Solution manual for intermediate algebra 8th edition by aufmann

Solution Manual for Intermediate Algebra 8th Edition by Aufmann

NOT FOR SALE

Full file at />
CHAPTER 1: REVIEW OF REAL NUMBERS
CHAPTER 1 PREP TEST
1.

5
7
25 14 39 13
+
=
+
=
=
12 30 60 60 60 20

2.

8
7 32 21 11
−
=
−
=
15 20 60 60 60

3.

2
9

4.

4 2 4 5 2
÷ =
⋅ =
15 5 15 2 3

5.

44.405

6.

73.63

7.

7.446

8.

54.06

9.

i, iii, iv

10.

a.

1
= 0.5 C
2

b.

7
= 0.7
10

D

c.

3
= 0.75
4

A

d.

89
= 0.89
100

2.

3.

7 : c, d
4.

–17: a, b, d
0.3412: b, d
3
: c, d
π
–1.010010001: c, d
27
: b, d
91

6.12 : b, d
5.

A terminating decimal is a decimal number that has a
finite number of decimal places – for example, 0.75.

6.

A repeating decimal is a decimal number that has a
block of digits that repeats with no other digits
between the repeating blocks; an example is
8.454545 … = 8.45 .

7.

The additive inverse of a number is the number that is
the same distance from zero on the number line, but
which is on the opposite side of zero.

8.

The absolute value of a number is a measure of its
distance from zero on the number line.

9.

The union of two sets will contain all the elements
that are in either set. The intersection of the two sets
will contain only the elements that are in both sets.

10.

{x | x < 5} does not include the value 5, but
{x | x < 5} does include the value 5.

B

SECTION 1.1
CONCEPT CHECK
1.

5
: c, d

4

Objective 1.1.1

–14: c, e
9: a, b, c, d
0: b, c
53: a, b, c, d
7.8: none
–626: c, e

11.

A number such as 0.63633633363333…, whose
decimal notation neither ends nor repeats, is an
example of an irrational number.

12.

The additive inverse of a negative number is a positive
number.

13.

31: a, b, c, d
–45: c, e
–2: c, e
9.7: none
8600: a, b, c, d
1

: none
2

Exercises

y ∈ {1, 3, 5, 7, 9} is read “y is an element of the set
{1, 3, 5, 7, 9} .”

15
: b, d
2
0: a, b, d
–3: a, b, d
ʌ F G

14.

In symbols the phrase “the opposite of the absolute
value of n” is − n .

15.

–27

16.

3

17.

−

18.

− 17

19.

0

20.

ʌ

−

2.33 : b, d
4.232232223: c, d

3
4

INSTRUCTOR USE ONLY
© Cengage Learning. All Rights Reserved.

Full file at />

Solution Manual for Intermediate Algebra 8th Edition by Aufmann

NOT FOR SALE

Full file
2 at />Chapter 1: Review
iew of Real Numbers
Numbe
21.

33

22.

1.23

23.

91

24.

2
3

25.

26.

27.

28.

29.

30.

31.

32.

Replace a with each element in the set and evaluate the
expression.
–a
–(–3) = 3
–(–2) = 2
–(0) = 0

33.

Replace c with each element in the set and evaluate the
expression.
c

Replace x with each element in the set and determine
whether the inequality is true.
x<5
–3 < 5 True
0 < 5 True
7 < 5 False
The inequality is true for –3 and 0.
Replace z with each element in the set and determine
whether the inequality is true.

z > –2
–4 > –2 False
–1 > –2 True
4 > –2 True
The inequality is true for –1 and 4.
Replace y with each element in the set and determine
whether the inequality is true.
y > –4
–6 > –4 False
–4 > –4 False
7 > –4 True
The inequality is true for 7.
Replace x with each element in the set and determine
whether the inequality is true.
x < –3
–6 < –3 True
–3 < –3 False
3 < –3 False
The inequality is true for –6.

−4 = 4
0 =0

4 =4
34.

−3 = 3
0 =0
7 =7

35.

Replace b with each element in the set and evaluate the
expression.
–b
–(–9) = 9
–(0) = 0
–(9) = –9

Replace m with each element in the set and evaluate
the expression.
−m

− −6 = −6
− −2 = −2
− 0 =0
− 1 = −1

− 4 = −4
36.

Replace w with each element in the set and determine
whether the inequality is true.
w ” –1
–2 ” –1 True
–1 ” –1 True
0 ” –1 False
1 ” –1 False
The inequality is true for –2 and –1.
Replace p with each element in the set and determine

whether the inequality is true.
p•
–10 •  )DOVH
–5 •  )DOVH
0 •  7UXH
5 •  7UXH
The inequality is true for 0 and 5.

Replace q with each element in the set and evaluate the
expression.
q

Replace x with each element in the set and evaluate the
expression.
−x

− −5 = −5
− −3 = −3
− 0 =0

− 2 = −2
− 5 = −5
37.

Yes, negative real numbers are numbers such that
− x > 0.

38.

No

Objective 1.1.2 Exercises
39.

Two ways to write the set of natural numbers less than
five are {1, 2, 3, 4} and
{n| n < 5, n ∈ natural numbers}. The first way uses
the roster method, and the second way uses set-builder
notation.

40.

The symbol for “union” is ∪. The symbol for
“intersection” is ∩.
The symbol
y
∞ is called the infinity
y symbol.
y

INSTRUCTOR USE
E ONLY
O
41.

© Cengage Learning. All Rights Reserved.

Full file at />

Solution Manual for Intermediate Algebra 8th Edition by Aufmann

NOT FOR SALE

Full file at />
Chapter
hapter 1: Review of Real Numbers

66.

{x x ≤ −2}

67.

{x

68.

{x − 2 < x < 4}

{2, 4, 6, 8, 10, 12}

69.

{x − 5 ≤ x ≤ 7}

46.

{1, 3, 5, 7, 9, 11, 13}

70.

{x

47.

{3, 6, 9, 12, 15, 18, 21, 24, 27, 30}
{–20, –16, –12, –8, –4}

71.

48.

{x − 3 ≤ x < 6}

49.

{–35, –30, –25, –20, –15, –10, –5}

72.

{x

50.

{6, 12, 18, 24, 30, 36}

73.

51.

{x

x > 4, x is an integer} or

{x x ≤ 4}

74.

{x x < −2}

{x

x < −2, x is an integer} or

75.

52.

{x x > 5}

76.

{x x ≥ −2}

53.

{x

x ≥ −2}

54.

{x

x ≤ 2}

79. [–1, 5]

55.

{x

0 < x < 1}

80. [0, 3]

56.

{x

− 2 < x < 5}

57.

{x 1 ≤ x ≤ 4}

58.

{x

59.

{x − 1 < x < 5}

42.

Replace each question mark with “includes” or
“does not include” to make the following statement
true. The set [−4, 7) includes the number −4 and
does not include the number 7.

43.

{–2, –1, 0, 1, 2, 3, 4}

44.

{–3, –2, –1}

45.

60.

{x

3

0 < x < 8}

3 ≤ x ≤ 4}

4 < x ≤ 5}

77. (–2, 4)
78. (0, 3)

81. (–’ 

82. (–’ @
83. [–2, 6)

0 ≤ x ≤ 2}

84. [3, ’

85. (–’ ’

86. (–1, ’

87. (–2, 5)

1 < x < 3}

88. (0, 3)
61.

{x

0 ≤ x ≤ 3}

89. [–1, 2]
62.

{x − 1 ≤ x ≤ 1}

90. [–3, 2]

63.

{x x < 2}

91. (–’ @

64.

{x

92. (–’ –1)

65.

{x x ≥ 1}

x < −1}

93. [3, ’


INSTRUCTOR USE ONLY
© Cengage Learning. All Rights Reserved.

Full file at />

Solution Manual for Intermediate Algebra 8th Edition by Aufmann

NOT FOR SALE

Full file
4 at />Chapter 1: Review
iew of Real Numbers
Numbe
94. [–2, ’


117. iii
118. ii

95.

A ∪ B = {1, 2, 4, 6, 9}; A ∩ B = {4}

96.

A ∪ B = {−1, 0, 1, 2}; A ∩ B = {0,1}

97.

A ∪ B = {2, 3, 5, 8, 9, 10}; A ∩ B = ∅

119. A ∪ B is

{x − 1 ≤ x ≤ 1} ∪ {x 0 ≤ x ≤ 1} = {x − 1 ≤ x ≤ 1} = A

98.

A ∪ B = {1, 2, 3, 4, 5, 6, 7, 8}; A ∩ B = ∅

120. A ∪ A is set A.

99.

A ∪ B = {– 4, –2, 0, 2, 4, 8}; A ∩ B = {0,4}

121. B ∩ B is set B.

Applying Concepts 1.1

100. A ∪ B = {–3, –2, –1, 0, 1}; A ∩ B = {-2,-1}

122. A ∪ C is {x – 1 ≤ x ≤ 1} , which is set A.

101. A ∪ B = {1, 2, 3, 4, 5}; A ∩ B = {3,4,5}

123. A ∩ R is {x − 1 ≤ x ≤ 1} , which is set A.

102. A ∪ B = {0, 1, 2, 3, 4, 5}; A ∩ B = {2,4}
103. {x x > 1} ∪ {x x < −1}

124. C ∩ R is {x − 1 ≤ x ≤ 0} , which is set C.
125. B ∪ R is the set of real numbers, R.
126. A ∪ R is the set of real numbers, R.

104. {x x ≤ 2} ∪ {x x > 4}

127. R ∪ R is the set R.
128. R ∩∅ is the empty set ∅.

105. {x x ≤ 2} ∩ {x x ≥ 0}

129. B ∩ C is {x 0 ≤ x ≤ 1} ∩ {x − 1 ≤ x ≤ 0} , which
contains only the number 0.

106. {x x > −1} ∪ {x x ≤ 4}

130. –3 > x > 5 means the numbers that are less than
–3 and greater than 5. There is no number that is
both less than –3 and greater than 5. Therefore,
this is incorrect.

107. {x x > 1} ∩ {x x ≥ −2}

131.
108. {x x < 4} ∩ {x x ≤ 0}

132.

109. {x x > 2} ∪ {x x > 1}

133.

110. {x x < −2} ∪ {x x < −4}

134.

111. (–’ @ ∪[4, ’


135. The answer is ii and iii. For example:
i.

112. (–3, 4] ∪ [–1, 5)
113. [–1, 2] ∩ [0, 4]

ii.
114. [–5, 4) ∩(–2, ’

115. (2, ’
∪ (–2, 4]

iii.

116. (–’ @ ∪ (4, ’


5−4
≤0
3−2
1≤ 0
False
2−3
≤0

5−4
−1 ≤ 0
True

5−4
≤0
2−3
−1 ≤ 0
True

INSTRUCTOR USE ONLY
© Cengage Learning. All Rights Reserved.

Full file at />

Solution Manual for Intermediate Algebra 8th Edition by Aufmann

NOT FOR SALE

Full file at />iv.

4−5
≤0
2−3
1≤ 0
False

Chapter
hapter 1: Review of Real Numbers

5

Objective 1.2.1 Exercises
11.

Rewrite subtraction as addition of the opposite
-8 – (-3)
-8 + 3 = -5

Projects or Group Activities 1.1
c

136.

E = {1,3,5,7,9}

137.

Ec = {1,4, 6, 8,9}

138.

Ec = {even natural numbers}

139.

Ec = {irrational numbers}

140.

a. E∪Ec = U

12.
13.

Negative because only the 7 would be raised
to the 8th power.

14.

-45 negative, only 4 raised to the 5th power
(-4)5 negative, -4 multiplied together an odd
number (5) of times

b. E ∩ Ec = ∅

-46 negative, only 4 raised to the 6th power
(-4)6 positive, -4 multiplied together an even
number (6) of times

SECTION 1.2
Concept Check
Students should paraphrase the rule: Add the
absolute values of the numbers, then attach the
sign of the addends.

15.

2 – (-7) = 2+7 = 9

16.

192 ÷ (-32) = -6

Students should paraphrase the rule: Find the
absolute value of each number, subtract the
smaller of the two numbers from the larger,
then attach the sign of the number with the
larger absolute value.

17.

14 + (-26) = -12

18.

(-10)(-27) = 270

19.

29 + (-2) = 27

The word minus refers to the operation of subtraction,
and the word negative indicates a number that is less
than zero.

20.

24 – (-2) = 24 + 2 = 26

21.

(-8)(29) = -232

3.

No, for example -5 + (-3) = -8

22.

(-16)(32) = -512

4.

If the product of two numbers is positive, both
numbers would be negative or both numbers would be
positive

23.

(-20)(2) = -40

24.

210 ÷ (-30) = -7

25.

-16 + 33 = 17

26.

-140 ÷ (-28) = 5

1.

a.

b.

2.

5.
6.

If quotient of two numbers is negative, one number
must be positive and one must be negative.
Yes. For instance -3 – (-7) = -3 + 7 = 4

27.

13 + (-29) = -16

7.

If the product of two numbers is zero, at least one of the
numbers is zero.

28.

(-28)(32) = -896

8.

37

29.

-21-6 = -21 + (-6) = -27

30.

-16 – 35 = -16 + (-35) = -51

6

9.

(-5)

10.

-2 · 5 ? (8-2) · 5

31.

(-30)(-3) = 90

-10

? 6 ·5

32.

34 + (-6) = 28

-10

? 30

33.

-4 + (-8) = -12

-10 < 30

34.

(-5)(12)= -60

35.

48 ÷ -12 = -4

36.

2 – 5 = -3

INSTRUCTOR USE ONLY
© Cengage Learning. All Rights Reserved.

Full file at />

Solution Manual for Intermediate Algebra 8th Edition by Aufmann
Full file
6 at />Chapter 1: Review
iew of Real Numbers
Numbe
37.

-23 – (41) = -23 + (-41) = -64

38.

b.

The quotient − 416 ÷ 52 is negative.

c.

The quotient − 693 is positive.

d.

The quotient −87 ÷ 0 is undefined.

−99

39.

17 – 21 = -4

40.

-27 + 9 = -18

41.

-42 + 16 or 16 + (-42) = -26

42.

-4-14=-18

= 25 − 125 ÷ 5

43.

-33-21 = -54

44.

-21 + (-15) = -36

= 25 − 25
=0

Objective 1.2.2 Exercises
59.

52 − (10 ÷ 2)3 ÷ 5 = 52 − ( 5 )3 ÷ 5

60. We need an Order of Operations Agreement
to ensure that there is only one way in which
an expression can be correctly simplified.

3
45. 5 = 5 ⋅ 5 ⋅ 5 = 125
4
46. 3 = 3 ⋅ 3 ⋅ 3 ⋅ 3 = 81

61.

3
47. −2 = −(2 ⋅ 2 ⋅ 2) = −8

27 – 12 ÷ 3 – 52
27 – 12 ÷ 3 – (5)(5)

3
48. −4 = −(4 ⋅ 4 ⋅ 4) = −64

27 – 4 – 25

49. ( −5) = ( −5)( −5)( −5) = −125
3

23 – 25 = -2

50. ( −8) = ( −8)( −8) = 64

2

62.

-3 · 23 – 5(-6)

2
4
51. 2 ⋅ 3 = (2)(2) ⋅ (3)(3)(3)(3) = 4 ⋅ 81 = 324

52.

-3 · 23 – 5(1-7)
-3 · (2)(2)(2) -5(-6)

4 2 ⋅ 33 = (4)(4) ⋅ (3)(3)(3) = 16 ⋅ 27 = 432

-3 · 8 -5(-6)

53. −2 2 ⋅ 32 = −(2)(2) ⋅ (3)(3) = −4 ⋅ 9 = −36

-24 – (-30)

54. −3 ⋅ 5 = −(3)(3) ⋅ (5)(5)(5) = −9 ⋅ 125 = −1125

-24 + 30 = 6

2

3

55. ( −2) ⋅ ( −3) = ( −2)( −2)( −2) ⋅ ( −3)( −3)
3

2

= −8 ⋅ 9
= −72

56.

57. a.

15 – (3)(3)(-2) ÷ 6

3

567 + (−812) is negative

b.

−259 − (−327) is positive

c.

The product of four positive numbers
and
three negative numbers is negative.

d.

58. a.

15 – 32(5-7) ÷ 6
15 – 32(-2) ÷ 6

( −4) ⋅ ( −2) = ( −4)( −4)( −4) ⋅ ( −2)( −2)( −2)
= −64 ⋅ ( −8)
= 512
3

63.

The product of three positive numbers
and
four negative numbers is positive.

15 – 9(-2) ÷ 6
15 – (-18) ÷ 6
15 – (-3)
15 + 3 = 18
64. 5 − 3(8 ÷ 4)2 = 5 − 3(2)2 = 5 − 3(4) = 5 − 12 = −7
65. 4 2 − (5 − 2)2 ⋅ 3 = 4 2 − (3)2 ⋅ 3
= 16 − 9 ⋅ 3

= 16 − 27
= −11

The quotient 0 is zero.
−91

INSTRUCTOR USE ONLY
© Cengage Learning. All Rights Reserved.

Full file at />

Solution Manual for Intermediate Algebra 8th Edition by Aufmann

NOT FOR SALE

Full file at />66. 16 −

22 − 5
4−5
= 16 −
32 + 2
9+2
−1
= 16 −
11
1
= 16 +
11
177
=
11

Chapter
hapter 1: Review of Real Numbers

73.

7

2(8-11)-12÷3÷4+18·3÷6
=2(-3)-12÷3÷4+18·3÷6
= -6 – 12÷3÷4+18·3÷6
= -6 – 4 ÷4 + 18 · 3 ÷ 6
= -6 – 1 + 18 ·3 ÷6
= - 6 – 1 + 54 ÷ 6

67. 5[(2 − 4) ⋅ 3 − 2] = 5[( −2) ⋅ 3 − 2]
= 5[−6 − 2]
= 5[−8]
= −40
68. 2[(16 ÷ 8) − ( −2)] + 4 = 2[2 − ( −2)] + 4

= 2[2 + 2] + 4
= 2[4] + 4
=8+4
= 12

⎛ 8 − 2 ⎞ ÷ 1 = 16 − 4 ⎛ 6 ⎞ ÷ 1
69. 16 − 4 ⎜
⎟
⎜ ⎟
⎝3−6⎠ 2
⎝ −3 ⎠ 2
1
= 16 − 4( −2) ÷

2
1
= 16 − ( −8) ÷
2
= 16 − ( −8) ⋅ 2

= -6 -1 + 9
= -7+9
=2
74.

= -3(-4)3 ÷ 4 · (-2)
= -3(-64) ÷ 4 · (-2)
= 192 ÷ 4 · (-2)
= 48 · (-2)
= -96
75.

= 6 – 12 – 18÷ 9
= 6 -12 - 2

= 32

71. 6[3 − ( −4 + 2) ÷ 2] = 6[3 − ( −2) ÷ 2]

= 6[3 − ( −1)]
= 6[3 + 1]
= 6[4]
= 24

6 – 4 · 3 – 18÷ (-3)2
= 6 – 4 · 3 – 18 ÷ 9

= 16 − ( −16)
= 16 + 16
16 + 8 ⎞
⎛ 16 + 8 ⎞ − 5
70. 25 ÷ 5 ⎛⎜ 2
⎟ − 5 = 25 ÷ 5 ⎜
⎟
⎝ −2 + 8 ⎠
⎝ −4 + 8 ⎠
24
= 25 ÷ 5 ⎛⎜ ⎞⎟ − 5
⎝ 4 ⎠
= 25 ÷ 5(6) − 5
= 5(6) − 5
= 30 − 5
= 25

-3(5-9)3÷4 ·(-2)

= -6 - 2
= -8
76.

-9 -2[4-(3-8)2]÷7-4
= -9 -2[4-(-5)2]÷7-4
= -9 -2[4- 25]÷7-4
= -9 -2[-21] ÷7 -4

= -9 + 42÷7 – 4
= -9 + 6 – 4
= -3 – 4
= -7

72. 12 − 4[2 − ( −3 + 5) − 8] = 12 − 4[2 − (2) − 8]

= 12 − 4[−8]
= 12 − ( −32)
= 12 + 32
= 44

INSTRUCTOR USE ONLY
© Cengage Learning. All Rights Reserved.

Full file at />

Solution Manual for Intermediate Algebra 8th Edition by Aufmann

NOT FOR SALE

Full file
8 at />Chapter 1: Review
iew of Real Numbers
Numbe
77.

5+3[52+4(2-5)3]2

81.

3 2

= 5+3[52+4(-3) ]

= 5+3[52+4(-27)]2
= 5+3[52 – 108]2
= 5 +3[56]2
= 5 +3(3136)
= 5 + 9408
= 9413
78.

-3(5-8)3 + (19-7) ÷ (1-3)
= -3(-3)3+ 12 ÷ -2
= -3(-27) - 6
= 81 - 6

= 15 ÷ 5
=3

= 75
79.

28 ÷ (7-9)2·(1-3)4÷14

82. iii

= 28 ÷ (-2)2 · (-2)4 ÷ 14

32 + 32 ÷ 4 − 2 3 = 32 + 32 ÷ 4 − 8 = 32 + 8 − 8

= 28 ÷ 4 · 16 ÷ 14
83. ii

= 7 · 16 ÷ 14

8 2 − 2 2 (5 − 3)3 = 8 2 − 2 2 (2)3 = 64 − 4(8)

= 112 ÷ 14
=8

Applying Concepts 1.2
84. 1122 = 81,402,749,386,839,761,113,321
The tens digit is 2.

80.

85. 7 18 = 1,628,413,597,910,449
The ones digit is 9.
86. 533 = 116,415,321,826,934,814,453,125
The last two digits are 25.
87. 5234 has over 150 digits. The last three are 625.
88. (23)4 = 212 = 4096
4

2( 3 ) = 2 81 = 2,417,851,639,229,258,349,412,352
They do not equal each other, and the second expression
is larger.
c

(b )
c
89. Find b . Then find a .

Projects or Group Activities 1.2

=7+1
=8

90.

Abundant, 1+2+4+5+10 = 22 > 20

91.

Perfect, 1+ 2+4+7+14 = 28 = 28

92.

Deficient, example 32=9, 1+3 = 4 < 9

INSTRUCTOR USE ONLY
© Cengage Learning. All Rights Reserved.

Full file at />

Solution Manual for Intermediate Algebra 8th Edition by Aufmann

NOT FOR SALE

Full file at />
Chapter
hapter 1: Review of Real Numbers

9

11.

SECTION 1.3
Concept Check
1.

2.

3.

4.
5.

The least common multiple (LCM) of 2 or
more numbers is the smallest number that is a
multiple of all the numbers. When adding
fractions, the LCM of all the denominators is
the least common denominator these numbers
will have.
The greatest common factor (GCF) of 2 or
more numbers is the greatest number that
divides evenly into all numbers. When
simplifying fractions, you divide both top and
bottom by the GCF for the two numbers.

Yes, all integers are rational numbers because
they can be written as fractions by writing the
number with a denominator of 1. Example: 7
= 7/1.

12.

13.

14.

15.

and -2.34 are not integers but are rational.
Yes, the smallest positive integer = 1

16.

=

No, positive rational numbers continue to
grow forever.
6.

No, zero does not have a reciprocal.

17.
18.

Objective 1.3.1 Exercises

7.

8.

The LCM of 8, 28, and 7 is 56.
,

,

The reciprocal of

is

19.
20.

.

To find the quotient of two fractions, take the
reciprocal of the second fraction and find the
product.

21.
22.
23.

24.

9.

25.
10.

26.
27.
28.

INSTRUCTOR USE ONLY
© Cengage Learning. All Rights Reserved.

Full file at />

Solution Manual for Intermediate Algebra 8th Edition by Aufmann

NOT FOR SALE

Full file
10at />Chapter 1: Review
iew of Real Numbers
Numbe

50.

29.
30.

51.

31.
52.

32.

=

33.
53.
34.

=
35.
36.

=

37.
54.
38.
55.
39.
40.
41.
56.
42.
43.

(reduce fractions for smaller numbers)
44.

=
57.

45.

=

46.

58.
47.

48.

No. For instance, there is no integer between
2 and 3.

=

Yes, add the two numbers and divide by 2.

=

Objective 1.3.2 Exercises
49.

59.

Fractions

=

INSTRUCTOR USE ONLY
© Cengage Learning. All Rights Reserved.

Full file at />

Solution Manual for Intermediate Algebra 8th Edition by Aufmann

NOT FOR SALE

Full file at />
Chapter
apter 1: Review of Real N
Numbers

11

66.

60.

=
=
61.
67.

=
62.
68.

=

63.

64.

69.

65.

INSTRUCTOR USE ONLY
© Cengage Learning. All Rights Reserved.

Full file at />

Solution Manual for Intermediate Algebra 8th Edition by Aufmann

NOT FOR SALE

Full file
12at />Chapter 1: Review
iew of Real Numbers
Numbe

=

=

73.

70.

74.

71.

75.

i, ii, and iv

72.

INSTRUCTOR USE ONLY
© Cengage Learning. All Rights Reserved.

Full file at />

Solution Manual for Intermediate Algebra 8th Edition by Aufmann

NOT FOR SALE

Full file at />
Chapter
apter 1: Review of Real N
Numbers

13

0.5833… = 0.583

80.
12

-60
100
-96
40
-36
40
-36
4

0.14545…

81.

= 0.145

55
-55
250
-220
300
-275
250
-220
300
-275
25

76.

? needs to be a multiple of 5 so that the
fraction will reduce to an integer.

0.1919…

82.

Objective 1.3.3 Exercises

-99
910
-891
190
-99
910
-891
19

0.625

77.

= 0.19

99

8
-48
20
-16

40
-40
0

0.23076923… = 0.230769

83.
13

-26
40
-39
10
-0
100
-91
90
-78
120
-117
30
-26
40
-39

0.3125

78.
16

-48
20
-16
40
-32
80
-80
0
0.166… = 0.16

79.
6

-6
40
-36
40
-36
4

0.07692307…

84.

= 0.076923

26
-0
200

INSTRUCTOR USE ONLY
© Cengage Learning. All Rights Reserved.

Full file at />

Solution Manual for Intermediate Algebra 8th Edition by Aufmann

NOT FOR SALE

Full file
14at />Chapter 1: Review
iew of Real Numbers
Numbe
-182
180
-156
240
-234
60
-52
80
-78
20
-0
200
-182
18

-4
-4

32
-32
0
96. -0.0009
0.21
-9
-0
18
-18
09
-09
0

85. 3
86. 4
87. 0.0015
-0.0027
-0.0012
88.

97. 4.5
-0.013
45

0.31
x (-0.1)
-0.031

-0
05

-00
58
-45
135
-135
0

89. -0.0008
+3.5
3.4992
90.

91.

0.0022
x (-0.8)
-0.00176

98. 0.02
-0.40
-0.38

0.0003
- 0.39
-0.3897

3.8
x(-3.9)
342
+1140

-14.82
100. -3.5
99.

92. 3.1

0.026

-.01
-35

31

-0
09
-00
91
-70
210
-210
0

-0
31
-31
0
93.

-0.024
x -0.019

216
240
0.000456

94.

0.0029
-0.003
-0.0001

95.

-0.004

101.

102.

-0.0026
+0.028
0.0254

2.7
+0.007
2.707

INSTRUCTOR USE ONLY
-0.018
01

© Cengage Learning. All Rights Reserved.

Full file at />

Solution Manual for Intermediate Algebra 8th Edition by Aufmann

NOT FOR SALE

Full file at />
Chapter
apter 1: Review of Real N
Numbers

15

103. 0.016
0.012

114.

16
-00
19
-16
32
-32
0
104.

-0.18

-0.007
0.187

105.
0.4(1.21)+5.8
0.484+5.8
6.284
106.
5.4-(0.09)
5.4-1
4.4
107.
7-1.5625
5.4375
108.

0.49-1.4
-0.91
109.

6.44
110.
2.8224-4.07
2.8224-14.8962
-12.0738
111. No. 5/23 is a rational number, so its decimal
representation either terminates or repeats.
112. No. By the Order of Opeartions Agreement, the correct
expression to enter is (2/3)(3/4). The student must use
the parentheses in order to get the correct answer.

115.

Applying Concepts 1.3
113.

=

INSTRUCTOR USE ONLY
© Cengage Learning. All Rights Reserved.

Full file at />