solution

$-\Large\frac{7}{20}\normalsize ,-\Large\frac{1}{3}\normalsize,-0.3$
$-0.2,-\Large\frac{3}{20}\normalsize ,-\Large\frac{1}{6}$
$-\Large\frac{3}{4}\normalsize ,-\Large\frac{7}{9}\normalsize,-0.7$
Show Solution

$-\Large\frac{7}{9}\normalsize ,-\Large\frac{3}{4}\normalsize ,-0.7$
$-\Large\frac{8}{9}\normalsize ,-\Large\frac{4}{5}\normalsize,-0.9$

Simplify Expressions Using the Order of Operations

In the following exercises, simplify.

$10\left(25.1 - 43.8\right)$
Show Solution

−187
$30\left(18.1 - 32.5\right)$
$62\left(9.75 - 4.99\right)$
Show Solution

295.12
$42\left(8.45 - 5.97\right)$
$\Large\frac{3}{4}\normalsize\left(12.4 - 4.2\right)$
Show Solution

6.15
$\Large\frac{4}{5}\normalsize\left(8.6+3.9\right)$
$\Large\frac{5}{12}\normalsize\left(30.58+17.9\right)$
Show Solution

20.2
$\Large\frac{9}{16}\normalsize\left(21.96 - 9.8\right)$
$10\div 0.1+\left(1.8\right)4-{\left(0.3\right)}^{2}$
Show Solution

107.11
$5\div 0.5+\left(3.9\right)6-{\left(0.7\right)}^{2}$
$\left(37.1+52.7\right)\div \left(12.5\div 62.5\right)$
Show Solution

449
$\left(11.4+16.2\right)\div \left(18\div 60\right)$
${\Large\left(\frac{1}{5}\right)}^{2}\normalsize+\left(1.4\right)\left(6.5\right)$
Show Solution

9.14
${\Large\left(\frac{1}{2}\right)}^{2}\normalsize+\left(2.1\right)\left(8.3\right)$
$-\Large\frac{9}{10}\normalsize\cdot\Large\frac{8}{15}\normalsize+0.25$
Show Solution

−0.23
$-\Large\frac{3}{8}\normalsize\cdot\Large\frac{14}{15}\normalsize+0.72$

Mixed Practice

In the following exercises, simplify. Give the answer as a decimal.

$3\Large\frac{1}{4}\normalsize -6.5$
Show Solution

−3.25
$5\Large\frac{2}{5}\normalsize -8.75$
$10.86\div\Large\frac{2}{3}$
Show Solution

16.29
$5.79\div\Large\frac{3}{4}$
$\Large\frac{7}{8}\normalsize\left(103.48\right)+1\Large\frac{1}{2}\normalsize\left(361\right)$
Show Solution

632.045
$\Large\frac{5}{16}\normalsize\left(117.6\right)+2\Large\frac{1}{3}\normalsize\left(699\right)$
$3.6\left(\Large\frac{9}{8}\normalsize-2.72\right)$
Show Solution

−5.742
$5.1\left(\Large\frac{12}{5}\normalsize-3.91\right)$

Find the Circumference and Area of Circles

In the following exercises, approximate the a) circumference and b) area of each circle. If measurements are given in fractions, leave answers in fraction form.

$\text{radius}=\text{5 in.}$
Show Solution

ⓐ 31.4 in ⓑ 78.5 sq.in.
$\text{radius}=\text{20 in.}$
$\text{radius}=\text{9 ft.}$
Show Solution

ⓐ 56.52.ft. ⓑ 254.34 sq.ft.
$\text{radius}=\text{4 ft.}$
$\text{radius}=\text{46 cm}$
Show Solution

ⓐ 288.88 cm ⓑ 6644.24 sq.cm
$\text{radius}=\text{38 cm}$
$\text{radius}=\text{18.6 m}$
Show Solution

ⓐ 116.808 m ⓑ 1086.3144 sq.m
$\text{radius}=\text{57.3 m}$
$\text{radius}=\Large\frac{7}{10}\normalsize\text{mile}$
Show Solution

ⓐ $\Large\frac{22}{5}\normalsize\text{mile}$ ⓑ $\Large\frac{77}{50}\normalsize\text{sq.mile}$
$\text{radius}=\Large\frac{7}{11}\normalsize\text{mile}$
$\text{radius}=\Large\frac{3}{8}\normalsize\text{yard}$
Show Solution

ⓐ $\Large\frac{33}{14}\normalsize\text{yard}$ ⓑ $\Large\frac{99}{224}\normalsize\text{sq.yard}$
$\text{radius}=\Large\frac{5}{12}\normalsize\text{yard}$
$\text{diameter}=\Large\frac{5}{6}\normalsize\text{m}$
Show Solution

ⓐ $\Large\frac{55}{21}\normalsize\text{m}$ ⓑ $\Large\frac{275}{504}\normalsize\text{sq.m}$
$\text{diameter}=\Large\frac{3}{4}\normalsize\text{m}$

Everyday Math

Shopping Trip

Kelly wants to buy a pair of boots that are on sale for $\Large\frac{2}{3}$ of the original price. The original price of the boots is ${$84.99}$ . What is the sale price of the shoes?

Show Solution

Creating a Mosaic

An architect is planning to put a circular mosaic in the entry of a new building. The mosaic will be in the shape of a circle with radius of $6$ feet. How many square feet of tile will be needed for the mosaic? (Round your answer up to the next whole number.)

Writing Exercises

Is it easier for you to convert a decimal to a fraction or a fraction to a decimal? Explain.

Describe a situation in your life in which you might need to find the area or circumference of a circle.

Solving Equations with Decimals

Calculate the Mean of a Set of Numbers

In the following exercises, find the mean.

$3$ , $8$ , $2$ , $2$ , $5$
Show Solution

4
$6$ , $1$ , $9$ , $3$ , $4$ , $7$
$65$ , $13$ , $48$ , $32$ , $19$ , $33$
Show Solution

35
$34$ , $45$ , $29$ , $61$ , and $41$
$202$ , $241$ , $265$ , $274$
Show Solution

245.5
$525$ , $532$ , $558$ , $574$
$12.45$ , $12.99$ , $10.50$ , $11.25$ , $9.99$ , $12.72$
Show Solution

11.65
$28.8$ , $32.9$ , $32.5$ , $27.9$ , $30.4$ , $32.5$ , $31.6$ , $32.7$

Calculate the Mean of a Set of Numbers in Applications

In the following exercises, find the mean.

Four girls leaving a mall were asked how much money they had just spent. The amounts were ${$0}$ , ${$14.95}$ , ${$35.25}$ , and ${$25.16}$ . Find the mean amount of money spent.
Show Solution

$18.84
Juan bought $5$ shirts to wear to his new job. The costs of the shirts were ${$32.95}$ , ${$38.50}$ , ${$30.00}$ , ${$17.45}$ , and ${$24.25}$ . Find the mean cost.
The number of minutes it took Jim to ride his bike to school for each of the past six days was $21$ , $18$ , $16$ , $19$ , $24$ , and $19$ . Find the mean number of minutes.
Show Solution

19.5 minutes
Norris bought six books for his classes this semester. The costs of the books were ${$74.28}$ , ${$120.95}$ , ${$52.40}$ , ${$10.59}$ , ${$35.89}$ , and ${$59.24}$ . Find the mean cost.
The top eight hitters in a softball league have batting averages of $.373$ , $.360$ , $.321$ , $.321$ , $.320$ , $.312$ , $.311$ , and $.311$ . Find the mean of the batting averages. Round your answer to the nearest thousandth.
Show Solution

0.329
The monthly snowfall at a ski resort over a six-month period was $60.3$ , $79.7$ , $50.9$ , $28.0$ , $47.4$ , and $46.1$ inches. Find the mean snowfall.

Find the Median of a Set of Numbers

In the following exercises, find the median.

$24$ , $19$ , $18$ , $29$ , $21$
Show Solution

21
$48$ , $51$ , $46$ , $42$ , $50$
$65$ , $56$ , $35$ , $34$ , $44$ , $39$ , $55$ , $52$ , $45$
Show Solution

45
$121$ , $115$ , $135$ , $109$ , $136$ , $147$ , $127$ , $119$ , $110$
$4$ , $8$ , $1$ , $5$ , $14$ , $3$ , $1$ , $12$
Show Solution

4.5
$3$ , $9$ , $2$ , $6$ , $20$ , $3$ , $3$ , $10$
$99.2$ , $101.9$ , $98.6$ , $99.5$ , $100.8$ , $99.8$
Show Solution

99.65
$28.8$ , $32.9$ , $32.5$ , $27.9$ , $30.4$ , $32.5$ , $31.6$ , $32.7$

Find the Median of a Set of Numbers in Applications

In the following exercises, find the median.

Last week Ray recorded how much he spent for lunch each workday. He spent ${$6.50}$ , ${$7.25}$ , ${$4.90}$ , ${$5.30}$ , and ${$12.00}$ . Find the median.
Show Solution

$6.50
Michaela is in charge of 6 two-year olds at a daycare center. Their ages, in months, are $25$ , $24$ , $28$ , $32$ , $29$ , and $31$ . Find the median age.
Brian is teaching a swim class for $6$ three-year olds. Their ages, in months, are $38,41,45,36,40,\text{and}42$ . Find the median age.
Show Solution

40.5 months
Sal recorded the amount he spent for gas each week for the past $8$ weeks. The amounts were ${$38.65}$ , ${$32.18}$ , ${$40.23}$ , ${$51.50}$ , ${$43.68}$ , ${$30.96}$ , ${$41.37}$ , and ${$44.72}$ . Find the median amount.

Identify the Mode of a Set of Numbers

In the following exercises, identify the mode.

$2$ , $5$ , $1$ , $5$ , $2$ , $1$ , $2$ , $3$ , $2$ , $3$ , $1$
Show Solution

2
$8$ , $5$ , $1$ , $3$ , $7$ , $1$ , $1$ , $7$ , $1$ , $8$ , $7$
$18$ , $22$ , $17$ , $20$ , $19$ , $20$ , $22$ , $19$ , $29$ , $18$ , $23$ , $25$ , $22$ , $24$ , $23$ , $22$ , $18$ , $20$ , $22$ , $20$
Show Solution

22
$42$ , $28$ , $32$ , $35$ , $24$ , $32$ , $48$ , $32$ , $32$ , $24$ , $35$ , $28$ , $30$ , $35$ , $45$ , $32$ , $28$ , $32$ , $42$ , $42$ , $30$
The number of children per house on one block: $1$ , $4$ , $2$ , $3$ , $3$ , $2$ , $6$ , $2$ , $4$ , $2$ , $0$ , $3$ , $0$ .
Show Solution

2 children
The number of movies watched each month last year: $2$ , $0$ , $3$ , $0$ , $0$ , $8$ , $6$ , $5$ , $0$ , $1$ , $2$ , $3$ .
The number of units being taken by students in one class: $12$ , $5$ , $11$ , $10$ , $10$ , $11$ , $5$ , $11$ , $11$ , $11$ , $10$ , $12$ .
Show Solution

11 units
The number of hours of sleep per night for the past two weeks: $8$ , $5$ , $7$ , $8$ , $8$ ,
$6$ , $6$ , $6$ , $6$ , $9$ , $7$ , $8$ , $8$ , $8$ .

Use the Basic Definition of Probability

In the following exercises, express the probability as both a fraction and a decimal. (Round to three decimal places, if necessary.)

Josue is in a book club with $20$ members. One member is chosen at random each month to select the next month’s book. Find the probability that Josue will be chosen next month.
Show Solution

$\Large\frac{1}{20}\normalsize,0.05$
Jessica is one of eight kindergarten teachers at Mandela Elementary School. One of the kindergarten teachers will be selected at random to attend a summer workshop. Find the probability that Jessica will be selected.
There are $24$ people who work in Dane’s department. Next week, one person will be selected at random to bring in doughnuts. Find the probability that Dane will be selected. Round your answer to the nearest thousandth.
Show Solution

$\Large\frac{1}{24}\normalsize,0.041\stackrel{-}{6}\approx 0.042$
Monica has two strawberry yogurts and six banana yogurts in her refrigerator. She will choose one yogurt at random to take to work. Find the probability Monica will choose a strawberry yogurt.
Michel has four rock CDs and six country CDs in his car. He will pick one CD to play on his way to work. Find the probability Michel will pick a rock CD.
Show Solution

$\Large\frac{4}{10}\normalsize,0.4$
Noah is planning his summer camping trip. He can’t decide among six campgrounds at the beach and twelve campgrounds in the mountains, so he will choose one campground at random. Find the probability that Noah will choose a campground at the beach.
Donovan is considering transferring to a $\text{4-year college}$ . He is considering $10$ out-of state colleges and $4$ colleges in his state. He will choose one college at random to visit during spring break. Find the probability that Donovan will choose an out-of-state college.
Show Solution

$\Large\frac{10}{14}\normalsize,0.\stackrel{\text{---}}{714285}\approx 0.714$
There are $258,890,850$ number combinations possible in the Mega Millions lottery. One winning jackpot ticket will be chosen at random. Brent chooses his favorite number combination and buys one ticket. Find the probability Brent will win the jackpot. Round the decimal to the first digit that is not zero, then write the name of the decimal.

Everyday Math

Joaquin gets paid every Friday. His paychecks for the past $8$ Fridays were ${$315}$ , ${$236.25}$ , ${$236.25}$ , ${$236.25}$ , ${$315}$ , ${$315}$ , ${$236.25}$ , ${$393.75}$ . Find the ⓐ mean, ⓑ median, and ⓒ mode.
Show Solution

ⓐ $285.47 ⓑ $275.63 ⓒ $236.25
The cash register receipts each day last week at a coffee shop were ${$1,845}$ , ${$1,520}$ , ${$1,438}$ , ${$1,682}$ , ${$1,850}$ , ${$2,721}$ , ${$2,539}$ . Find the ⓐ mean, ⓑ median, and ⓒ mode.

Writing Exercises

Explain in your own words the difference between the mean, median, and mode of a set of numbers.

Make an example of probability that relates to your life. Write your answer as a fraction and explain what the numerator and denominator represent.

Write a Ratio as a Fraction

In the following exercises, write each ratio as a fraction.

$20$ to $36$
Show Solution

$\Large\frac{5}{9}$
$20$ to $32$
$42$ to $48$
Show Solution

$\Large\frac{7}{8}$
$45$ to $54$
$49$ to $21$
Show Solution

$\Large\frac{7}{3}$
$56$ to $16$
$84$ to $36$
Show Solution

$\Large\frac{7}{3}$
$6.4$ to $0.8$
$0.56$ to $2.8$
Show Solution

$\Large\frac{1}{5}$
$1.26$ to $4.2$
$1\Large\frac{2}{3}$ to $2\Large\frac{5}{6}$
Show Solution

$\Large\frac{10}{17}$
$1\Large\frac{3}{4}$ to $2\Large\frac{5}{8}$
$4\Large\frac{1}{6}$ to $3\Large\frac{1}{3}$
Show Solution

$\Large\frac{5}{4}$
$5\Large\frac{3}{5}$ to $3\Large\frac{3}{5}$
${$18}$ to ${$63}$
Show Solution

$\Large\frac{2}{7}$
${$16}$ to ${$72}$
${$1.21}$ to ${$0.44}$
Show Solution

$\Large\frac{11}{4}$
${$1.38}$ to ${$0.69}$
$28$ ounces to $84$ ounces
Show Solution

$\Large\frac{1}{3}$
$32$ ounces to $128$ ounces
$12$ feet to $46$ feet
Show Solution

$\Large\frac{6}{23}$
$15$ feet to $57$ feet
$246$ milligrams to $45$ milligrams
Show Solution

$\Large\frac{82}{15}$
$304$ milligrams to $48$ milligrams
total cholesterol of $175$ to HDL cholesterol of $45$
Show Solution

$\Large\frac{35}{9}$
total cholesterol of $215$ to HDL cholesterol of $55$
$27$ inches to $1$ foot
Show Solution

$\Large\frac{9}{4}$
$28$ inches to $1$ foot

Write a Rate as a Fraction

In the following exercises, write each rate as a fraction.

$140$ calories per $12$ ounces
Show Solution

$\Large\frac{\text{35 calories}}{\text{3 ounces}}$
$180$ calories per $16$ ounces
$8.2$ pounds per $3$ square inches
Show Solution

$\Large\frac{\text{41 lbs}}{\text{15 sq. in}.}$
$9.5$ pounds per $4$ square inches
$488$ miles in $7$ hours
Show Solution

$\Large\frac{\text{488 miles}}{\text{7 hours}}$
$527$ miles in $9$ hours
${$595}$ for $40$ hours
Show Solution

$\Large\frac{{$119}}{{8 hours}}$
${$798}$ for $40$ hours

Find Unit Rates

Exercise 1

In the following exercises, find the unit rate. Round to two decimal places, if necessary.

$140$ calories per $12$ ounces
Show Solution

11.67 calories/ounce
$180$ calories per $16$ ounces
$8.2$ pounds per $3$ square inches
Show Solution

2.73 lbs./sq. in.
$9.5$ pounds per $4$ square inches
$488$ miles in $7$ hours
Show Solution

69.71 mph
$527$ miles in $9$ hours
${$595}$ for $40$ hours
Show Solution

$14.88/hour
${$798}$ for $40$ hours
$576$ miles on $18$ gallons of gas
Show Solution

32 mpg
$435$ miles on $15$ gallons of gas
$43$ pounds in $16$ weeks
Show Solution

2.69 lbs./week
$57$ pounds in $24$ weeks
$46$ beats in $0.5$ minute
Show Solution

92 beats/minute
$54$ beats in $0.5$ minute

Exercise 2

The bindery at a printing plant assembles $96,000$ magazines in $12$ hours. How many magazines are assembled in one hour?
Show Solution

8,000
The pressroom at a printing plant prints $540,000$ sections in $12$ hours. How many sections are printed per hour?

Find Unit Price

Exercise 1

In the following exercises, find the unit price. Round to the nearest cent.

Soap bars at $8$ for ${$8.69}$
Show Solution

$1.09/bar
Soap bars at $4$ for ${$3.39}$
Women’s sports socks at $6$ pairs for ${$7.99}$
Show Solution

$1.33/pair
Men’s dress socks at $3$ pairs for ${$8.49}$
Snack packs of cookies at $12$ for ${$5.79}$
Show Solution

$0.48/pack
Granola bars at $5$ for ${$3.69}$
CD-RW discs at $25$ for ${$14.99}$
Show Solution

$0.60/disc
CDs at $50$ for ${$4.49}$

Exercise 2

The grocery store has a special on macaroni and cheese. The price is ${$3.87}$ for $3$ boxes. How much does each box cost?
Show Solution

$1.29/box
The pet store has a special on cat food. The price is ${$4.32}$ for $12$ cans. How much does each can cost?

Find Unit Price

In the following exercises, find each unit price and then identify the better buy. Round to three decimal places.

Mouthwash, ${50.7-ounce}$ size for ${$6.99}$ or ${33.8-ounce}$ size for ${$4.79}$
Show Solution

The 50.7-ounce size costs $0.138 per ounce. The 33.8-ounce size costs $0.142 per ounce. The 50.7-ounce size is the better buy.
Toothpaste, $6$ ounce size for ${$3.19}$ or $7.8-ounce$ size for ${$5.19}$
Breakfast cereal, $18$ ounces for ${$3.99}$ or $14$ ounces for ${$3.29}$
Show Solution

The 18-ounce size costs $0.222 per ounce. The 14-ounce size costs $0.235 per ounce. The 18-ounce size is a better buy.
Breakfast Cereal, $10.7$ ounces for ${$2.69}$ or $14.8$ ounces for ${$3.69}$
Ketchup, ${40-ounce}$ regular bottle for ${$2.99}$ or ${64-ounce}$ squeeze bottle for ${$4.39}$
Show Solution

The regular bottle costs $0.075 per ounce. The squeeze bottle costs $0.069 per ounce. The squeeze bottle is a better buy.
Mayonnaise ${15-ounce}$ regular bottle for ${$3.49}$ or ${22-ounce}$ squeeze bottle for ${$4.99}$
Cheese ${$6.49}$ for $1$ lb. block or ${$3.39}$ for $\Large\frac{1}{2}$ lb. block
Show Solution

The half-pound block costs $6.78/lb, so the 1-lb. block is a better buy.
Candy ${$10.99}$ for a $1$ lb. bag or ${$2.89}$ for $\Large\frac{1}{4}$ lb. of loose candy

Translate Phrases to Expressions with Fractions

In the following exercises, translate the English phrase into an algebraic expression.

$793$ miles per $p$ hours
Show Solution

$\Large\frac{\text{793 miles}}{p \text{hours}}$
$78$ feet per $r$ seconds
${$3}$ for $0.5$ lbs.
Show Solution

$\Large\frac{{$3}}{{0.5 lbs}.}$
$j$ beats in $0.5$ minutes
$105$ calories in $x$ ounces
Show Solution

$\Large\frac{\text{105 calories}} {x \text {ounces}}$
$400$ minutes for $m$ dollars
the ratio of $y$ and $5x$
Show Solution

$\Large\frac{y}{5x}$
the ratio of $12x$ and $y$

Everyday Math

Everyday math

One elementary school in Ohio has $684$ students and $45$ teachers. Write the student-to-teacher ratio as a unit rate.
Show Solution

15.2 students per teacher
The average American produces about $1,600$ pounds of paper trash per year (365 days). How many pounds of paper trash does the average American produce each day? (Round to the nearest tenth of a pound.)
A popular fast food burger weighs $7.5$ ounces and contains $540$ calories, $29$ grams of fat, $43$ grams of carbohydrates, and $25$ grams of protein. Find the unit rate of ⓐ calories per ounce ⓑ grams of fat per ounce ⓒ grams of carbohydrates per ounce ⓓ grams of protein per ounce. Round to two decimal places.
Show Solution

ⓐ 72 calories/ounce ⓑ 3.87 grams of fat/ounce ⓒ 5.73 grams carbs/once ⓓ 3.33 grams protein/ounce
A $16-ounce$ chocolate mocha coffee with whipped cream contains $470$ calories, $18$ grams of fat, $63$ grams of carbohydrates, and $15$ grams of protein. Find the unit rate of ⓐ calories per ounce ⓑ grams of fat per ounce ⓒ grams of carbohydrates per ounce ⓓ grams of protein per ounce.

Writing Exercises

Would you prefer the ratio of your income to your friend’s income to be $\text{3/1}$ or $1/3?$ Explain your reasoning.
Answers will vary.
The parking lot at the airport charges ${$0.75}$ for every $15$ minutes. ⓐ How much does it cost to park for $1$ hour? ⓑ Explain how you got your answer to part ⓐ. Was your reasoning based on the unit cost or did you use another method?
Kathryn ate a $4-ounce$ cup of frozen yogurt and then went for a swim. The frozen yogurt had $115$ calories. Swimming burns $422$ calories per hour. For how many minutes should Kathryn swim to burn off the calories in the frozen yogurt? Explain your reasoning.
Answers will vary.
Mollie had a $16-ounce$ cappuccino at her neighborhood coffee shop. The cappuccino had $110$ calories. If Mollie walks for one hour, she burns $246$ calories. For how many minutes must Mollie walk to burn off the calories in the cappuccino? Explain your reasoning.

Simplify Expressions with Square Roots

In the following exercises, simplify.

$\sqrt{36}$
Show Solution

6
$\sqrt{4}$
$\sqrt{64}$
Show Solution

8
$\sqrt{144}$
$-\sqrt{4}$
Show Solution

−2
$-\sqrt{100}$
$-\sqrt{1}$
Show Solution

−1
$-\sqrt{121}$
$\sqrt{-121}$
Show Solution

not a real number
$\sqrt{-36}$
$\sqrt{-9}$
Show Solution

not a real number
$\sqrt{-49}$
$\sqrt{9+16}$
Show Solution

5
$\sqrt{25+144}$
$\sqrt{9}+\sqrt{16}$
Show Solution

7
$\sqrt{25}+\sqrt{144}$

Estimate Square Roots

In the following exercises, estimate each square root between two consecutive whole numbers.

$\sqrt{70}$
Show Solution

$8<\sqrt{70}<9$
$\sqrt{55}$
$\sqrt{200}$
Show Solution

$14<\sqrt{200}<15$
$\sqrt{172}$

Approximate Square Roots with a Calculator

In the following exercises, use a calculator to approximate each square root and round to two decimal places.

$\sqrt{19}$
Show Solution

4.36
$\sqrt{21}$
$\sqrt{53}$
Show Solution

7.28
$\sqrt{47}$

Simplify Variable Expressions with Square Roots

In the following exercises, simplify. (Assume all variables are greater than or equal to zero.)

$\sqrt{{y}^{2}}$
Show Solution

y
$\sqrt{{b}^{2}}$
$\sqrt{49{x}^{2}}$
Show Solution

7x
$\sqrt{100{y}^{2}}$
$-\sqrt{64{a}^{2}}$
Show Solution

−8a
$-\sqrt{25{x}^{2}}$
$\sqrt{144{x}^{2}{y}^{2}}$
Show Solution

12xy
$\sqrt{196{a}^{2}{b}^{2}}$

Use Square Roots in Applications

In the following exercises, solve. Round to one decimal place.

Landscaping Reed wants to have a square garden plot in his backyard. He has enough compost to cover an area of $75$ square feet. How long can a side of his garden be?

Show Solution

Landscaping Vince wants to make a square patio in his yard. He has enough concrete to pave an area of $130$ square feet. How long can a side of his patio be?

Gravity An airplane dropped a flare from a height of $1,024$ feet above a lake. How many seconds did it take for the flare to reach the water?

Show Solution

Gravity A hang glider dropped his cell phone from a height of $350$ feet. How many seconds did it take for the cell phone to reach the ground?

Gravity A construction worker dropped a hammer while building the Grand Canyon skywalk, $4,000$ feet above the Colorado River. How many seconds did it take for the hammer to reach the river?

Show Solution

Accident investigation The skid marks from a car involved in an accident measured $54$ feet. What was the speed of the car before the brakes were applied?

Accident investigation The skid marks from a car involved in an accident measured $216$ feet. What was the speed of the car before the brakes were applied?

Show Solution

Accident investigation An accident investigator measured the skid marks of one of the vehicles involved in an accident. The length of the skid marks was $175$ feet. What was the speed of the vehicle before the brakes were applied?

Accident investigation An accident investigator measured the skid marks of one of the vehicles involved in an accident. The length of the skid marks was $117$ feet. What was the speed of the vehicle before the brakes were applied?

Show Solution

Everyday Math

Decorating Denise wants to install a square accent of designer tiles in her new shower. She can afford to buy $625$ square centimeters of the designer tiles. How long can a side of the accent be?

Decorating Morris wants to have a square mosaic inlaid in his new patio. His budget allows for $2,025$ tiles. Each tile is square with an area of one square inch. How long can a side of the mosaic be?

Show Solution

Writing exercises

Why is there no real number equal to $\sqrt{-64}?$
What is the difference between ${9}^{2}$ and $\sqrt{9}?$
Answers will vary. 9² reads: “nine squared” and means nine times itself. The expression $\sqrt{9}$ reads: “the square root of nine” which gives us the number such that if it were multiplied by itself would give you the number inside of the square root.

Chapter Review Exercises

Decimals

Name Decimals

In the following exercises, name each decimal.

$0.8$
$0.375$
Show Solution

three hundred seventy-five thousandths
$0.007$
$5.24$
Show Solution

five and twenty-four hundredths
$-12.5632$
$-4.09$
Show Solution

negative four and nine hundredths

Write Decimals
In the following exercises, write as a decimal.

three tenths
nine hundredths
Show Solution

0.09
twenty-seven hundredths
ten and thirty-five thousandths
Show Solution

10.035
negative twenty and three tenths
negative five hundredths
Show Solution

−0.05

Convert Decimals to Fractions or Mixed Numbers

In the following exercises, convert each decimal to a fraction. Simplify the answer if possible.

$0.43$
$0.825$
Show Solution

$\Large\frac{33}{40}$
$9.7$
$3.64$
Show Solution

$3\Large\frac{16}{25}$

Locate Decimals on the Number Line

$0.6$
$-0.9$
$2.2$
$-1.3$

Order Decimals
In the following exercises, order each of the following pairs of numbers, using $<$ ; or $\text{>.}$

$0.6\text{___}0.8$
Show Solution

<
$0.2\text{___}0.15$
$0.803\text{____}0.83$
Show Solution

<
$-0.56\text{____} - 0.562$

Round Decimals
In the following exercises, round each number to the nearest: ⓐ hundredth ⓑ tenth ⓒ whole number.

$12.529$
Show Solution

ⓐ 12.53 ⓑ 12.5 ⓒ 13
$4.8447$
$5.897$
Show Solution

ⓐ 5.90 ⓑ 5.9 ⓒ 6

Decimal Operations

Add and Subtract Decimals
In the following exercises, add or subtract.

$5.75+8.46$
$32.89 - 8.22$
Show Solution

24.67
$24 - 19.31$
$10.2+14.631$
Show Solution

24.831
$-6.4+\left(-2.9\right)$
$1.83 - 4.2$
Show Solution

−2.37

Multiply Decimals

In the following exercises, multiply.

$\left(0.3\right)\left(0.7\right)$
$\left(-6.4\right)\left(0.25\right)$
Show Solution

−1.6
$\left(-3.35\right)\left(-12.7\right)$
$\left(15.4\right)\left(1000\right)$
Show Solution

15,400

Divide Decimals

In the following exercises, divide.

$0.48\div 6$
$4.32\div 24$
Show Solution

0.18
${$6.29}\div 12$
$\left(-0.8\right)\div \left(-0.2\right)$
Show Solution

4
$1.65\div 0.15$
$9\div 0.045$
Show Solution

200

Use Decimals in Money Applications

In the following exercises, use the strategy for applications to solve.

Miranda got ${$40}$ from her ATM. She spent ${$9.32}$ on lunch and ${$16.99}$ on a book. How much money did she have left? Round to the nearest cent if necessary.
Jessie put $8$ gallons of gas in her car. One gallon of gas costs ${$3.528.}$ How much did Jessie owe for all the gas?
Show Solution

$28.22
A pack of $16$ water bottles cost ${$6.72.}$ How much did each bottle cost?
Alice bought a roll of paper towels that cost ${$2.49.}$ She had a coupon for ${$0.35}$ off, and the store doubled the coupon. How much did Alice pay for the paper towels?
Show Solution

$1.79

Decimals and Fractions

Convert Fractions to Decimals
In the following exercises, convert each fraction to a decimal.

$\Large\frac{3}{5}$
$\Large\frac{7}{8}$
Show Solution

0.875
$-\Large\frac{19}{20}$
$-\Large\frac{21}{4}$
Show Solution

−5.25
$\Large\frac{1}{3}$
$\Large\frac{6}{11}$
Show Solution

$0.\stackrel{\text{-}}{54}$

Order Decimals and Fractions

In the following exercises, order each pair of numbers, using $<$ ; or $\text{>.}$

$\Large\frac{1}{2}\text{___}\normalsize 0.2$
$\Large\frac{3}{5}\text{___}\normalsize 0$ .
Show Solution

>
$-\Large\frac{7}{8}\text{___}\normalsize - 0.84$
$-\Large\frac{5}{12}\text{___}\normalsize - 0.42$
Show Solution

>
$0.625\text{___}\Large\frac{13}{20}$
$0.33\text{___}\Large\frac{5}{16}$
Show Solution

>

In the following exercises, write each set of numbers in order from least to greatest.

$\Large\frac{2}{3}\normalsize ,\Large\frac{17}{20}\normalsize ,0.65$
$\Large\frac{7}{9}\normalsize ,0.75\normalsize ,\Large\frac{11}{15}$
Show Solution

$\Large\frac{11}{15}\normalsize ,0.75,\Large\frac{7}{9}$

Simplify Expressions Using the Order of Operations
In the following exercises, simplify

$4\left(10.3 - 5.8\right)$
$\Large\frac{3}{4}\normalsize\left(15.44 - 7.4\right)$
Show Solution

6.03
$30\div \left(0.45+0.15\right)$
$1.6+\Large\frac{3}{8}$
Show Solution

1.975
$52\left(0.5\right)+{\left(0.4\right)}^{2}$
$-\Large\frac{2}{5}\normalsize\cdot\Large\frac{9}{10}\normalsize +0.14$
Show Solution

−0.22

Find the Circumference and Area of Circles

In the following exercises, approximate the ⓐ circumference and ⓑ area of each circle.

$\text{radius}=\text{6 in.}$
$\text{radius}=\text{3.5 ft.}$
Show Solution

ⓐ 21.98 ft. ⓑ 38.465 sq.ft.
$\text{radius}=\Large\frac{7}{33}\normalsize\text{m}$
$\text{diameter}=\text{11 cm}$
Show Solution

ⓐ 34.54 cm ⓑ 379.94 sq.cm

Solving Equations With Decimals

Determine Whether a Decimal is a Solution of an Equation
In the following exercises, determine whether each number is a solution of the given equation.

$x - 0.8=2.3$

Show Solution

$y+0.6=-3.4$

$\Large\frac{h}{1.5}\normalsize =-4.3$

Show Solution

$0.75k=-3.6$

Solve Equations with Decimals

In the following exercises, solve the equation.

$y+2.9=5.7$
Show Solution

y = 2.8
$m+4.6=6.5$
$f+3.45=2.6$
Show Solution

f = −0.85
$h+4.37=3.5$
$a+6.2=-1.7$
Show Solution

a = −7.9
$b+5.8=-2.3$
$c+1.15=-3.5$
Show Solution

c = −4.65
$d+2.35=-4.8$
$n - 2.6=1.8$
Show Solution

n = 4.4
$p - 3.6=1.7$
$x - 0.4=-3.9$
Show Solution

x = −3.5
$y - 0.6=-4.5$
$j - 1.82=-6.5$
Show Solution

j = −4.68
$k - 3.19=-4.6$
$m - 0.25=-1.67$
Show Solution

m = −1.42
$q - 0.47=-1.53$
$0.5x=3.5$
Show Solution

x = 7
$0.4p=9.2$
$-1.7c=8.5$
Show Solution

c = −5
$-2.9x=5.8$
$-1.4p=-4.2$
Show Solution

p = 3
$-2.8m=-8.4$
$-120=1.5q$
Show Solution

q = −80
$-75=1.5y$
$0.24x=4.8$
Show Solution

x = 20
$0.18n=5.4$
$-3.4z=-9.18$
Show Solution

z = 2.7
$-2.7u=-9.72$
$\Large\frac{a}{0.4}\normalsize =-20$
Show Solution

a = −8
$\Large\frac{b}{0.3}\normalsize =-9$
$\Large\frac{x}{0.7}\normalsize =-0.4$
Show Solution

x = −0.28
$\Large\frac{y}{0.8}\normalsize =-0.7$
$\Large\frac{p}{-5}\normalsize =-1.65$
Show Solution

p = 8.25
$\Large\frac{q}{-4}\normalsize =-5.92$
$\Large\frac{r}{-1.2}\normalsize =-6$
Show Solution

r = 7.2
$\Large\frac{s}{-1.5}\normalsize =-3$

Mixed Practice

In the following exercises, solve the equation. Then check your solution.

$x - 5=-11$
Show Solution

x = −6
$-\Large\frac{2}{5}\normalsize =x+\Large\frac{3}{4}$
$p+8=-2$
Show Solution

p = −10
$p+\Large\frac{2}{3}\normalsize =\Large\frac{1}{12}$
$-4.2m=-33.6$
Show Solution

m = 8
$q+9.5=-14$
$q+\Large\frac{5}{6}\normalsize =\Large\frac{1}{12}$
Show Solution

$q=-\Large\frac{3}{4}$

$\Large\frac{8.6}{15}\normalsize =-d$

$\Large\frac{7}{8}\normalsize m=\Large\frac{1}{10}$

$m=\Large\frac{4}{35}$

$\Large\frac{j}{-6.2}\normalsize =-3$

$-\Large\frac{2}{3}\normalsize =y+\Large\frac{3}{8}$

$y=-\Large\frac{25}{24}$

$s - 1.75=-3.2$

$\Large\frac{11}{20}\normalsize =-f$

$f=-\Large\frac{11}{20}$

$-3.6b=2.52$

$-4.2a=3.36$

a = −0.8

$-9.1n=-63.7$

$r - 1.25=-2.7$

r = −1.45

$\Large\frac{1}{4}\normalsize n=\Large\frac{7}{10}$

$\Large\frac{h}{-3}\normalsize =-8$

h = 24

$y - 7.82=-16$

Translate to an Equation and Solve

In the following exercises, translate and solve.

The difference of $n$ and $1.9$ is $3.4$ .
Show Solution

$n - 1.9=3.4;5.3$
The difference $n$ and $1.5$ is $0.8$ .
The product of $-6.2$ and $x$ is $-4.96$ .
Show Solution

−6.2x = −4.96; 0.8
The product of $-4.6$ and $x$ is $-3.22$ .
The quotient of $y$ and $-1.7$ is $-5$ .
Show Solution

$\Large\frac{y}{-1.7}\normalsize =-5;8.5$
The quotient of $z$ and $-3.6$ is $3$ .
The sum of $n$ and $-7.3$ is $2.4$ .
Show Solution

n + (−7.3) = 2.4; 9.7
The sum of $n$ and $-5.1$ is $3.8$ .class=”p3″>

Everyday math

Shawn bought a pair of shoes on sale for $$78$ . Solve the equation $0.75p=78$ to find the original price of the shoes, $p$ .
Show Solution

$104
Mary bought a new refrigerator. The total price including sales tax was ${$1,350}$ . Find the retail price, $r$ , of the refrigerator before tax by solving the equation $1.08r=1,350$ .

Writing Exercises

Think about solving the equation $1.2y=60$ , but do not actually solve it. Do you think the solution should be greater than $60$ or less than $60?$ Explain your reasoning. Then solve the equation to see if your thinking was correct.
Answers will vary.
Think about solving the equation $0.8x=200$ , but do not actually solve it. Do you think the solution should be greater than $200$ or less than $200?$ Explain your reasoning. Then solve the equation to see if your thinking was correct.

Find the Mean of a Set of Numbers

In the following exercises, find the mean of the numbers.

$2,4,1,0,1,\text{and}1$
${$270}$ , ${$310.50}$ , ${$243.75}$ , and ${$252.15}$
Show Solution

$269.10
Each workday last week, Yoshie kept track of the number of minutes she had to wait for the bus. She waited $3,0,8,1, and 8$ minutes. Find the mean
In the last three months, Raul’s water bills were ${$31.45}, {$48.76},\text{and} {$42.60}$ . Find the mean.
Show Solution

$40.94

Find the Median of a Set of Numbers

In the following exercises, find the median.

$41$ , $45$ , $32$ , $60$ , $58$
$25$ , $23$ , $24$ , $26$ , $29$ , $19$ , $18$ , $32$
Show Solution

24.5
The ages of the eight men in Jerry’s model train club are $52,63,45,51,55,75,60,\text{and}59$ . Find the median age.
The number of clients at Miranda’s beauty salon each weekday last week were $18,7,12,16,\text{and}20$ . Find the median number of clients.
Show Solution

16 clients

Find the Mode of a Set of Numbers

In the following exercises, identify the mode of the numbers.

$6$ , $4$ , $4,5$ , $6,6$ , $4$ , $4$ , $4$ , $3$ , $5$
The number of siblings of a group of students: $2$ , $0$ , $3$ , $2$ , $4$ , $1$ , $6$ , $5$ , $4$ , $1$ , $2$ , $3$
Show Solution

2

Use the Basic Definition of Probability

In the following exercises, solve. (Round decimals to three places.)

The Sustainability Club sells $200$ tickets to a raffle, and Albert buys one ticket. One ticket will be selected at random to win the grand prize. Find the probability Albert will win the grand prize. Express your answer as a fraction and as a decimal.
Luc has to read $3$ novels and $12$ short stories for his literature class. The professor will choose one reading at random for the final exam. Find the probability that the professor will choose a novel for the final exam. Express your answer as a fraction and as a decimal.

Ratios and Rate

Write a Ratio as a Fraction

In the following exercises, write each ratio as a fraction. Simplify the answer if possible.

$28$ to $40$ $56$ to $32$
Show Solution

$\Large\frac{7}{4}$
$3.5$ to $0.5$
$1.2$ to $1.8$
Show Solution

$\Large\frac{2}{3}$
$1\Large\frac{3}{4}\normalsize\text{to}1\Large\frac{5}{8}$
$2\Large\frac{1}{3}\normalsize\text{to}5\Large\frac{1}{4}$
Show Solution

$\Large\frac{4}{9}$
$64$ ounces to $30$ ounces
$28$ inches to $3$ feet
Show Solution

$\Large\frac{7}{9}$

Write a Rate as a Fraction

In the following exercises, write each rate as a fraction. Simplify the answer if possible.

$180$ calories per $8$ ounces
$90$ pounds per $7.5$ square inches
Show Solution

$\Large\frac{90\text{pounds}}{7.5\text{square inches}}$
$126$ miles in $4$ hours
${$612.50}$ for $35$ hours
Show Solution

$\Large\frac{$612.50}{35\text{hours}}$

Find Unit Rates

In the following exercises, find the unit rate.

$180$ calories per $8$ ounces
$90$ pounds per $7.5$ square inches
Show Solution

12 pounds/sq.in.
$126$ miles in $4$ hours
${$612.50}$ for $35$ hours
Show Solution

$17.50/hour

Find Unit Price

In the following exercises, find the unit price.

t-shirts: $3$ for ${$8.97}$
Highlighters: $6$ for ${$2.52}$
Show Solution

$0.42
An office supply store sells a box of pens for ${$11}$ . The box contains $12$ pens. How much does each pen cost?
Anna bought a pack of $8$ kitchen towels for ${$13.20}$ . How much did each towel cost? Round to the nearest cent if necessary.
Show Solution

$1.65

In the following exercises, find each unit price and then determine the better buy.

Shampoo: $12$ ounces for ${$4.29}$ or $22$ ounces for ${$7.29}?$
Vitamins: $60$ tablets for ${$6.49}$ or $100$ for ${$11.99}?$
Show Solution

$0.11, $0.12; 60 tablets for $6.49

Translate Phrases to Expressions with Fractions

In the following exercises, translate the English phrase into an algebraic expression.

$535$ miles per $h\text{hours}$
$a$ adults to $45$ children
Show Solution

$\Large\frac{a\text{adults}}{45\text{children}}$
the ratio of $4y$ and the difference of $x$ and $10$
the ratio of $19$ and the sum of $3$ and $n$
Show Solution

$\Large\frac{19}{3+n}$

Simplify and Use Square Roots

Simplify Expressions with Square Roots
In the following exercises, simplify.

$\sqrt{64}$
$\sqrt{144}$
Show Solution

12
$-\sqrt{25}$
$-\sqrt{81}$
Show Solution

−9
$\sqrt{-9}$
$\sqrt{-36}$
Show Solution

not a real number
$\sqrt{64}+\sqrt{225}$
$\sqrt{64+225}$
Show Solution

17

Estimate Square Roots

In the following exercises, estimate each square root between two consecutive whole numbers.

$\sqrt{28}$
$\sqrt{155}$
Show Solution

$12<\sqrt{155}<13$

Approximate Square Roots
In the following exercises, approximate each square root and round to two decimal places.

$\sqrt{15}$
$\sqrt{57}$
Show Solution

7.55

Simplify Variable Expressions with Square Roots

In the following exercises, simplify. (Assume all variables are greater than or equal to zero.)

$\sqrt{{q}^{2}}$
$\sqrt{64{b}^{2}}$
Show Solution

8b
$-\sqrt{121{a}^{2}}$
$\sqrt{225{m}^{2}{n}^{2}}$
Show Solution

15mn
$-\sqrt{100{q}^{2}}$
$\sqrt{49{y}^{2}}$
Show Solution

7y
$\sqrt{4{a}^{2}{b}^{2}}$
$\sqrt{121{c}^{2}{d}^{2}}$
Show Solution

11cd

Use Square Roots in Applications

In the following exercises, solve. Round to one decimal place.

Art Diego has $225$ square inch tiles. He wants to use them to make a square mosaic. How long can each side of the mosaic be?

Landscaping Janet wants to plant a square flower garden in her yard. She has enough topsoil to cover an area of $30$ square feet. How long can a side of the flower garden be?

Show Solution

Gravity A hiker dropped a granola bar from a lookout spot $576$ feet above a valley. How long did it take the granola bar to reach the valley floor?

Accident investigation The skid marks of a car involved in an accident were $216$ feet. How fast had the car been going before applying the brakes?

Show Solution

Chapter Practice Test

Write six and thirty-four thousandths as a decimal.
Write $1.73$ as a fraction.
Show Solution

$1\Large\frac{73}{100}$
Write $\Large\frac{5}{8}$ as a decimal.
Write the numbers $\Large\frac{4}{5}\normalsize ,-0.1,0.804,\Large\frac{2}{9}\normalsize ,-7.4,0.21$ in order from smallest to largest.

In the following exercises, simplify each expression.

$15.4+3.02$
Show Solution

18.42
$20 - 5.71$
$\left(0.64\right)\left(0.3\right)$
Show Solution

0.192
$\left(-4.2\right)\left(100\right)$
$0.96\div \left(-12\right)$
Show Solution

−0.08
$-5\div 0.025$
$-0.6\div \left(-0.3\right)$
Show Solution

2
${\left(0.7\right)}^{2}$
$24\div \left(0.1+0.02\right)$
Show Solution

200
$4\left(10.3 - 5.8\right)$
$1.6+\Large\frac{3}{8}$
Show Solution

1.975
$\Large\frac{2}{3}\normalsize\left(14.65 - 4.6\right)$

In the following exercises, solve.

$m+3.7=2.5$
Show Solution

−1.2
$\Large\frac{h}{0.5}\normalsize =4.38$
$-6.5y=-57.2$
Show Solution

8.8
$1.94=a - 2.6$
Three friends went out to dinner and agreed to split the bill evenly. The bill was ${$79.35}$ . How much should each person pay?
Show Solution

$26.45
A circle has radius $12$ . Find the ⓐ circumference and ⓑ area. $\text{[}\text{Use}3.14\text{for}\pi \text{.]}$
The ages, in months, of $10$ children in a preschool class are: $55$ , $55$ , $50$ , $51$ , $52$ , $50$ , $53$ , $51$ , $55$ , $49$ Find the ⓐ mean ⓑ median ⓒ mode
Show Solution

ⓐ 59 ⓑ 51.5 ⓒ 55
Of the $16$ nurses in Doreen’s department, $12$ are women and $4$ are men. One of the nurses will be assigned at random to work an extra shift next week. ⓐ Find the probability a woman nurse will be assigned the extra shift. ⓑ Convert the fraction to a decimal.

Find each unit price and then the better buy.

Laundry detergent: $64$ ounces for ${$10.99}$ or $48$ ounces for ${$8.49}$

Show Solution

In the following exercises, simplify.

$\sqrt{36+64}$
$\sqrt{144{n}^{2}}$
Show Solution

12n
Estimate $\sqrt{54}$ to between two whole numbers.
Yanet wants a square patio in her backyard. She has $225$ square feet of tile. How long can a side of the patio be?
Show Solution

15 feet

Module 5: Decimals