Comparing rational vs irrational numbers definition and examples for Grade 8

📚 Quick Study Guide

🔍 Rational Numbers: Numbers that can be expressed as a fraction $\frac{p}{q}$, where $p$ and $q$ are integers and $q \neq 0$. 💡 Examples of Rational Numbers: Whole numbers (e.g., 5), integers (e.g., -3), fractions (e.g., $\frac{1}{2}$), terminating decimals (e.g., 0.25), and repeating decimals (e.g., 0.333...). 📝 Irrational Numbers: Numbers that cannot be expressed as a fraction $\frac{p}{q}$. Their decimal representations are non-terminating and non-repeating. ♾️ Examples of Irrational Numbers: $\pi$ (pi), $\sqrt{2}$, $\sqrt{3}$, $e$ (Euler's number, approx. 2.718). ➕ Key Difference: Rational numbers can be written as a simple fraction, while irrational numbers cannot. 📐 Decimals: Terminating or repeating decimals are rational. Non-terminating, non-repeating decimals are irrational.

Practice Quiz

1. Which of the following is a rational number?
   1. $\sqrt{5}$
   2. $\pi$
   3. $\frac{2}{3}$
   4. $0.123456789...$
2. Which of the following is an irrational number?
   1. $0.5$
   2. $\sqrt{16}$
   3. $\sqrt{7}$
   4. $-4$
3. Which statement is always true about rational numbers?
   1. They are non-terminating decimals.
   2. They can be expressed as a fraction $\frac{p}{q}$, where $p$ and $q$ are integers and $q \neq 0$.
   3. They are non-repeating decimals.
   4. They are always positive.
4. Which of the following numbers, when squared, results in a rational number?
   1. $\sqrt{3}$
   2. $\sqrt{8}$
   3. $\sqrt{9}$
   4. $\pi$
5. Which of the following is a repeating decimal and, therefore, rational?
   1. $3.14159...$
   2. $1.41421...$
   3. $0.33333...$
   4. $2.71828...$
6. Which set of numbers does $\sqrt{25}$ belong to?
   1. Irrational numbers only
   2. Rational numbers only
   3. Both rational and irrational numbers
   4. Neither rational nor irrational numbers
7. Classify 0.121221222... as rational or irrational.
   1. Rational
   2. Irrational