Class 9 Maths Chapter 3, The World of Numbers, is the number-system chapter of Ganita Manjari, told as a history. It moves from herders counting cattle with pebbles to zero, negative numbers, fractions, √2 and π, and closes with a timeline of how each kind of number entered mathematics. The chapter replaces the old Class 9 Number Systems chapter and covers rational and irrational numbers and their decimal expansions.
What Class 9 Maths Chapter 3 Covers
3.1 The Dawn of Mathematics begins in a settlement on the Saraswati river, where a herder checks that every cow has come home by one-to-one correspondence with pebbles in a pot.
3.2 The Revolution of Śhūnya explains how zero became a number and lists Brahmagupta’s rules for zero, followed by 3.3 Integers: Expanding the Horizon.
3.4 Filling the Spaces: Fractions and Rational Numbers places rationals on the number line and works through finding rational numbers between two given ones.
3.5 Irrational Numbers shows why some lengths cannot be written as fractions, asks you to try proving an irrationality yourself, and constructs line segments of irrational length such as √2 on the number line.
3.6 Real Numbers: Decimals and Cyclic Patterns covers terminating, repeating and non-repeating decimals, with a table of steps for converting pure and general repeating decimals into fractions, and the cyclic number 142857 from 1/7, whose multiples by 1 to 6 reuse the same digits in rotation.
Exercises in Chapter 3
- Exercise Sets 3.1 to 3.5: counting and correspondence, operations with zero and integers, rationals between rationals, irrational numbers, and deciding without long division whether fractions such as 7/20, 4/15 and 13/250 give terminating or repeating decimals.
- End-of-Chapter Exercises follow the section 3.7 timeline, The Evolution of Our World of Numbers.
Read Class 9 Maths Chapter 3 Online
More Chapters
- Previous: Chapter 2: Introduction to Linear Polynomials
- Next: Chapter 4: Exploring Algebraic Identities
- Hindi medium: Class 9 Maths Chapter 3 PDF in Hindi (संख्याओं का संसार)
- All Maths chapters and the other Class 9 books: Class 9 NCERT books 2026-27
- All Class 1 to 12 NCERT Textbooks: NCERT Books PDF (Class 1–12)
FAQ
Where are rational and irrational numbers in the new Class 9 maths book?
In Chapter 3, The World of Numbers: rationals in section 3.4, irrationals in 3.5, and decimal expansions in 3.6.
What is the cyclic number in Class 9 Maths Chapter 3?
142857, the repeating block of 1/7. Multiplying it by 1, 2, 3, 4, 5 or 6 gives the same six digits in a rotated order, for example 142857 × 3 = 428571.