Understanding Rational Numbers: Definition and Examples

📚 Quick Study Guide

🔢 Definition: A rational number is any number that can be expressed as a fraction $\frac{p}{q}$, where $p$ and $q$ are integers and $q \neq 0$. ➕ Integers: Remember that integers include all whole numbers (positive, negative, and zero). ➗ Non-Zero Denominator: The denominator ($q$) cannot be zero, as division by zero is undefined. ➕ Examples:
💡 Fractions: $\frac{1}{2}$, $\frac{-3}{4}$, $\frac{5}{1}$ ✅ Decimals: 0.5, -0.75, 2.0 (terminating or repeating decimals) 💯 Integers: -3, 0, 5 (can be written as $\frac{-3}{1}$, $\frac{0}{1}$, $\frac{5}{1}$)
➖ Non-Examples: Numbers that cannot be expressed as a fraction of two integers, like $\pi$ or $\sqrt{2}$, are not rational numbers. 📊 Representation on Number Line: Rational numbers can be accurately plotted on a number line.

Practice Quiz

1. Which of the following is a rational number?
   1. $\sqrt{3}$
   2. $\pi$
   3. $\frac{2}{7}$
   4. $\sqrt{-1}$
2. Which of the following decimals represents a rational number?
   1. 3.14159...
   2. 0.3333...
   3. 1.41421...
   4. 2.71828...
3. Which of the following numbers is NOT a rational number?
   1. 0
   2. -5
   3. $\sqrt{5}$
   4. $\frac{1}{3}$
4. Which of the following fractions is equivalent to a rational number?
   1. $\frac{\pi}{2}$
   2. $\frac{\sqrt{2}}{3}$
   3. $\frac{5}{0}$
   4. $\frac{7}{1}$
5. Which set of numbers are all rational?
   1. 2, $\sqrt{4}$, $\frac{1}{2}$
   2. 3, $\pi$, 0.5
   3. $\sqrt{2}$, 1, -1
   4. $\frac{1}{3}$, 0, $\sqrt{3}$
6. Is 0.121221222... a rational number?
   1. Yes, because it is a decimal.
   2. No, because the pattern does not repeat or terminate.
   3. Yes, because all decimals are rational.
   4. No, because it is too long.
7. Which of the following is a rational number between 0 and 1?
   1. $\sqrt{2}$
   2. $\pi$
   3. $\frac{1}{4}$
   4. $\sqrt{3}$