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2-5 Irrational Numbers
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Date
Irrational numbers are not rational numbers. They are numbers that
cannot be expressed as quotients of two integers, a , where b ! 0.
b
Some irrational numbers are:
38 ; " 95
square roots of nonperfect squares
0.3452799. . . , 0.101001000. . .
nonterminating and nonrepeating decimals (including #)
0.23233423342323. . .
decimals that have a pattern but do not terminate or repeat exactly
Find a rational approximate value for
On a calculator, press:
38 to the nearest hundredth.
6.164414003.
38
38 ! 6.16.
To the nearest hundredth,
Classify each number as rational or irrational.
1. 6
2. 0.4321
3. 12
rational
6. 0.245245245. . .
rational
11. ("0.3)4
Copyright © by William H. Sadlier, Inc. All rights reserved.
13.
17. "14#
rational
21. 0.1234
14.
20
4
irrational
irrational
15.
40
9
25
irrational
16
81
rational
20. "0.407
rational
rational
24. 1 78
rational
irrational
irrational
19.
22. 0.454564567. . . 23. 3 25
rational
irrational
rational
18.
rational
9. 0.676776777. . . 10. " 5
13#
#
irrational
5. (6.3)2
rational
rational
rational
rational
16. "14
8. 0.707
12. 8#
25
irrational
23
7. " 768
rational
4.
25.
rational
118
irrational
Find a rational approximate value to the given place.
Use a calculator.
26.
27. " 34 to the nearest thousandth
19 to the nearest tenth
Press
19
4.358898944
to the nearest tenth, 19 ≈ 4.4
28.
5 to the nearest hundredth
3
!5.831
29. 2 to the nearest thousandth
7
0.756
0.75
Lesson 2-5, pages 44–45.
Chapter 2
47
For More Practice Go To:
Find a rational approximate value to the given place.
Use a calculator.
30. " 11 to the nearest tenth
—3.316624790
31.
Press
11
7
8
to the nearest tenth
.
0.9
!3.3
32.
6 to the nearest thousandth
3
33.
19
11
to the nearest thousandth
1.314
0.816
Find one rational and one irrational number between each pair
of numbers. Check students’ answers. Possible answers shown.
10 " 102 " 100
11 " 112 " 121
101, 102, . . . , 119, 120
35. 3 and 4
10.5 and 107
37. "2 and "1
3.1 and
38.
20 and
!7.5 and ! 50
11
39.
27
5 and
!1.4 and ! 2
40. 4 12 and 5
36. "8 and "7
50
42. 3 and 3.5
!12 and !0.010010001. . .
43. George buys 450 tiles. Each tile is 1 foot
by 1 foot. Is it possible for George to use
exactly 450 tiles to cover the floor of a square
room? Explain your answer.
51
7 and
21
41. 0 and " 34
4.75 and
4.606006000. . .
48 and
3.25 and #
44. A square reflecting pool has an area of
183.84 square meters. What is the
approximate perimeter of the reflecting pool?
s " 183.84 " 13.5587. . . ! 13.56
P " 4(13.56) " 54.24 meters
The approximate perimeter is 54.24 m.
No; since 450 is irrational, a square
room cannot be exactly 450 ft2.
Simplify.
3
5
45. ["3(12(12
) " 23)]
!2197
48
Chapter 2
2
46. 5[(25) " (3 • 15 $ 115)]
!815
2
3
• (" 12 )
47. (34 • 45) " 1 $ 10
79
! 100
Copyright © by William H. Sadlier, Inc. All rights reserved.
34. 10 and 11