12.4.5: Chapter 5

Be Prepared

5.1

Four million, nine hundred twenty-six thousand, fifteen

5.2

$750$

5.3

5.4

$\frac{7}{10}$

5.5

$\frac{27}{100}$

5.6

$4$

5.7

$0.03$

5.8

$>$

5.9

$<$

5.10

$\frac{5}{12}$

5.11

$20$

5.12

$-294$

5.13

$5$

5.14

$50$

5.15

$2.5$

5.16

$\frac{2}{3}$

5.17

$0.24$

5.18

$\frac{6}{11}$

5.19

$81$

5.20

$3.85$

5.21

$960$

Try It

5.1

1. ⓐ six and seven tenths
2. ⓑ nineteen and fifty-eight hundredths
3. ⓒ eighteen thousandths
4. ⓓ negative two and fifty-three thousandths

5.2

1. ⓐfive and eight tenths
2. ⓑthree and fifty-seven hundredths
3. ⓒ five thousandths
4. ⓓ negative thirteen and four hundred sixty-one thousandths

5.3

13.68

5.4

5.894

5.5

0.058

5.6

0.067

5.7

1. ⓐ $5\frac{3}{10}$
2. ⓑ$6\frac{7}{100}$
3. ⓒ $-\frac{117}{500}$

5.8

1. ⓐ $8\frac{7}{10}$
2. ⓑ $1\frac{3}{100}$
3. ⓒ $-\frac{3}{125}$

5.9

5.10

5.11

5.12

5.13

1. ⓐ >
2. ⓑ >

5.14

1. ⓐ <
2. ⓑ <

5.15

>

5.16

>

5.17

1.05

5.18

9.17

5.19

1. ⓐ 6.58
2. ⓑ 6.6
3. ⓒ 7

5.20

1. ⓐ 15.218
2. ⓑ 15.22
3. ⓒ 15.2

5.21

17.6

5.22

33.11

5.23

16.49

5.24

23.593

5.25

0.42

5.26

12.58

5.27

−1.53

5.28

−3.58

5.29

27.4815

5.30

87.6148

5.31

−13.427

5.32

−38.122

5.33

0.00348

5.34

0.00603

5.35

1. ⓐ 25.8
2. ⓑ 258
3. ⓒ 2,580

5.36

1. ⓐ 142
2. ⓑ 1,420
3. ⓒ 14,200

5.37

0.07

5.38

0.08

5.39

$0.19

5.40

$0.42

5.41

−0.39

5.42

−0.4

5.43

587.3

5.44

34.25

5.45

200

5.46

350

5.47

$16.52

5.48

$65.97

5.49

$41.28

5.50

$48.75

5.51

$15.47

5.52

$14.25

5.53

$5.97

5.54

$43.00

5.55

0.25

5.56

0.375

5.57

−2.25

5.58

−5.5

5.59

$2.\stackrel{\text{—}}{45}$

5.60

$2.3\stackrel{\text{—}}{18}$

5.61

5.275

5.62

6.35

5.63

>

5.64

<

5.65

<

5.66

>

5.67

$\frac{4}{5},0.82,\frac{7}{8}$

5.68

$\frac{3}{4},\frac{13}{16},0.835$

5.69

1. ⓐ −183.2
2. ⓑ 4.5

5.70

1. ⓐ −776.25
2. ⓑ 2.2

5.71

11.16

5.72

1.51

5.73

1. ⓐ 314 in.
2. ⓑ 7850 sq. in.

5.74

1. ⓐ 628 ft.
2. ⓑ 31,400 sq. ft.

5.75

1. ⓐ 325.304 cm
2. ⓑ 8425.3736 sq. cm

5.76

1. ⓐ 165.792 m
2. ⓑ 2188.4544 sq. m

5.77

1. ⓐ $\frac{220}{147}\text{m}$
2. ⓑ $\frac{550}{3087}\text{sq. m}$

5.78

1. ⓐ $\frac{40}{21}\text{in.}$
2. ⓑ $\frac{200}{693}\text{sq.in.}$

5.79

1. ⓐ no
2. ⓑ yes
3. ⓒ no

5.80

1. ⓐ yes
2. ⓑ no
3. ⓒ no

5.81

y = −8

5.82

y = −8.4

5.83

a = 1.07

5.84

n = 0.83

5.85

b = −12

5.86

c = −8

5.87

c = 11.7

5.88

b = 6.48

5.89

y − 4.9 = 2.8; y = 7.7

5.90

z − 5.7 = 3.4; z = 9.1

5.91

−4.3x = 12.04; x = −2.8

5.92

−3.1m = 26.66; m = −8.6

5.93

$\frac{q}{\mathrm{-3.4}}=4.5;q=\mathrm{-15.3}$

5.94

$\frac{r}{\mathrm{-2.6}}=2.5;r=\mathrm{-6.5}$

5.95

j + 3.8 = 2.6; j = −1.2

5.96

k + 4.7 = 0.3; k = −4.4

5.97

8.5

5.98

9

5.99

21.5 years

5.100

10

5.101

$7.19

5.102

$39.62

5.103

43

5.104

30

5.105

8.5

5.106

20.5

5.107

2

5.108

5

5.109

21

5.110

5

5.111

1. ⓐ $\frac{1}{10}$
2. ⓑ $0.1$

5.112

1. ⓐ $\frac{1}{20}$
2. ⓑ $0.05$

5.113

1. ⓐ $\frac{5}{8}$
2. ⓑ $0.625$

5.114

1. ⓐ $\frac{2}{8}$
2. ⓑ $0.25$

5.115

1. ⓐ$\frac{3}{8}$
2. ⓑ$\frac{3}{2}$

5.116

1. ⓐ$\frac{3}{8}$
2. ⓑ$\frac{3}{2}$

5.117

1. ⓐ $\frac{2}{5}$
2. ⓑ $\frac{10}{3}$

5.118

1. ⓐ$\frac{2}{9}$
2. ⓑ$\frac{5}{1}$

5.119

$\frac{2}{3}$

5.120

$\frac{9}{22}$

5.121

$\frac{37}{8}$

5.122

$\frac{102}{19}$

5.123

$\frac{8}{3}$

5.124

$\frac{2}{9}$

5.125

$\frac{\text{123 miles}}{\text{2 hours}}$

5.126

$\frac{\text{121 miles}}{\text{3 hours}}$

5.127

$18.00/hour

5.128

$19.00/hour

5.129

23.5 mpg

5.130

28 mpg

5.131

$0.29/box

5.132

$0.53/bottle

5.133

Brand A costs $0.11 per bag. Brand B costs $0.13 per bag. Brand A is the better buy.

5.134

Brand C costs $0.07 per ounce. Brand D costs $0.09 per ounce. Brand C is the better buy.

5.135

1. ⓐ 689 mi/h hours
2. ⓑ y parents/22 students
3. ⓒ $d/9 min

5.136

1. ⓐ m mi/9 h
2. ⓑ x students/8 buses
3. ⓒ $y/40 h

5.137

1. ⓐ 6
2. ⓑ 13

5.138

1. ⓐ 4
2. ⓑ 14

5.139

1. ⓐ −2
2. ⓑ −15

5.140

1. ⓐ −9
2. ⓑ −8

5.141

1. ⓐ not a real number
2. ⓑ −9

5.142

1. ⓐ not a real number
2. ⓑ −11

5.143

1. ⓐ 7
2. ⓑ 5

5.144

1. ⓐ 17
2. ⓑ 23

5.145

$6<\sqrt{38}<7$

5.146

$9<\sqrt{84}<10$

5.147

≈ 3.32

5.148

≈ 3.61

5.149

y

5.150

m

5.151

8x

5.152

13y

5.153

−11y

5.154

−10p

5.155

10ab

5.156

15mn

5.157

19.2 feet

5.158

52 centimeters

5.159

9 seconds

5.160

3.5 seconds

5.161

42.7 mph

5.162

54.1 mph

Section 5.1 Exercises

1.

five and five tenths

3.

five and one hundredth

5.

eight and seventy-one hundredths

7.

two thousandths

9.

three hundred eighty-one thousandths

11.

negative seventeen and nine tenths

13.

8.03

15.

29.81

17.

0.7

19.

0.001

21.

0.029

23.

−11.0009

25.

13.0395

27.

$1\frac{99}{100}$

29.

$15\frac{7}{10}$

31.

$\frac{239}{1000}$

33.

$\frac{13}{100}$

35.

$\frac{11}{1000}$

37.

$-\frac{7}{100000}$

39.

$6\frac{2}{5}$

41.

$7\frac{1}{20}$

43.

$4\frac{3}{500}$

45.

$10\frac{1}{4}$

47.

$1\frac{81}{250}$

49.

$14\frac{1}{8}$

51.

53.

55.

57.

59.

>

61.

<

63.

>

65.

>

67.

<

69.

<

71.

0.7

73.

2.8

75.

0.85

77.

5.79

79.

0.30

81.

4.10

83.

1. ⓐ 5.78
2. ⓑ 5.8
3. ⓒ 6

85.

1. ⓐ 63.48
2. ⓑ 63.5
3. ⓒ 63

87.

1. ⓐ $58,966
2. ⓑ $59,000
3. ⓒ $60,000

89.

1. ⓐ $142.19
2. ⓑ $142

91.

Answers will vary.

93.

Tim had the faster time. 12.3 is less than 12.32, so Tim had the faster time.

Section 5.2 Exercises

95.

24.48

97.

170.88

99.

−9.23

101.

49.73

103.

−40.91

105.

−7.22

107.

−13.5

109.

35.8

111.

−27.5

113.

15.73

115.

42.51

117.

102.212

119.

51.31

121.

−4.89

123.

0.12

125.

0.144

127.

42.008

129.

26.7528

131.

−11.653

133.

337.8914

135.

2.2302

137.

1.305

139.

92.4

141.

55,200

143.

0.03

145.

0.19

147.

$0.71

149.

$2.44

151.

3

153.

−4.8

155.

35

157.

2.08

159.

150

161.

20

163.

19.2

165.

12.09

167.

32.706

169.

$48.60

171.

20

173.

2

175.

$17.80

177.

$24.89

179.

$29.06

181.

$3.19

183.

181.7 pounds

185.

$15.00

187.

$296.00

189.

$12.75

191.

1. ⓐ $3
2. ⓑ $2
3. ⓒ $1.50
4. ⓓ $1.20
5. ⓔ $1

193.

$18.64

195.

$259.45

197.

1. ⓐ $243.57
2. ⓑ $79.35

199.

The difference: 0.03 seconds. Three hundredths of a second.

Section 5.3 Exercises

201.

0.4

203.

−0.375

205.

0.85

207.

2.75

209.

−12.4

211.

$0.\bar{5}$

213.

$1.\stackrel{\text{—}}{36}$

215.

$0.\stackrel{\text{—}}{135}$

217.

7

219.

3.025

221.

10.58

223.

<

225.

>

227.

<

229.

<

231.

>

233.

>

235.

$0.55,\frac{9}{16},\frac{3}{5}$

237.

$\frac{5}{8},\frac{13}{20},0.702$

239.

$-\frac{7}{20},-\frac{1}{3},-0.3$

241.

$-\frac{7}{9},-\frac{3}{4},\mathrm{-0.7}$

243.

−187

245.

295.12

247.

6.15

249.

20.2

251.

107.11

253.

449

255.

9.14

257.

−0.23

259.

−3.25

261.

16.29

263.

632.045

265.

−5.742

267.

1. ⓐ 31.4 in
2. ⓑ 78.5 sq.in.

269.

1. ⓐ 56.52.ft.
2. ⓑ 254.34 sq.ft.

271.

1. ⓐ 288.88 cm
2. ⓑ 6644.24 sq.cm

273.

1. ⓐ 116.808 m
2. ⓑ 1086.3144 sq.m

275.

1. ⓐ $\frac{22}{5}\text{mile}$
2. ⓑ $\frac{77}{50}\text{sq.mile}$

277.

1. ⓐ $\frac{33}{14}\text{yard}$
2. ⓑ $\frac{99}{224}\text{sq.yard}$

279.

1. ⓐ $\frac{55}{21}\text{m}$
2. ⓑ $\frac{275}{504}\text{sq.m}$

281.

$56.66

283.

Answers will vary.

Section 5.4 Exercises

285.

1. ⓐ no
2. ⓑ no
3. ⓒ yes

287.

1. ⓐ no
2. ⓑ yes
3. ⓒ no

289.

y = 2.8

291.

f = −0.85

293.

a = −7.9

295.

c = −4.65

297.

n = 4.4

299.

x = −3.5

301.

j = −4.68

303.

m = −1.42

305.

x = 7

307.

c = −5

309.

p = 3

311.

q = −80

313.

x = 20

315.

z = 2.7

317.

a = −8

319.

x = −0.28

321.

p = 8.25

323.

r = 7.2

325.

x = −6

327.

p = −10

329.

m = 8

331.

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

333.

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

335.

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

337.

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

339.

a = −0.8

341.

r = −1.45

343.

h = 24

345.

$n-1.9=3.4;5.3$

347.

−6.2x = −4.96; 0.8

349.

$\frac{y}{-1.7}=\mathrm{-5};8.5$

351.

n + (−7.3) = 2.4; 9.7

353.

$104

355.

Answers will vary.

Section 5.5 Exercises

357.

4

359.

35

361.

245.5

363.

11.65

365.

$18.84

367.

19.5 minutes

369.

0.329

371.

21

373.

45

375.

4.5

377.

99.65

379.

$6.50

381.

40.5 months

383.

2

385.

22

387.

2 children

389.

11 units

391.

$\frac{1}{20},0.05$

393.

$\frac{1}{24},0.041\bar{6}\approx 0.042$

395.

$\frac{2}{5},0.4$

397.

$\frac{5}{7},0.\stackrel{\text{———}}{714285}\approx 0.714$

399.

1. ⓐ $285.47
2. ⓑ $275.63
3. ⓒ $236.25

401.

Answers will vary.

Section 5.6 Exercises

403.

$\frac{5}{9}$

405.

$\frac{7}{8}$

407.

$\frac{7}{3}$

409.

$\frac{7}{3}$

411.

$\frac{1}{5}$

413.

$\frac{10}{17}$

415.

$\frac{5}{4}$

417.

$\frac{2}{7}$

419.

$\frac{11}{4}$

421.

$\frac{1}{3}$

423.

$\frac{6}{23}$

425.

$\frac{82}{15}$

427.

$\frac{35}{9}$

429.

$\frac{9}{4}$

431.

$\frac{\text{35 calories}}{\text{3 ounces}}$

433.

$\frac{\text{41 lbs}}{\text{15 sq. in}.}$

435.

$\frac{\text{488 miles}}{\text{7 hours}}$

437.

$\frac{\text{\$119}}{\text{8 hours}}$

439.

11.67 calories/ounce

441.

2.73 lbs./sq. in.

443.

69.71 mph

445.

$14.88/hour

447.

32 mpg

449.

2.69 lbs./week

451.

92 beats/minute

453.

8,000

455.

$1.09/bar

457.

$1.33/pair

459.

$0.48/pack

461.

$0.60/disc

463.

$1.29/box

465.

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.

467.

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.

469.

The regular bottle costs $0.075 per ounce. The squeeze bottle costs $0.069 per ounce. The squeeze bottle is a better buy.

471.

The half-pound block costs $6.78/lb, so the 1-lb. block is a better buy.

473.

$\frac{\text{793 miles}}{p\text{hours}}$

475.

$\frac{\text{\$3}}{\text{0.5 lbs}.}$

477.

$\frac{\text{105 calories}}{x\text{ounces}}$

479.

$\frac{y}{5x}$

481.

15.2 students per teacher

483.

1. ⓐ 72 calories/ounce
2. ⓑ 3.87 grams of fat/ounce
3. ⓒ 5.73 grams carbs/ounce
4. ⓓ 3.33 grams protein/ounce

485.

Answers will vary.

487.

Kathryn should swim for approximately 16.35 minutes. Explanations will vary.

Section 5.7 Exercises

489.

6

491.

8

493.

−2

495.

−1

497.

not a real number

499.

not a real number

501.

5

503.

7

505.

$8<\sqrt{70}<9$

507.

$14<\sqrt{200}<15$

509.

4.36

511.

7.28

513.

y

515.

7x

517.

−8a

519.

12xy

521.

8.7 feet

523.

8 seconds

525.

15.8 seconds

527.

72 mph

529.

53.0 mph

531.

45 inches

533.

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.

Review Exercises

535.

three hundred seventy-five thousandths

537.

five and twenty-four hundredths

539.

negative four and nine hundredths

541.

0.09

543.

10.035

545.

−0.05

547.

$\frac{33}{40}$

549.

$3\frac{16}{25}$

551.

<

553.

<

555.

1. ⓐ 12.53
2. ⓑ 12.5
3. ⓒ 13

557.

1. ⓐ 5.90
2. ⓑ 5.9
3. ⓒ 6

559.

24.67

561.

24.831

563.

−2.37

565.

−1.6

567.

15,400

569.

0.18

571.

4

573.

200

575.

$28.22

577.

$1.79

579.

0.875

581.

−5.25

583.

$0.\stackrel{\text{—}}{54}$

585.

>

587.

>

589.

>

591.

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

593.

6.03

595.

1.975

597.

−0.22

599.

1. ⓐ 21.98 ft.
2. ⓑ 38.465 sq.ft.

601.

1. ⓐ 34.54 cm
2. ⓑ 94.985 sq.cm

603.

1. ⓐ no
2. ⓑ yes

605.

1. ⓐ no
2. ⓑ yes

607.

h = −3.51

609.

p = 2.65

611.

j = 3.72

613.

x = −4

615.

a = −7.2

617.

s = 25

619.

−5.9x = −3.54; x = 0.6

621.

m + (−4.03) = 6.8; m = 10.83

623.

$269.10

625.

$40.94

627.

24.5

629.

16 clients

631.

2

633.

$\frac{1}{5};0.2$

635.

$\frac{7}{4}$

637.

$\frac{2}{3}$

639.

$\frac{4}{9}$

641.

$\frac{7}{9}$

643.

$\frac{12\text{pounds}}{1\text{square inch}}$

645.

$\frac{\text{\$35}}{2\text{hours}}$

647.

12 pounds/sq.in.

649.

$17.50/hour

651.

$0.42

653.

$1.65

655.

$0.11, $0.12; 60 tablets for $6.49

657.

$\frac{a\text{adults}}{45\text{children}}$

659.

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

661.

12

663.

−9

665.

not a real number

667.

17

669.

$12<\sqrt{155}<13$

671.

7.55

673.

8b

675.

15mn

677.

7y

679.

11cd

681.

5.5 feet

683.

72 mph

Practice Test

685.

$1\frac{73}{100}$

687.

1. ⓐ 16.7
2. ⓑ 16.75
3. ⓒ 17

689.

18.42

691.

0.192

693.

−0.08

695.

2

697.

200

699.

1.975

701.

−1.2

703.

8.8

705.

$26.45

707.

1. ⓐ 52.1
2. ⓑ 51.5
3. ⓒ 55

709.

The unit prices are $0.172 per ounce for 64 ounces, and $0.177 per ounce for 48 ounces; 64 ounces is the better buy.

711.

12n

713.

15 feet