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```Name:__________________________________
th
5.3 Homework: Number Classification
Period: ____
Each of the following numbers are Rational. Write the number as a fraction (a ratio of
two integers, a/b).
3
1. 0
4. 0.8
2. 2 5
3. -√49
3
5. √8
7. -5
6. √20.25
8. 0.22222…
Use their decimal expansions to help classify each number as rational or irrational.
9. 𝜋 = 3.14159…
Irrational
Decimal expansion does not
terminate.
10. √27
12. √18
13.
15.
𝜋
2
18. √6.25
3
3
11. √4
√1
√49
14. √30
16. -18
17. √12
19. 0.1666666…
20. 3.1
5
21. √8
22.
24. 0
25. √169
6
3
3
23. 1.75642689764….
26.
525
7896
27-46 Place each number in the correct box in the diagram above.
-5
7
1
3
4
√12
3
√2
1
−1
2
2.75
0.6666…
√1
3
2𝜋
𝜋
-607
2.5454
52
0
𝜋
2
-2.56
3
√8
√36
√1
Use the diagram above to help you determine if each statement is true of false. Explain
47. Negative numbers are always integers.
48. Irrational numbers are never rational.
49. A whole number is always rational.
50. Decimals can be rational or irrational.
Use their decimal expansions to help you plot the numbers on the number line. Compare the
numbers. Remember that negative numbers get smaller the further you go to the left on the
number line. Use the symbols <,=,>.
3
52.
24
56.
-1.5
√5
-1.55
53. - √36
-2𝜋
54. 23
57.
3
58.
√25
√27
10
3
2
√64
55.
3.333…
59. √16
√2
3
4𝜋
3
Convert the following terminating decimals to fractions. Reduce to lowest terms.
60. 0.35
61. 0.424
62. - 0.13
63. 0.2
Convert each repeating decimal to a fraction a/b. Show all steps. Reduce to lowest terms.
64.
0.4545 …
65.
0.5777…
̅̅̅
0.04
66.
67.
-1.55555…
68. List the first 12 Perfect Squares (without a calculator):
69. List the first 5 Perfect Cubes (without a calculator):
Give the decimal equivalent of the following Benchmark Fractions (without a calculator).
70.
74.
1
2
= _____
71.
= _____
8
75.
1
1
4
= _____
72.
= _____
4
76.
3
78. √45 is in between _____ & ______
3
= _____
73.
3
8
= _____
= _____
3
77.
7
8
= _____
1
3
2
79. √20 is in between _____ & ______
5.3 KEY
1. 0/1
3. -7/1
5. 2/1
7. -5/1
9. GIVEN
11. 2, Rational: It is a Natural Number
13. 1/7, Rational: It can be written as a fraction.
15. 1.57…, Irrational: Decimal does not terminate or repeat.
17. 3.4641…, Irrational: Decimal does not terminate or repeat.
19. Rational, Decimal repeats.
21. 2, Rational: Cube root of a Perfect Cube and 2 is a Natural Number.
23. Irrational: Decimal does not repeat or terminate.
25. 13, Rational, Square root of a Perfect Square and 13 is a Natural Number.
27. -5 is in the Integers Box
29. Square Root of 2 is in the Irrational Box
31. 2.75 is in the Rational Box
33. Square Root of 1 is in the Natural Box
35. 2 pi is in the Irrational Box
37. 7/1 is in the Natural Box
39. Pi is in the Irrational Box
41. 2. 5454 is in the Rational Box
43. 0 is in the Whole Box
45. -2.56 is in the Rational Box
47. False, Some rational numbers are negative and not integers. Ex: -2.56. Irrational numbers
can be negative too.
49. True, Rational Numbers can be written as a fraction and whole numbers can be written as a
fraction by putting a 1 in the denominator
51. No number 51
53. Greater than
55. Less than
57. Greater than
59. Less than
61. 53/125
63. 1/5
65. 26/45
67. -14/9
69. 1, 8, 27, 64, 125
71. 0.25
73. 0.375
75. 0.75
77. 0.875
79. 2 & 3
```
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