What are Irrational Numbers? Definition & Examples for Grade 8

📚 Quick Study Guide

• 🔢 An irrational number is a real number that cannot be expressed as a simple fraction $\frac{p}{q}$, where $p$ and $q$ are integers and $q \neq 0$.
• ♾️ Irrational numbers have decimal representations that neither terminate nor repeat.
• ➗ Rational numbers can be written as a fraction, while irrational numbers cannot.
• 🌱 Examples of irrational numbers include $\sqrt{2}$, $\sqrt{3}$, and $\pi$ (pi).
• 💡 The set of irrational numbers, combined with rational numbers, makes up the set of real numbers.

Practice Quiz

1. Which of the following numbers is an irrational number?
   1. 3.14
   2. $\frac{1}{3}$
   3. $\sqrt{4}$
   4. $\sqrt{5}$
2. Which statement is true about irrational numbers?
   1. They can be expressed as a ratio of two integers.
   2. Their decimal representations terminate.
   3. Their decimal representations repeat.
   4. Their decimal representations neither terminate nor repeat.
3. Which of the following is a rational number?
   1. $\pi$
   2. $\sqrt{7}$
   3. 0.25
   4. $\sqrt{11}$
4. Which number is NOT an irrational number?
   1. $\sqrt{2}$
   2. $\sqrt{3}$
   3. $\sqrt{9}$
   4. $\pi$
5. Which of the following is an irrational number?
   1. $\frac{2}{5}$
   2. 0.75
   3. $\sqrt{16}$
   4. $\sqrt{8}$
6. Is the sum of two irrational numbers always irrational?
   1. Yes
   2. No
   3. Sometimes
   4. It depends on the numbers
7. Which of the following correctly identifies $\pi$?
   1. Rational number
   2. Integer
   3. Irrational number
   4. Whole number