Grade 8 Math Practice Test: Rational and Irrational Numbers
- Rational and Irrational Numbers
- 10 questions
- 15 minutes
This test covers telling rational and irrational numbers apart, writing repeating decimals as fractions, estimating square roots and solving x2 = p and x3 = p. Tip: the square root of a whole number that is not a perfect square is irrational.
Tap an option to mark your answer. You can change your mind, or tap the same option again to leave the question blank. The correct answers and explanations appear when you finish the test.Tap an option to answer; tap it again to leave the question blank.
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Question 1
Which number is irrational?
Correct answer: D
50 is not a perfect square, so 50 is a non-repeating, non-terminating decimal. 49 = 7, a repeating decimal is rational, and 37 is a fraction of integers.
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Question 2
Which fraction is equal to 0.444… (the 4 repeats forever)?
Correct answer: B
Let x = 0.444…; then 10x = 4.444…, so 9x = 4 and x = 49. 25 = 0.4 ends after one digit.
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Question 3
Which fraction is equal to 0.181818… (the 18 repeats forever)?
Correct answer: C
Let x = 0.1818…; then 100x = 18.1818…, so 99x = 18 and x = 1899 = 211. 950 = 0.18 does not repeat.
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Question 4
Between which two consecutive whole numbers does 70 lie?
Correct answer: A
82 = 64 and 92 = 81, and 70 lies between them, so 70 is between 8 and 9. 34 and 36 come from halving 70.
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Question 5
Which is the best estimate of 30?
Correct answer: A
5.52 = 30.25, very close to 30. 5.12 = 26.01 and 6.22 = 38.44 are much farther away. 15 is half of 30, not its square root.
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Question 6
Which list orders the numbers from least to greatest?
10, π, 3.2, 196
Correct answer: A
π ≈ 3.142, 10 ≈ 3.162, 196 ≈ 3.167 and 3.2. Writing each as a decimal to three places makes the order clear.
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Question 7
What are all the solutions of x2 = 81?
Correct answer: C
Both 9 · 9 and (−9)(−9) equal 81, so there are two solutions. Writing only 9 misses the negative root.
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Question 8
Solve: x3 = −64
Correct answer: B
(−4)(−4)(−4) = −64. The cube root of a negative number is negative. −8 confuses cubing with squaring: 8 · 8 = 64, but (−8)3 = −512.
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Question 9
Which statement is true?
Correct answer: D
If a nonzero rational times an irrational were rational, dividing by the rational would make the irrational number rational. 2 + (−2) = 0 is rational, 9 = 3 is rational, and 22/7 is only an approximation of π.
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Question 10
A square garden has an area of 200 m2. Between which two whole numbers is the length of one side, in meters?
Correct answer: B
The side is 200. 142 = 196 and 152 = 225, so the side is between 14 and 15 m. 50 comes from dividing the area by 4 as if it were the perimeter.
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