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Rational vs. Irrational Numbers

This worksheet covers Rational vs. Irrational Numbers, which is part of the Number Systems module in the Middle School Math course. Practice problems are designed to strengthen key concepts and build confidence.

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Rational vs. Irrational Numbers

Number Systems • Middle School Math

Set 5 — Mastery

Which of the following numbers is irrational? $\sqrt{2}$ , $\frac{3}{4}$ , $\pi$ , 5

$\sqrt{2}$

$\frac{3}{4}$

$\pi$

Which of the following is a rational number? $\sqrt{3}$ , $\sqrt{16}$ , $\pi$ , e

$\sqrt{3}$

$\sqrt{16}$

$\pi$

Which of the following statements is true? $\pi$ is a rational number; all integers are rational; $\frac{1}{3}$ is irrational.

$\pi$ \text{ is a rational number}

\text{All integers are rational}

$\frac{1}{3}$ \text{ is irrational}

\text{None of the above}

Which of the following is an example of an irrational number? 0.333..., $\frac{22}{7}$ , $\sqrt{5}$ , $\frac{6}{9}$

0.333...

$\frac{22}{7}$

$\sqrt{5}$

$\frac{6}{9}$

Identify the set that contains only rational numbers: { $\frac{1}{2}$ , 3, 0.75 }, { $\sqrt{2}$ , $\sqrt{4}$ }, { $\pi$ , 5.5 }, { 7, -2 }

{ $\frac{1}{2}$ , 3, 0.75 }

{ $\sqrt{2}$ , $\sqrt{4}$ }

{ $\pi$ , 5.5 }

{ 7, -2 }

Which of the following numbers is not a rational number? 5, 0.1, $\sqrt{9}$ , $\sqrt{10}$

0.1

$\sqrt{9}$

$\sqrt{10}$

Which of the following represents a rational number? -4, $\sqrt{11}$ , $\pi$ , 0.142857142857...

-4

$\sqrt{11}$

$\pi$

0.142857142857...

Which number is irrational? -1, $\frac{5}{2}$ , 0.666..., $\sqrt{8}$

-1

$\frac{5}{2}$

0.666...

$\sqrt{8}$

Which of the following is true about $\frac{7}{8}$ ? It is irrational; it can be expressed as a decimal; it cannot be expressed as a fraction.

\text{It is irrational}

\text{It can be expressed as a decimal}

\text{It cannot be expressed as a fraction}

\text{None of the above}

10.

Which of the following is not an irrational number? $\sqrt{7}$ , 3.14, $\sqrt{12}$ , e

$\sqrt{7}$

3.14

$\sqrt{12}$

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