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1. Which of these sets of numbers contains no rational numbers?
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[A] 12,
2
, - 13
[B] - 3.5041, √99, 0.143635
7
[C] - 6, -√225, 48
[D] √81 , 0.75, 0
2. What is the best classification for - 4?
[A] irrational number, real number
[B] integer, rational number, real number
[C] whole number, integer, real number
[D] rational number, real number
3. Which of the following square roots is an irrational number?
[A] −√16
[B] √64
[C] √8
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[D] √64
4. The number 0.8 belongs to which of these sets? Natural number, whole
numbers, integers, rational numbers, irrational numbers, and real numbers.
Name all that apply.
5. Given the following set of numbers, name the irrational numbers.
23,
√3,
2.35, 0,
- 6.555,
4
9
,
-2
6. State whether √168 is a rational number or an irrational number.
7. Classify √9 as rational or irrational.
8. Let ℕ be the set of natural numbers, ℤ the set of integers, ℚ the set of rational
numbers, and ℝ the set of real numbers. Indicate to which sets each of the
following belong:
a.
b.
c.
d.
– 70
0.333…
22
2.7182
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WORKSHEET – CLASSIFYING NUMBERS
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9. The formula 𝑠 = √15𝑑 relates the length of a skid mark d with the speed the
car was traveling, s. If you solved the equation, what type of number would s
be if 0 < d < 15? If d = 15?
10. Classify −√25 as rational or irrational.
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WORKSHEET – CLASSIFYING NUMBERS
www.emathematics.net
KEYS
1. [B]
2. [B]
3. [C]
4. Rational numbers, real numbers.
5. √3
6. Irrational
7. Rational
8. a. ℤ, ℚ, ℝ
b. ℚ, ℝ
c. ℕ, ℤ, ℚ, ℝ
d. ℚ, ℝ
9. real, irrational; real, rational, whole
10. rational
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