Mathematics · Class 9
Number Systems
Rational, irrational, and real numbers; laws of exponents and number line.
3 sections15–25 min read5 MCQs · 2 examples
Chapter Overview
√2 and √3 are irrational — they cannot be written as p/q where p, q are integers and q ≠ 0.
Number Systems in Class 9 introduces rational, irrational, and real numbers. You learn to represent numbers on the number line, convert recurring decimals to fractions, and apply laws of exponents for real numbers.
Types of Numbers
- Natural numbers ℕ, whole numbers, integers ℤ
- Rational numbers ℚ: expressible as p/q
- Irrational numbers: non-terminating non-recurring decimals
- Real numbers ℝ = rational ∪ irrational
Laws of Exponents (a, b > 0)
Product
aᵐ × aⁿ = aᵐ⁺ⁿ
Quotient
aᵐ / aⁿ = aᵐ⁻ⁿ
Power of power
(aᵐ)ⁿ = aᵐⁿ
Rational exponent
a^(m/n) = ⁿ√(aᵐ)
Solved Examples
Step-by-step solutions — read each step before checking the final answer.
Example 1: Classify √7
Is √7 rational or irrational?
- 17 is not a perfect square
- 2√7 cannot be written as p/q
- 3Therefore irrational
Answer
Irrational number
Example 2: Simplify
Simplify 2^(1/3) × 2^(2/3).
- 1Same base: add exponents
- 22^(1/3 + 2/3) = 2¹
Answer
2
Key Points to Remember
- ✓ Every real number has a unique point on number line
- ✓ Between any two rationals, another rational exists
- ✓ Terminating and recurring decimals are rational
Exam Tips
- • Show steps when rationalising denominators
- • Use number line for representation questions
Practice MCQs — Number Systems
Test your understanding with topic-wise multiple choice questions. Explanations appear after each answer.
Question 1 of 5Score: 0/0
π is: