Prealgebra

Carol E. Malloy, Rhonda J. Molix-Bailey, Jack Price

Chapter 5

Rational Numbers - all with Video Answers

Educators

Section 1

Writing Fractions as Decimals

Problem 1

Write each fraction or mixed number as a decimal. Use a bar to show a repeating decimal.
$$\frac{7}{8}$$

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Sarah Wharton

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Problem 2

Write each fraction or mixed number as a decimal. Use a bar to show a repeating decimal.
$$\frac{3}{5}$$

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Problem 3

Write each fraction or mixed number as a decimal. Use a bar to show a repeating decimal.
$$\frac{5}{16}$$

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Problem 4

Write each fraction or mixed number as a decimal. Use a bar to show a repeating decimal.
$$1 \frac{3}{20}$$

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Problem 5

Write each fraction or mixed number as a decimal. Use a bar to show a repeating decimal.
$$2 \frac{2}{5}$$

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Problem 6

Write each fraction or mixed number as a decimal. Use a bar to show a repeating decimal.
$$6 \frac{3}{4}$$

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Problem 7

Write each fraction or mixed number as a decimal. Use a bar to show a repeating decimal.
$$\frac{2}{3}$$

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Problem 8

Write each fraction or mixed number as a decimal. Use a bar to show a repeating decimal.
$$-\frac{5}{9}$$

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Problem 9

Write each fraction or mixed number as a decimal. Use a bar to show a repeating decimal.
$$4 \frac{2}{11}$$

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Problem 10

In $2004,$ the San Francisco 49ers led the NFL in converting on 14 of 19 fourth downs. To the nearest thousandth, what part of the time did the 49ers convert on fourth down?

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Problem 11

Replace each with $<,>,$ or $=$ to make a true sentence.
$$\frac{9}{10} \circ 0.90$$

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Problem 12

Replace each with $<,>,$ or $=$ to make a true sentence.
$$0.3 \circ \frac{1}{3}$$

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Problem 13

Replace each with $<,>,$ or $=$ to make a true sentence.
$$-\frac{3}{4} \circ-\frac{7}{8}$$

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Problem 14

Seven-fiftieths of water usage comes from leaky plumbing and $\frac{3}{20}$ come from faucets. Does a greater fraction of water usage come from leaky plumbing or from faucets?

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Problem 15

Write each fraction or mixed number as a decimal. Use a bar to show a repeating decimal.
$$\frac{1}{5}$$

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Problem 16

Write each fraction or mixed number as a decimal. Use a bar to show a repeating decimal.
$$\frac{7}{20}$$

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Problem 17

Write each fraction or mixed number as a decimal. Use a bar to show a repeating decimal.
$$-\frac{8}{25}$$

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Problem 18

Write each fraction or mixed number as a decimal. Use a bar to show a repeating decimal.
$$-\frac{5}{8}$$

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Problem 19

Write each fraction or mixed number as a decimal. Use a bar to show a repeating decimal.
$$7 \frac{3}{10}$$

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Problem 20

Write each fraction or mixed number as a decimal. Use a bar to show a repeating decimal.
$$1 \frac{1}{2}$$

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Problem 21

Write each fraction or mixed number as a decimal. Use a bar to show a repeating decimal.
$$-5 \frac{1}{8}$$

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Problem 22

Write each fraction or mixed number as a decimal. Use a bar to show a repeating decimal.
$$-3 \frac{3}{4}$$

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Problem 23

Write each fraction or mixed number as a decimal. Use a bar to show a repeating decimal.
$$\frac{1}{9}$$

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Problem 24

Write each fraction or mixed number as a decimal. Use a bar to show a repeating decimal.
$$\frac{2}{9}$$

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Problem 25

Write each fraction or mixed number as a decimal. Use a bar to show a repeating decimal.
$$-\frac{5}{11}$$

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Problem 26

Write each fraction or mixed number as a decimal. Use a bar to show a repeating decimal.
$$-\frac{4}{11}$$

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Problem 27

The customer service department resolved 106 of 120 customer complaints in a one-hour time span. To the nearest thousandth, find the resolve rate of the customer service department.

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Problem 28

During the $2003-2004$ season, Kevin Weekes of the Carolina Hurricanes saved 1506 out of 1652 shots on goal. To the nearest thousandth, what part of the time did Weekes save shots on goal?

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Problem 29

Replace each $\circ$ with $<,>,$ or $=$ to make a true sentence.
$$0.3 \circ \frac{1}{4}$$

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Problem 30

Replace each $\circ$ with $<,>,$ or $=$ to make a true sentence.
$$\frac{5}{8} \circ 0.65$$

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Problem 31

Replace each $\circ$ with $<,>,$ or $=$ to make a true sentence.
$$\frac{2}{5} \circ 0.4$$

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Problem 32

Replace each $\circ$ with $<,>,$ or $=$ to make a true sentence.
$$0.3 \circ \frac{1}{2}$$

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Problem 33

Replace each $\circ$ with $<,>,$ or $=$ to make a true sentence.
$$\frac{7}{8} \circ \frac{8}{9}$$

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Problem 34

Replace each $\circ$ with $<,>,$ or $=$ to make a true sentence.
$$\frac{5}{7} \circ \frac{10}{14}$$

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Problem 35

Replace each $\circ$ with $<,>,$ or $=$ to make a true sentence.
$$-\frac{1}{8} \circ-\frac{1}{10}$$

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Problem 36

Replace each $\circ$ with $<,>,$ or $=$ to make a true sentence.
$$-\frac{6}{25} \circ-\frac{1}{4}$$

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Problem 37

Replace each $\circ$ with $<,>,$ or $=$ to make a true sentence.
$$\frac{1}{5} \circ 0 . \overline{5}$$

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Problem 38

Replace each $\circ$ with $<,>,$ or $=$ to make a true sentence.
$$1 \frac{1}{20} \circ 1.01$$

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Problem 39

Replace each $\circ$ with $<,>,$ or $=$ to make a true sentence.
$$3 \frac{4}{9} \circ 3 . \overline{4}$$

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Problem 40

Replace each $\circ$ with $<,>,$ or $=$ to make a true sentence.
$$6.18 \circ 6 \frac{1}{5}$$

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Problem 41

For Exercises 41 and 42 use the graph at the right.
Did more or less than one-fourth of an inch of rain fall on Tuesday? Explain.

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Problem 42

For Exercises 41 and 42 use the graph at the right.
Suppose it rained $\frac{9}{10}$ inch on Saturday. How does this compare to the previous five days?

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Problem 43

Replace each $\circ$ with $<,>,$ or $=$ to make a true sentence.
$$-0.75 \circ-\frac{7}{9}$$

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Problem 44

Replace each $\circ$ with $<,>,$ or $=$ to make a true sentence.
$$\frac{34}{99} \circ 0.3 \overline{4}$$

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Problem 45

Replace each $\circ$ with $<,>,$ or $=$ to make a true sentence.
$$-2 \frac{1}{12} \circ-2.09$$

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Problem 46

Replace each $\circ$ with $<,>,$ or $=$ to make a true sentence.
$$-\frac{5}{16} \circ-\frac{8}{25}$$

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Problem 47

Replace each $\circ$ with $<,>,$ or $=$ to make a true sentence.
$$-2.2 \circ-2 \frac{2}{7}$$

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Problem 48

Replace each $\circ$ with $<,>,$ or $=$ to make a true sentence.
$$-5 \frac{1}{3} \circ-5 \frac{3}{10}$$

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Problem 49

Of all the cars sold in the United States in $2003, \frac{2}{5}$ were imported from Japan and 0.26 were imported from Germany. Are more Japanese or German cars sold in the United States? Explain.

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Problem 50

Order each group of numbers from least to greatest.
$$\frac{7}{8}, 0.8, \frac{7}{9}$$

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Problem 51

Order each group of numbers from least to greatest.
$$-0.29,-\frac{3}{11},-\frac{2}{7}$$

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Problem 52

Order each group of numbers from least to greatest.
$$2 \frac{3}{5}, 2.67,2 \frac{2}{3}$$

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Problem 53

Order each group of numbers from least to greatest.
$$-1 . \overline{1},-1 \frac{1}{8},-1 \frac{1}{10}$$

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Problem 54

Find a fraction or mixed number that might represent each point on the graph at the right.

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Problem 55

For Exercises 55 and $56,$ use the following information.
Write $\frac{5}{6}$ as a decimal rounded to the nearest hundredth.

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Problem 56

For Exercises 55 and $56,$ use the following information.
Which form of the number is best to use? Explain.

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Problem 57

Give one example each of real-world situations where it is most appropriate to give a response in fractional form and in decimal form.

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Problem 58

Find a terminating and a repeating decimal between $\frac{1}{6}$ and $\frac{8}{9} .$ Explain how you found them.

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Problem 59

Write the prime factorization of each denominator and the decimal equivalent of each fraction. Then explain how prime factors of denominators and the decimal equivalents of fractions are related.
$$\frac{1}{2}, \frac{1}{3}, \frac{1}{4}, \frac{1}{5}, \frac{1}{6}, \frac{1}{8}, \frac{1}{9}, \frac{1}{10}, \frac{1}{12}, \frac{1}{15}, \frac{1}{20}$$

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Problem 60

Luke is making lasagna that calls for $\frac{4}{5}$ pound of mozzarella cheese. The store only has packages that contain 0.75 - and 0.85 -pound of mozzarella cheese. Which of the following techniques might Luke use to determine which package to buy? Justify your selection(s). Then use the technique(s) to solve the problem.

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Problem 61

Explain how 0.5 and$0 . \overline{5}$are different. Which is greater?

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Problem 62

Which decimal represents the shaded portion of the figure?
A 0.6
B $0 . \overline{6}$
C 0.63
D $0.6 \overline{3}$

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Problem 63

The fraction $\frac{7}{9}$ is found between which pair of fractions on a number line?
F. $\frac{3}{5}$ and $\frac{3}{4}$
G. $\frac{7}{10}$ and $\frac{4}{5}$
H. $\frac{7}{10}$ and $\frac{3}{4}$
J. $\frac{3}{5}$ and $\frac{2}{3}$

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Problem 64

Write each number in scientific notation.
$$854,000,000$$

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Problem 65

Write each number in scientific notation.
$$0.077$$

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Problem 66

Write each number in scientific notation.
$$0.00016$$

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Problem 67

Write each number in scientific notation.
$$925,000$$

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Problem 68

Write each expression using a positive exponent.
$$10^{-5}$$

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Problem 69

Write each expression using a positive exponent.
$$(-2)^{-7}$$

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Problem 70

Write each expression using a positive exponent.
$$x^{-4}$$

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Problem 71

Write each expression using a positive exponent.
$$y^{-3}$$

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Problem 72

Write $(a \cdot a \cdot a)(a \cdot a)$ using an exponent.

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Problem 73

A car travels an average of 464 miles on one tank of gas. If the tank holds 16 gallons, how many miles per gallon does it get?

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Problem 74

A scuba diver descends from the surface of the lake at a rate of 6 meters per minute. Where will the diver be in relation to the lake's surface after 4 minutes?

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Problem 75

Simplify each fraction.
$$\frac{4}{30}$$

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Problem 76

Simplify each fraction.
$$\frac{5}{65}$$

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Problem 77

Simplify each fraction.
$$\frac{36}{60}$$

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Problem 78

Simplify each fraction.
$$\frac{12}{18}$$

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Problem 79

Simplify each fraction.
$$\frac{21}{24}$$

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Problem 80

Simplify each fraction.
$$\frac{16}{28}$$

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Problem 81

Simplify each fraction.
$$\frac{32}{48}$$

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Problem 82

Simplify each fraction.
$$\frac{125}{1000}$$

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