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5.3 Decimals and Fractions

Division turning a fraction into a terminating or repeating decimal, ordering mixed sets of both forms, and circumference and area of a circle.

Prealgebra 2e, 5.3 Decimals and Fractions

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77 exercises

5.3 Exercise 1

Before you get started, take this readiness quiz.

Divide: 0.24÷8.0.24 \div 8 .
If you missed this problem, review the reference.

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5.3 Exercise 2

Order 0.64__0.60.64 __ 0.6 using << or >.>.
If you missed this problem, review the reference.

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5.3 Exercise 3

Order −0.2__−0.1−0.2 __ −0.1 using << or >.>.
If you missed this problem, review the reference.

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5.3 Exercise 5

Write the fraction as a decimal: 14.\frac{1}{4} .

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5.3 Exercise 6

Write the fraction as a decimal: 38.\frac{3}{8} .

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5.3 Exercise 8

Write the fraction as a decimal: −94.- \frac{9}{4} .

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5.3 Exercise 9

Write the fraction as a decimal: −112.- \frac{11}{2} .

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5.3 Exercise 11

Write as a decimal: 2711.\frac{27}{11} .

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5.3 Exercise 12

Write as a decimal: 5122.\frac{51}{22} .

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5.3 Exercise 14

Simplify: 38+4.9.\frac{3}{8} + 4.9 .

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5.3 Exercise 15

Simplify: 5.7+1320.5.7 + \frac{13}{20} .

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5.3 Exercise 16

Order 38__0.4\frac{3}{8} __ 0.4 using << or >.>.

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5.3 Exercise 17

Order each of the following pairs of numbers, using << or >.>.

1720__0.82\frac{17}{20} __ 0.82

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5.3 Exercise 18

Order each of the following pairs of numbers, using << or >.>.

34__0.785\frac{3}{4} __ 0.785

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5.3 Exercise 19

Order −0.5___−34−0.5 ___ - \frac{3}{4} using << or >.>.

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5.3 Exercise 20

Order each of the following pairs of numbers, using << or >:>:

−58__−0.58- \frac{5}{8} __ −0.58

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5.3 Exercise 21

Order each of the following pairs of numbers, using << or >:>:

−0.53__−1120−0.53 __ - \frac{11}{20}

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5.3 Exercise 22

Write the numbers 1320,0.61,1116\frac{13}{20} , 0.61 , \frac{11}{16} in order from smallest to largest.

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5.3 Exercise 23

Write each set of numbers in order from smallest to largest: 78,45,0.82.\frac{7}{8} , \frac{4}{5} , 0.82 .

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5.3 Exercise 24

Write each set of numbers in order from smallest to largest: 0.835,1316,34.0.835 , \frac{13}{16} , \frac{3}{4} .

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5.3 Exercise 25

Simplify the expressions:

  1. ⓐ 7(18.3−21.7)7 \left(18.3 - 21.7\right)
  2. ⓑ 23(8.3−3.8)\frac{2}{3} \left(8.3 - 3.8\right)
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5.3 Exercise 26

Simplify: ⓐ 8(14.6−37.5)8 \left(14.6 - 37.5\right) ⓑ 35(9.6−2.1).\frac{3}{5} \left(9.6 - 2.1\right) .

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5.3 Exercise 27

Simplify: ⓐ 25(25.69−56.74)25 \left(25.69 - 56.74\right) ⓑ 27(11.9−4.2).\frac{2}{7} \left(11.9 - 4.2\right) .

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5.3 Exercise 28

Simplify each expression:

  1. ⓐ 6÷0.6+(0.2)4−(0.1)26 \div 0.6 + \left(0.2\right) 4 - \left(0.1\right)^{2}
  2. ⓑ (110)2+(3.5)(0.9)\left(\frac{1}{10}\right)^{2} + \left(3.5\right) \left(0.9\right)
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5.3 Exercise 29

Simplify: 9÷0.9+(0.4)3−(0.2)2.9 \div 0.9 + \left(0.4\right) 3 - \left(0.2\right)^{2} .

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5.3 Exercise 30

Simplify: (12)2+(0.3)(4.2).\left(\frac{1}{2}\right)^{2} + \left(0.3\right) \left(4.2\right) .

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5.3 Exercise 31

A circle has radius 1010 centimeters. Approximate its ⓐ circumference and ⓑ area.

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5.3 Exercise 32

A circle has radius 5050 inches. Approximate its ⓐ circumference and ⓑ area.

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5.3 Exercise 33

A circle has radius 100100 feet. Approximate its ⓐ circumference and ⓑ area.

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5.3 Exercise 34

A circle has radius 42.542.5 centimeters. Approximate its ⓐ circumference and ⓑ area.

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5.3 Exercise 35

A circle has radius 51.851.8 centimeters. Approximate its ⓐ circumference and ⓑ area.

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5.3 Exercise 36

A circle has radius 26.426.4 meters. Approximate its ⓐ circumference and ⓑ area.

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5.3 Exercise 37

A circle has radius 1415\frac{14}{15} meter. Approximate its ⓐ circumference and ⓑ area.

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5.3 Exercise 38

A circle has radius 521\frac{5}{21} meters. Approximate its ⓐ circumference and ⓑ area.

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5.3 Exercise 39

A circle has radius 1033\frac{10}{33} inches. Approximate its ⓐ circumference and ⓑ area.

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5.3 Exercise 40

Convert each fraction to a decimal.

25\frac{2}{5}

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5.3 Exercise 42

Convert each fraction to a decimal.

−38- \frac{3}{8}

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5.3 Exercise 44

Convert each fraction to a decimal.

1720\frac{17}{20}

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5.3 Exercise 46

Convert each fraction to a decimal.

114\frac{11}{4}

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5.3 Exercise 48

Convert each fraction to a decimal.

−31025- \frac{310}{25}

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5.3 Exercise 50

Convert each fraction to a decimal.

59\frac{5}{9}

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5.3 Exercise 52

Convert each fraction to a decimal.

1511\frac{15}{11}

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5.3 Exercise 54

Convert each fraction to a decimal.

15111\frac{15}{111}

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5.3 Exercise 56

Simplify the expression.

12+6.5\frac{1}{2} + 6.5

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5.3 Exercise 58

Simplify the expression.

2.4+582.4 + \frac{5}{8}

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5.3 Exercise 60

Simplify the expression.

9.73+17209.73 + \frac{17}{20}

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5.3 Exercise 62

Order each pair of numbers, using << or >.>.

18___0.8\frac{1}{8} ___ 0.8

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5.3 Exercise 64

Order each pair of numbers, using << or >.>.

25___0.25\frac{2}{5} ___ 0.25

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5.3 Exercise 66

Order each pair of numbers, using << or >.>.

0.725___340.725 ___ \frac{3}{4}

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5.3 Exercise 68

Order each pair of numbers, using << or >.>.

0.66___230.66 ___ \frac{2}{3}

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5.3 Exercise 70

Order each pair of numbers, using << or >.>.

−0.75___−45−0.75 ___ - \frac{4}{5}

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5.3 Exercise 72

Order each pair of numbers, using << or >.>.

−34___−0.925- \frac{3}{4} ___ −0.925

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5.3 Exercise 74

Write each set of numbers in order from least to greatest.

35,916,0.55\frac{3}{5} , \frac{9}{16} , 0.55

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5.3 Exercise 76

Write each set of numbers in order from least to greatest.

0.702,1320,580.702 , \frac{13}{20} , \frac{5}{8}

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5.3 Exercise 78

Write each set of numbers in order from least to greatest.

−0.3,−13,−720−0.3 , - \frac{1}{3} , - \frac{7}{20}

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5.3 Exercise 80

Write each set of numbers in order from least to greatest.

−34,−79,−0.7- \frac{3}{4} , - \frac{7}{9} , −0.7

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5.3 Exercise 82

Simplify.

10(25.1−43.8)10 \left(25.1 - 43.8\right)

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5.3 Exercise 84

Simplify.

62(9.75−4.99)62 \left(9.75 - 4.99\right)

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5.3 Exercise 86

Simplify.

34(12.4−4.2)\frac{3}{4} \left(12.4 - 4.2\right)

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5.3 Exercise 88

Simplify.

512(30.58+17.9)\frac{5}{12} \left(30.58 + 17.9\right)

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5.3 Exercise 90

Simplify.

10÷0.1+(1.8)4−(0.3)210 \div 0.1 + \left(1.8\right) 4 - \left(0.3\right)^{2}

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5.3 Exercise 92

Simplify.

(37.1+52.7)÷(12.5÷62.5)\left(37.1 + 52.7\right) \div \left(12.5 \div 62.5\right)

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5.3 Exercise 94

Simplify.

(15)2+(1.4)(6.5)\left(\frac{1}{5}\right)^{2} + \left(1.4\right) \left(6.5\right)

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5.3 Exercise 96

Simplify.

−910·815+0.25- \frac{9}{10} \cdot \frac{8}{15} + 0.25

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5.3 Exercise 98

Simplify. Give the answer as a decimal.

314−6.53 \frac{1}{4} - 6.5

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5.3 Exercise 100

Simplify. Give the answer as a decimal.

10.86÷2310.86 \div \frac{2}{3}

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5.3 Exercise 102

Simplify. Give the answer as a decimal.

78(103.48)+112(361)\frac{7}{8} \left(103.48\right) + 1 \frac{1}{2} \left(361\right)

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5.3 Exercise 104

Simplify. Give the answer as a decimal.

3.6(98−2.72)3.6 \left(\frac{9}{8} - 2.72\right)

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5.3 Exercise 106

Approximate the ⓐ circumference and ⓑ area of each circle. If measurements are given in fractions, leave answers in fraction form.

radius=5 in.\text{radius} = \text{5 in}.

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5.3 Exercise 108

Approximate the ⓐ circumference and ⓑ area of each circle. If measurements are given in fractions, leave answers in fraction form.

radius=9 ft.\text{radius} = \text{9 ft}.

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5.3 Exercise 110

Approximate the ⓐ circumference and ⓑ area of each circle. If measurements are given in fractions, leave answers in fraction form.

radius=46 cm\text{radius} = \text{46 cm}

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5.3 Exercise 112

Approximate the ⓐ circumference and ⓑ area of each circle. If measurements are given in fractions, leave answers in fraction form.

radius=18.6 m\text{radius} = \text{18}.\text{6 m}

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5.3 Exercise 114

Approximate the ⓐ circumference and ⓑ area of each circle. If measurements are given in fractions, leave answers in fraction form.

radius=710mile\text{radius} = \frac{7}{10} \text{mile}

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5.3 Exercise 116

Approximate the ⓐ circumference and ⓑ area of each circle. If measurements are given in fractions, leave answers in fraction form.

radius=38yard\text{radius} = \frac{3}{8} \text{yard}

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5.3 Exercise 118

Approximate the ⓐ circumference and ⓑ area of each circle. If measurements are given in fractions, leave answers in fraction form.

diameter=56m\text{diameter} = \frac{5}{6} \text{m}

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5.3 Exercise 120

Kelly wants to buy a pair of boots that are on sale for 23\frac{2}{3} of the original price. The original price of the boots is $84.99.\$\text{84}.\text{99} . What is the sale price of the shoes?

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5.3 Exercise 122

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

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Adapted from Prealgebra 2e © 2020 Rice University. Licensed under CC BY 4.0. Source: Prealgebra 2e. Imported at revision 77a933c.