Rational and Irrational Numbers
ICSE · Class 9 · Mathematics
Quick revision notes for Rational and Irrational Numbers — ICSE Class 9 Mathematics. Key concepts, formulas, and definitions for last-minute revision.
Key Topics to Revise
1. Introduction to Real Number System
- Real numbers are divided into two main categories: Rational and Irrational numbers
- Imaginary numbers (like √-4) are not part of real numbers
- The complete hierarchy: Real Numbers → Rational/Irrational → Integers/Non-integral rationals → Natural/Whole/Negative integers
2. Rational Numbers (Q)
- Can be expressed as a/b where a, b are integers and b ≠ 0
- a and b must be co-primes (no common factor except 1)
- Every integer and decimal number is rational
3. Decimal Representation of Rational Numbers
- Rational numbers have either terminating or non-terminating recurring decimals
- Terminating: Division ends exactly (like 1/8 = 0.125)
- Non-terminating recurring: Division never ends but digits repeat (like 1/3 = 0.333...)
4. Irrational Numbers (Q̄)
- Cannot be expressed as a/b where a, b are integers
- Have non-terminating, non-recurring decimal representations
- Square roots of non-perfect squares are irrational
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