Writing and Identifying Characteristics of Decimals

Name Decimals

In the following exercises, name each decimal.

1. [latex]5.5[/latex]
   Show Solution

   five and five tenths
2. [latex]7.8[/latex]
3. [latex]5.01[/latex]
   Show Solution

   five and one hundredth
4. [latex]14.02[/latex]
5. [latex]8.71[/latex]
   Show Solution

   eight and seventy-one hundredths
6. [latex]2.64[/latex]
7. [latex]0.002[/latex]
   Show Solution

   two thousandths
8. [latex]0.005[/latex]
9. [latex]0.381[/latex]
   Show Solution

   three hundred eighty-one thousandths
10. [latex]0.479[/latex]
11. [latex]-17.9[/latex]
    Show Solution

    negative seventeen and nine tenths
12. [latex]-31.4[/latex]

Write Decimals

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

1. Eight and three hundredths
   Show Solution

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

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

   0.7
6. Six tenths
7. One thousandth
   Show Solution

   0.001
8. Nine thousandths
9. Twenty-nine thousandths
   Show Solution

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

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

    13.0395
14. 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. [latex]1.99[/latex]
   Show Solution

   [latex]1\Large\frac{99}{100}[/latex]
2. [latex]5.83[/latex]
3. [latex]15.7[/latex]
   Show Solution

   [latex]15\Large\frac{7}{10}[/latex]
4. [latex]18.1[/latex]
5. [latex]0.239[/latex]
   Show Solution

   [latex]\Large\frac{239}{1000}[/latex]
6. [latex]0.373[/latex]
7. [latex]0.13[/latex]
   Show Solution

   [latex]\Large\frac{13}{100}[/latex]
8. [latex]0.19[/latex]
9. [latex]0.011[/latex]
   Show Solution

   [latex]\Large\frac{11}{1000}[/latex]
10. [latex]0.049[/latex]
11. [latex]-0.00007[/latex]
    Show Solution

    [latex]-\Large\frac{7}{100000}[/latex]
12. [latex]-0.00003[/latex]
13. [latex]6.4[/latex]
    Show Solution

    [latex]6\Large\frac{2}{5}[/latex]
14. [latex]5.2[/latex]
15. [latex]7.05[/latex]
    Show Solution

    [latex]7\Large\frac{1}{20}[/latex]
16. [latex]9.04[/latex]
17. [latex]4.006[/latex]
    Show Solution

    [latex]4\Large\frac{3}{500}[/latex]
18. [latex]2.008[/latex]
19. [latex]10.25[/latex]
    Show Solution

    [latex]10\Large\frac{1}{4}[/latex]
20. [latex]12.75[/latex]
21. [latex]1.324[/latex]
    Show Solution

    [latex]1\Large\frac{81}{250}[/latex]
22. [latex]2.482[/latex]
23. [latex]14.125[/latex]
    Show Solution

    [latex]14\Large\frac{1}{8}[/latex]
24. [latex]20.375[/latex]

Locate Decimals on the Number Line

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

1. [latex]0.8[/latex]
   Show Solution

   
2. [latex]0.3[/latex]
3. [latex]-0.2[/latex]
   Show Solution

   
4. [latex]-0.9[/latex]
5. [latex]3.1[/latex]
   Show Solution

   
6. [latex]2.7[/latex]
7. [latex]-2.5[/latex]
   Show Solution

   
8. [latex]-1.6[/latex]

Order Decimals

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

1. [latex]0.9\text{__}0.6[/latex]
   Show Solution

   >
2. [latex]0.7\text{__}0.8[/latex]
3. [latex]0.37\text{__}0.63[/latex]
   Show Solution

   <
4. [latex]0.86\text{__}0.69[/latex]
5. [latex]0.6\text{__}0.59[/latex]
   Show Solution

   >
6. [latex]0.27\text{__}0.3[/latex]
7. [latex]0.91\text{__}0.901[/latex]
   Show Solution

   >
8. [latex]0.415\text{__}0.41[/latex]
9. [latex]-0.5\text{__} - 0.3[/latex]
   Show Solution

   <
10. [latex]-0.1\text{__} - 0.4[/latex]
11. [latex]-0.62\text{__} - 0.619[/latex]
    Show Solution

    <
12. [latex]-7.31\text{__} - 7.3[/latex]

Round Decimals

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

1. [latex]0.67[/latex]
   Show Solution

   0.7
2. [latex]0.49[/latex]
3. [latex]2.84[/latex]
   Show Solution

   2.8
4. [latex]4.63[/latex]

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

1. [latex]0.845[/latex]
   Show Solution

   0.85
2. [latex]0.761[/latex]
3. [latex]5.7932[/latex]
   Show Solution

   5.79
4. [latex]3.6284[/latex]
5. [latex]0.299[/latex]
   Show Solution

   0.30
6. [latex]0.697[/latex]
7. [latex]4.098[/latex]
   Show Solution

   4.10
8. [latex]7.096[/latex]

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

1. [latex]5.781[/latex]
   Show Solution

   ⓐ 5.78 ⓑ 5.8 ⓒ 6
2. [latex]1.638[/latex]
3. [latex]63.479[/latex]
   Show Solution

   ⓐ 63.48 ⓑ 63.5 ⓒ 63
4. [latex]84.281[/latex]

Operations on Decimals

Add and Subtract Decimals

In the following exercises, add or subtract.

1. [latex]16.92+7.56[/latex]
   Show Solution

   24.48
2. [latex]18.37+9.36[/latex]
3. [latex]256.37 - 85.49[/latex]
   Show Solution

   170.88
4. [latex]248.25 - 91.29[/latex]
5. [latex]21.76 - 30.99[/latex]
   Show Solution

   −9.23
6. [latex]15.35 - 20.88[/latex]
7. [latex]37.5+12.23[/latex]
   Show Solution

   49.73
8. [latex]38.6+13.67[/latex]
9. [latex]-16.53 - 24.38[/latex]
   Show Solution

   −40.91
10. [latex]-19.47 - 32.58[/latex]
11. [latex]-38.69+31.47[/latex]
    Show Solution

    −7.22
12. [latex]-29.83+19.76[/latex]
13. [latex]-4.2+\left(-9.3\right)[/latex]
    Show Solution

    −13.5
14. [latex]-8.6+\left(-8.6\right)[/latex]
15. [latex]100 - 64.2[/latex]
    Show Solution

    35.8
16. [latex]100 - 65.83[/latex]
17. [latex]72.5 - 100[/latex]
    Show Solution

    −27.5
18. [latex]86.2 - 100[/latex]
19. [latex]15+0.73[/latex]
    Show Solution

    15.73
20. [latex]27+0.87[/latex]
21. [latex]2.51+40[/latex]
    Show Solution

    42.51
22. [latex]9.38+60[/latex]
23. [latex]91.75-\left(-10.462\right)[/latex]
    Show Solution

    102.212
24. [latex]94.69-\left(-12.678\right)[/latex]
25. [latex]55.01 - 3.7[/latex]
    Show Solution

    51.31
26. [latex]59.08 - 4.6[/latex]
27. [latex]2.51 - 7.4[/latex]
    Show Solution

    −4.89
28. [latex]3.84 - 6.1[/latex]

Multiply Decimals

In the following exercises, multiply.

1. [latex]\left(0.3\right)\left(0.4\right)[/latex]
   Show Solution

   0.12
2. [latex]\left(0.6\right)\left(0.7\right)[/latex]
3. [latex]\left(0.24\right)\left(0.6\right)[/latex]
   Show Solution

   0.144
4. [latex]\left(0.81\right)\left(0.3\right)[/latex]
5. [latex]\left(5.9\right)\left(7.12\right)[/latex]
   Show Solution

   42.008
6. [latex]\left(2.3\right)\left(9.41\right)[/latex]
7. [latex]\left(8.52\right)\left(3.14\right)[/latex]
   Show Solution

   26.7528
8. [latex]\left(5.32\right)\left(4.86\right)[/latex]
9. [latex]\text{(-4.3)(2.71)}[/latex]
   Show Solution

   −11.653
10. [latex]\left(-8.5\right)\left(1.69\right)[/latex]
11. [latex]\text{(-5.18)(-65.23)}[/latex]
    Show Solution

    337.8914
12. [latex]\left(-9.16\right)\left(-68.34\right)[/latex]
13. [latex]\left(0.09\right)\left(24.78\right)[/latex]
    Show Solution

    2.2302
14. [latex]\left(0.04\right)\left(36.89\right)[/latex]
15. [latex]\left(0.06\right)\left(21.75\right)[/latex]
    Show Solution

    1.305
16. [latex]\left(0.08\right)\left(52.45\right)[/latex]
17. [latex]\left(9.24\right)\left(10\right)[/latex]
    Show Solution

    92.4
18. [latex]\left(6.531\right)\left(10\right)[/latex]
19. [latex]\left(55.2\right)\left(1,000\right)[/latex]
    Show Solution

    55,200
20. [latex]\left(99.4\right)\left(1,000\right)[/latex]

Divide Decimals

In the following exercises, divide.

1. [latex]0.15\div 5[/latex]
   Show Solution

   0.03
2. [latex]0.27\div 3[/latex]
3. [latex]4.75\div 25[/latex]
   Show Solution

   0.19
4. [latex]12.04\div 43[/latex]
5. [latex]{$8.49}\div 12[/latex]
   Show Solution

   $0.71
6. [latex]{$16.99}\div 9[/latex]
7. [latex]{$117.25}\div 48[/latex]
   Show Solution

   $2.44
8. [latex]{$109.24}\div 36[/latex]
9. [latex]0.6\div 0.2[/latex]
   Show Solution

   3
10. [latex]0.8\div 0.4[/latex]
11. [latex]1.44\div \left(-0.3\right)[/latex]
    Show Solution

    −4.8
12. [latex]1.25\div \left(-0.5\right)[/latex]
13. [latex]-1.75\div \left(-0.05\right)[/latex]
    Show Solution

    35
14. [latex]-1.15\div \left(-0.05\right)[/latex]
15. [latex]5.2\div 2.5[/latex]
    Show Solution

    2.08
16. [latex]6.5\div 3.25[/latex]
17. [latex]12\div 0.08[/latex]
    Show Solution

    150
18. [latex]5\div 0.04[/latex]
19. [latex]11\div 0.55[/latex]
    Show Solution

    20
20. [latex]14\div 0.35[/latex]

Mixed Practice

In the following exercises, simplify.

1. [latex]6\left(12.4 - 9.2\right)[/latex]
   Show Solution

   19.2
2. [latex]3\left(15.7 - 8.6\right)[/latex]
3. [latex]24\left(0.5\right)+{\left(0.3\right)}^{2}[/latex]
   Show Solution

   12.09
4. [latex]35\left(0.2\right)+{\left(0.9\right)}^{2}[/latex]
5. [latex]1.15\left(26.83+1.61\right)[/latex]
   Show Solution

   32.706
6. [latex]1.18\left(46.22+3.71\right)[/latex]
7. [latex]{$45}+0.08\left({$45}\right)[/latex]
   Show Solution

   $48.60
8. [latex]{$63}+0.18\left({$63}\right)[/latex]
9. [latex]18\div \left(0.75+0.15\right)[/latex]
   Show Solution

   20
10. [latex]27\div \left(0.55+0.35\right)[/latex]
11. [latex]\left(1.43+0.27\right)\div \left(0.9 - 0.05\right)[/latex]
    Show Solution

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

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

Use Decimals in Money Applications

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

Spending money

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

Spending money

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

Shopping

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

Restaurant

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

Coupon

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

Coupon

Diana bought a can of coffee that cost [latex]{$7.99}[/latex]. She had a coupon for [latex]{$0.75}[/latex] 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 [latex]190[/latex] pounds at the start of the program. During the first week, he lost [latex]4.3[/latex] pounds. During the second week, he had lost [latex]2.8[/latex] pounds. The third week, he gained [latex]0.7[/latex] pounds. The fourth week, he lost [latex]1.9[/latex] pounds. What did Leo weigh at the end of the fourth week?

Snowpack

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

Coffee

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

Subway Fare

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

Income

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

Income

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

Hourly Wage

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

Hourly Wage

Maria got her first paycheck from her new job. She worked [latex]25[/latex] hours and earned [latex]{$362.50}[/latex]. 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 [latex]\$6.00[/latex]. How much does each girl pay if the total number sharing the mud pie is

1. [latex]2?[/latex]
   Show Solution

   $3
2. [latex]3?[/latex]
   Show Solution

   $2
3. [latex]4?[/latex]
   Show Solution

   $1.50
4. [latex]5?[/latex]
   Show Solution

   $1.20
5. [latex]6?[/latex]
   Show Solution

   $1

Pizza

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

1.  [latex]2?[/latex]
2. [latex]3?[/latex]
3. [latex]4?[/latex]
4. [latex]5?[/latex]
5.  [latex]6?[/latex]

Fast Food

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

Home Goods

Chelsea needs towels to take with her to college. She buys [latex]2[/latex] bath towels that cost [latex]{$9.99}[/latex] each and [latex]6[/latex] washcloths that cost [latex]{$2.99}[/latex] 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 [latex]{$29.95}[/latex] and children’s tickets cost [latex]{$19.95}[/latex]. What will the total cost be for [latex]4[/latex] adults and [latex]7[/latex] children?

Ice Skating

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

Exploring The Relationship Between Decimals and Fractions

Convert Fractions to Decimals

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

1. [latex]\Large\frac{2}{5}[/latex]
   Show Solution

   0.4
2. [latex]\Large\frac{4}{5}[/latex]
3. [latex]-\Large\frac{3}{8}[/latex]
   Show Solution

   −0.375
4. [latex]-\Large\frac{5}{8}[/latex]
5. [latex]\Large\frac{17}{20}[/latex]
   Show Solution

   0.85
6. [latex]\Large\frac{13}{20}[/latex]
7. [latex]\Large\frac{11}{4}[/latex]
   Show Solution

   2.75
8. [latex]\Large\frac{17}{4}[/latex]
9. [latex]-\Large\frac{310}{25}[/latex]
   Show Solution

   −12.4
10. [latex]-\Large\frac{284}{25}[/latex]
11. [latex]\Large\frac{5}{9}[/latex]
    Show Solution

    [latex]0.\stackrel{-}{5}[/latex]
12. [latex]\Large\frac{2}{9}[/latex]
13. [latex]\Large\frac{15}{11}[/latex]
    Show Solution

    [latex]1.\stackrel{\text{-}}{36}[/latex]
14. [latex]\Large\frac{18}{11}[/latex]
15. [latex]\Large\frac{15}{111}[/latex]
    Show Solution

    [latex]0.\stackrel{\text{-}}{135}[/latex]
16. [latex]\Large\frac{25}{111}[/latex]

Convert Fractions to Decimals and Simplify

In the following exercises, simplify the expression.

1. [latex]\Large\frac{1}{2}\normalsize+6.5[/latex]
   Show Solution

   7
2. [latex]\Large\frac{1}{4}\normalsize+10.75[/latex]
3. [latex]2.4+\Large\frac{5}{8}[/latex]
   Show Solution

   3.025
4. [latex]3.9+\Large\frac{9}{20}[/latex]
5. [latex]9.73+\Large\frac{17}{20}[/latex]
   Show Solution

   10.58
6. [latex]6.29+\Large\frac{21}{40}[/latex]

Order Decimals and Fractions

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

1. [latex]\Large\frac{1}{8}\normalsize\text{___}0.8[/latex]
   Show Solution

   <
2. [latex]\Large\frac{1}{4}\normalsize\text{___}0.4[/latex]
3. [latex]\Large\frac{2}{5}\normalsize\text{___}0.25[/latex]
   Show Solution

   >
4. [latex]\Large\frac{3}{5}\normalsize\text{___}0.35[/latex]
5. [latex]\text {0.725___}\Large\frac{3}{4}[/latex]
   Show Solution

   <
6. [latex]\text {0.92___}\Large\frac{7}{8}[/latex]
7. [latex]\text {0.66___}\Large\frac{2}{3}[/latex]
   Show Solution

   <
8. [latex]\text {0.83___}\Large\frac{5}{6}[/latex]
9. [latex]\text {-0.75___}-\Large\frac{4}{5}[/latex]
   Show Solution

   >
10. [latex]\text {-0.44___}-\Large\frac{9}{20}[/latex]
11. [latex]-\Large\frac{3}{4}\normalsize\text{___} - 0.925[/latex]
    Show Solution

    >
12. [latex]-\Large\frac{2}{3}\normalsize\text{___} - 0.632[/latex]

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

1. [latex]\Large\frac{3}{5}\normalsize ,\Large\frac{9}{16}\normalsize,0.55[/latex]
   Show Solution

   [latex]0.55,\Large\frac{9}{16}\normalsize ,\Large\frac{3}{5}[/latex]
2. [latex]\Large\frac{3}{8}\normalsize ,\Large\frac{7}{20}\normalsize ,0.36[/latex]
3. [latex]0.702,\Large\frac{13}{20}\normalsize ,\Large\frac{5}{8}[/latex]
   Show Solution

   [latex]\Large\frac{5}{8}\normalsize ,\Large\frac{13}{20}\normalsize ,0.702[/latex]
4. [latex]0.15,\Large\frac{3}{16}\normalsize ,\Large\frac{1}{5}[/latex]
5. [latex]-0.3,-\Large\frac{1}{3}\normalsize ,-\Large\frac{7}{20}[/latex]
   Show Solution

   [latex]-\Large\frac{7}{20}\normalsize ,-\Large\frac{1}{3}\normalsize,-0.3[/latex]
6. [latex]-0.2,-\Large\frac{3}{20}\normalsize ,-\Large\frac{1}{6}[/latex]
7. [latex]-\Large\frac{3}{4}\normalsize ,-\Large\frac{7}{9}\normalsize,-0.7[/latex]
   Show Solution

   [latex]-\Large\frac{7}{9}\normalsize ,-\Large\frac{3}{4}\normalsize ,-0.7[/latex]
8. [latex]-\Large\frac{8}{9}\normalsize ,-\Large\frac{4}{5}\normalsize,-0.9[/latex]

Simplify Expressions Using the Order of Operations

In the following exercises, simplify.

1. [latex]10\left(25.1 - 43.8\right)[/latex]
   Show Solution

   −187
2. [latex]30\left(18.1 - 32.5\right)[/latex]
3. [latex]62\left(9.75 - 4.99\right)[/latex]
   Show Solution

   295.12
4. [latex]42\left(8.45 - 5.97\right)[/latex]
5. [latex]\Large\frac{3}{4}\normalsize\left(12.4 - 4.2\right)[/latex]
   Show Solution

   6.15
6. [latex]\Large\frac{4}{5}\normalsize\left(8.6+3.9\right)[/latex]
7. [latex]\Large\frac{5}{12}\normalsize\left(30.58+17.9\right)[/latex]
   Show Solution

   20.2
8. [latex]\Large\frac{9}{16}\normalsize\left(21.96 - 9.8\right)[/latex]
9. [latex]10\div 0.1+\left(1.8\right)4-{\left(0.3\right)}^{2}[/latex]
   Show Solution

   107.11
10. [latex]5\div 0.5+\left(3.9\right)6-{\left(0.7\right)}^{2}[/latex]
11. [latex]\left(37.1+52.7\right)\div \left(12.5\div 62.5\right)[/latex]
    Show Solution

    449
12. [latex]\left(11.4+16.2\right)\div \left(18\div 60\right)[/latex]
13. [latex]{\Large\left(\frac{1}{5}\right)}^{2}\normalsize+\left(1.4\right)\left(6.5\right)[/latex]
    Show Solution

    9.14
14. [latex]{\Large\left(\frac{1}{2}\right)}^{2}\normalsize+\left(2.1\right)\left(8.3\right)[/latex]
15. [latex]-\Large\frac{9}{10}\normalsize\cdot\Large\frac{8}{15}\normalsize+0.25[/latex]
    Show Solution

    −0.23
16. [latex]-\Large\frac{3}{8}\normalsize\cdot\Large\frac{14}{15}\normalsize+0.72[/latex]

Mixed Practice

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

1. [latex]3\Large\frac{1}{4}\normalsize -6.5[/latex]
   Show Solution

   −3.25
2. [latex]5\Large\frac{2}{5}\normalsize -8.75[/latex]
3. [latex]10.86\div\Large\frac{2}{3}[/latex]
   Show Solution

   16.29
4. [latex]5.79\div\Large\frac{3}{4}[/latex]
5. [latex]\Large\frac{7}{8}\normalsize\left(103.48\right)+1\Large\frac{1}{2}\normalsize\left(361\right)[/latex]
   Show Solution

   632.045
6. [latex]\Large\frac{5}{16}\normalsize\left(117.6\right)+2\Large\frac{1}{3}\normalsize\left(699\right)[/latex]
7. [latex]3.6\left(\Large\frac{9}{8}\normalsize-2.72\right)[/latex]
   Show Solution

   −5.742
8. [latex]5.1\left(\Large\frac{12}{5}\normalsize-3.91\right)[/latex]

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.

1. [latex]\text{radius}=\text{5 in.}[/latex]
   Show Solution

   ⓐ 31.4 in ⓑ 78.5 sq.in.
2. [latex]\text{radius}=\text{20 in.}[/latex]
3. [latex]\text{radius}=\text{9 ft.}[/latex]
   Show Solution

   ⓐ 56.52.ft. ⓑ 254.34 sq.ft.
4. [latex]\text{radius}=\text{4 ft.}[/latex]
5. [latex]\text{radius}=\text{46 cm}[/latex]
   Show Solution

   ⓐ 288.88 cm ⓑ 6644.24 sq.cm
6. [latex]\text{radius}=\text{38 cm}[/latex]
7. [latex]\text{radius}=\text{18.6 m}[/latex]
   Show Solution

   ⓐ 116.808 m ⓑ 1086.3144 sq.m
8. [latex]\text{radius}=\text{57.3 m}[/latex]
9. [latex]\text{radius}=\Large\frac{7}{10}\normalsize\text{mile}[/latex]
   Show Solution

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

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

    ⓐ [latex]\Large\frac{55}{21}\normalsize\text{m}[/latex] ⓑ [latex]\Large\frac{275}{504}\normalsize\text{sq.m}[/latex]
14. [latex]\text{diameter}=\Large\frac{3}{4}\normalsize\text{m}[/latex]

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.

[latex]x - 0.8=2.3[/latex]

ⓐ [latex]x=2[/latex] ⓑ [latex]x=-1.5[/latex] ⓒ [latex]x=3.1[/latex]

[latex]y+0.6=-3.4[/latex]

ⓐ [latex]y=-4[/latex] ⓑ [latex]y=-2.8[/latex] ⓒ [latex]y=2.6[/latex]

[latex]\Large\frac{h}{1.5}\normalsize =-4.3[/latex]

ⓐ [latex]h=6.45[/latex] ⓑ [latex]h=-6.45[/latex] ⓒ [latex]h=-2.1[/latex]

[latex]0.75k=-3.6[/latex]

ⓐ [latex]k=-0.48[/latex] ⓑ [latex]k=-4.8[/latex] ⓒ [latex]k=-2.7[/latex]

Solve Equations with Decimals

In the following exercises, solve the equation.

1. [latex]y+2.9=5.7[/latex]
   Show Solution

   y = 2.8

2. [latex]m+4.6=6.5[/latex]
3. [latex]f+3.45=2.6[/latex]
   Show Solution

   f = −0.85
4. [latex]h+4.37=3.5[/latex]
5. [latex]a+6.2=-1.7[/latex]
   Show Solution

   a = −7.9
6. [latex]b+5.8=-2.3[/latex]
7. [latex]c+1.15=-3.5[/latex]
   Show Solution

   c = −4.65
8. [latex]d+2.35=-4.8[/latex]
9. [latex]n - 2.6=1.8[/latex]
   Show Solution

   n = 4.4
10. [latex]p - 3.6=1.7[/latex]
11. [latex]x - 0.4=-3.9[/latex]
    Show Solution

    x = −3.5
12. [latex]y - 0.6=-4.5[/latex]
13. [latex]j - 1.82=-6.5[/latex]
    Show Solution

    j = −4.68
14. [latex]k - 3.19=-4.6[/latex]
15. [latex]m - 0.25=-1.67[/latex]
    Show Solution

    m = −1.42
16. [latex]q - 0.47=-1.53[/latex]
17. [latex]0.5x=3.5[/latex]
    Show Solution

    x = 7
18. [latex]0.4p=9.2[/latex]
19. [latex]-1.7c=8.5[/latex]
    Show Solution

    c = −5
20. [latex]-2.9x=5.8[/latex]
21. [latex]-1.4p=-4.2[/latex]
    Show Solution

    p = 3
22. [latex]-2.8m=-8.4[/latex]
23. [latex]-120=1.5q[/latex]
    Show Solution

    q = −80
24. [latex]-75=1.5y[/latex]
25. [latex]0.24x=4.8[/latex]
    Show Solution

    x = 20
26. [latex]0.18n=5.4[/latex]
27. [latex]-3.4z=-9.18[/latex]
    Show Solution

    z = 2.7
28. [latex]-2.7u=-9.72[/latex]
29. [latex]\Large\frac{a}{0.4}\normalsize =-20[/latex]
    Show Solution

    a = −8
30. [latex]\Large\frac{b}{0.3}\normalsize =-9[/latex]
31. [latex]\Large\frac{x}{0.7}\normalsize =-0.4[/latex]
    Show Solution

    x = −0.28
32. [latex]\Large\frac{y}{0.8}\normalsize =-0.7[/latex]
33. [latex]\Large\frac{p}{-5}\normalsize =-1.65[/latex]
    Show Solution

    p = 8.25
34. [latex]\Large\frac{q}{-4}\normalsize =-5.92[/latex]
35. [latex]\Large\frac{r}{-1.2}\normalsize =-6[/latex]
    Show Solution

    r = 7.2
36. [latex]\Large\frac{s}{-1.5}\normalsize =-3[/latex]

Mixed Practice

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

1. [latex]x - 5=-11[/latex]
   Show Solution

   x = −6

2. [latex]-\Large\frac{2}{5}\normalsize =x+\Large\frac{3}{4}[/latex]
3. [latex]p+8=-2[/latex]
   Show Solution

   p = −10
4. [latex]p+\Large\frac{2}{3}\normalsize =\Large\frac{1}{12}[/latex]
5. [latex]-4.2m=-33.6[/latex]
   Show Solution

   m = 8
6. [latex]q+9.5=-14[/latex]
7. [latex]q+\Large\frac{5}{6}\normalsize =\Large\frac{1}{12}[/latex]
   Show Solution