Class 9 Mathematics Chapter 3 The World of Numbers – Revision Notes

Quick revision notes for Class 9 Maths Chapter 3 (The World of Numbers). These Class 9 Mathematics Chapter 3 notes are ideal for quick revision just before exams.

Number Types

• Rational: p/q form, terminating or repeating decimal.
• Irrational: non-terminating, non-repeating decimal (√2, π).
• Real numbers = rational + irrational.

Operations

• rational ±×÷ rational = rational.
• rational ± irrational = irrational.
• irrational × irrational = rational OR irrational (depends).

Number Line Representation

• √2 via Pythagoras construction (legs=1,1 → hypotenuse=√2).

Laws of Exponents

• a^m×aⁿ=a^m+n; a^m/aⁿ=a^m-n; (a^m)ⁿ=a^mn; a^mb^m=(ab)^m.

Rationalisation

• Convert irrational denominator to rational by multiplying by suitable term.

One-Line Summary

Real numbers combine rationals (p/q form) and irrationals (non-terminating, non-repeating decimals), both representable on the number line, governed by exponent laws and rationalisation techniques for simplification.

Written by Satish

NCERTBooks.org is an independent educational resource run by a small team focused on making official NCERT textbooks easy to find, read, and download for students, parents, and teachers across India. We are not affiliated with NCERT or the Ministry of Education -- we organise publicly available NCERT content by class and subject, verify links against official sources, and build tools (like our in-browser reader) that make studying more convenient. Every guide we publish is written and reviewed by our team based on the actual NCERT curriculum and syllabus.