NCERT Solutions Class 9 Maths Chapter 3 — The World of Numbers#

Chapter 3 explores the number system — from natural numbers and integers to rational and irrational numbers that together make up the real numbers. You will represent numbers on the number line, work with decimal expansions, and understand what makes a number rational or irrational.

Exercises#

• Exercise Set 3.1 — Counting with natural numbers, the Ishango bone primes, closure under subtraction, base-12 finger counting (4 questions)
• Exercise Set 3.2 — Integers as fortunes and debts, Brahmagupta’s rules for signs (4 questions)
• Exercise Set 3.3 — Equal rational numbers, sum, difference, product, quotient, distributive property (8 questions)
• Exercise Set 3.4 — Rational numbers on the number line, rational numbers between two numbers (6 questions)
• Exercise Set 3.5 — Terminating and repeating decimals, cyclic numbers, rational or irrational, $0.\overline{9} = 1$ (5 questions)
• End-of-Chapter Exercises — Long division, proving $\sqrt{5}$ irrational, repeating decimals to $\dfrac{p}{q}$, successive magnification, the square root spiral (16 questions)

What you will learn#

• How number systems grew: natural numbers, integers, rational and irrational numbers.
• Brahmagupta’s rules for signs and operations on rational numbers.
• Terminating and repeating decimals, and turning repeating decimals into fractions.
• Proving that numbers like √5 are irrational, and placing numbers on the real number line.

Key formulas and results#

• A fraction $\dfrac{p}{q}$ in lowest terms has a terminating decimal exactly when $q$ has no prime factors other than 2 and 5.
• Every rational number has a terminating or repeating decimal; irrational numbers have neither.

Read and revise#

• NCERT Class 9 Maths Chapter 3 (PDF) — the Ganita Manjari Part I chapter itself.
• All Class 9 Maths chapters from Ganita Manjari Part I and Part II.

Frequently asked questions#