Download 1-1 Rational and Irrational Numbers

1-1 Rational and Irrational Numbers
Name
Date
Write all classifications of 2.1 that apply (rational number, fraction,
mixed number, integer, repeating decimal, terminating decimal,
irrational number).
21
2.1 can be written as the fraction 10 , so 2.1 is rational number.
2.1 is not a fraction, mixed number, integer, irrational number
or repeating decimal.
2.1 is a terminating decimal.
Remember: Numbers that are
not rational are irrational, such as
decimals that do not terminate or
repeat, square roots of nonperfect
squares, and the number ␲.
So 2.1 is rational number and a terminating decimal.
Approximate the value of 86 .
81
81 ⬍
9 ⬍
86
86 ⬍
86 ⬍
100
100
10
Locate 86 between two consecutive perfect squares.
81 ⫽ 92 and 100 ⫽ 102
Find the square roots of the two consecutive perfect squares.
So 86 lies between 9 and 10, closer to 9 (since 86 is closer to 81 than to 100).
For each number, list all the terms that apply: fraction, mixed number, integer,
repeating decimal, terminating decimal, rational number, and irrational number.
1. 36
integer,
terminating decimal,
rational number
2
Copyright © by William H. Sadlier, Inc. All rights reserved.
4. 5
integer,
terminating decimal,
rational number
5.
fraction,
rational number
7. 2.8
17
2. ⫺8
10. ⫺0.21384269. . .
irrational number
7
irrational number
11. ⫺ 36
integer,
terminating decimal,
rational number
12
mixed number,
rational number
16. 0
mixed number,
rational number
17. 9.25
integer,
terminating decimal,
rational number
terminating decimal,
rational number
Lesson 1-1, pages 2–3.
23
irrational number
9. 2.010010001. . .
repeating decimal,
rational number
14. ⫺9 13
13. 9 8
fraction,
rational number
6.
2
8. 6.1234
repeating decimal,
rational number
3. ⫺ 3
irrational number
12.
25
integer,
terminating decimal,
rational number
15. ⫺115
integer,
terminating decimal,
rational number
18. 13.0606
terminating decimal,
rational number
Chapter 1
1
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If the number is rational, find its square root. If the radicand is a nonperfect square,
give the two consecutive integers it lies between, and the closer integer.
19.
20.
30
25 30 36
5 30 6
5 and 6; 5
23.
27.
31.
13
9 13 16
3 13 4
3 and 4; 4
64 70 81
8 70 9
8 and 9; 8
24.
16 24 25
4 24 5
4 and 5; 5
28.
50
105
32.
3
100 105 121
10 105 11
10 and 11; 10
35. ⫺ 121
49 50 64
7 50 8
7 and 8; 7
1 3 4
1 3 2
1 and 2; 2
36. ⫺ 225
ⴚ 121 ⴝ ⴚ 11 • 11
ⴚ11
ⴚ 225 ⴝ ⴚ 15 • 15
ⴚ15
22.
81
9
81 ⴝ 9 • 9
9
25.
24
145
144 145 169
12 145 13
12 and 13; 12
21.
70
9ⴝ
26.
100
16
16 ⴝ 4 • 4
4
100 ⴝ 10 • 10
10
29.
79
30.
62
33.
10
34.
95
64 79 81
8 79 9
8 and 9; 9
9 10 16
3 10 4
3 and 4; 3
37. ⫺ 150
ⴚ 144 ⴚ 150 ⴚ 169
ⴚ12 ⴚ 150 ⴚ13
ⴚ13 and ⴚ12; ⴚ12
3•3
3
49 62 64
7 62 8
7 and 8; 8
81 95 100
9 95 10
9 and 10; 10
38. ⫺ 130
ⴚ 121 ⴚ 130 ⴚ 144
ⴚ11 ⴚ 130 ⴚ12
ⴚ12 and ⴚ11; ⴚ11
Solve. Show your work
A ⴝ s2; s ⴝ
A; 2 5 9; s 艐 2; 2 ft
41. The area of a square is 24.783 square feet.
Find the width of the side of the square to the
nearest integer. Explain your reasoning.
5 ft; round 24.783 to 25; the square root of
25 is 5.
40. A farmer’s square field covers 2000 square feet.
Find the length of the side of the field to the
nearest integer.
A ⴝ s2; s ⴝ
A; 44 42. If the lengths of the sides of a square are
between 3.7 feet and 5.2 feet and the area is a
perfect square, then what are the possible areas
of the square?
16 square feet and 25 square feet
43. Explain how to find the next five perfect squares after 100. Then find them.
Since 100 ⴝ 102, find 112, 122, 132, 142, and 152; 112 ⴝ 121, 122 ⴝ 144, 132 ⴝ 169,
142 ⴝ 196, and 152 ⴝ 225.
2
Chapter 1
2000 45; s 艐 45; 45 ft
Copyright © by William H. Sadlier, Inc. All rights reserved.
39. A cabinet door in the shape of a square covers
5 square feet. Find the length of the side of the
door to the nearest integer.