NCERT Ganita Manjari, Class 9, textbook pages 41–67 (Part I)

How to help your child with Class 9 Maths Chapter 3, The World of Numbers, at home

Number systems: rational and irrational numbers, explained for parents: a 30-minute study session, a quick challenge, a 5-day plan and the mistakes to watch for.

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NCERT Class 9 Maths Chapter 3 The World of Numbers: what it teaches

From counting numbers to integers, fractions and beyond: your teen explores rational numbers (terminating and repeating decimals), irrational numbers like √2 and π, locates them on the number line, and learns why √2 cannot be a fraction.

Why it matters later. Real numbers underpin algebra, surds and Class 10 real numbers.

See it: this chapter in pictures

1 ÷ 7= 0.142857142857…recurring: rational
Recurring decimals are rational.
x = 0.333…10x = 3.333…9x = 3 → x = 1/3
Subtract to cancel the repeating part.
natural ⊂ whole ⊂ integers⊂ rationals ⊂ realsirrationals: √2, π
Each set sits inside the next.

You need

  • a calculator
  • a ruler and compass
  • graph paper

Tonight’s 30 minutes

  1. Divide 1 by 7 and see the repeating decimal 0.142857…
  2. Construct √2 on a number line using a 1-by-1 square’s diagonal and a compass.
  3. Sort numbers into natural, whole, integer, rational, irrational: 0, −3, 2/5, √9, √5, π.
  4. Convert 0.333… to a fraction (1/3).

Words to use

  • natural
  • integer
  • rational
  • irrational
  • terminating
  • recurring
  • real numbers

Watch for

  • Thinking π = 22/7 exactly. 22/7 is an approximation; π is irrational.
  • Calling √9 irrational. √9 = 3, rational.

What it sounds like at home

A short example of the conversation. Your words will differ; the questions are what matter.

YouIs π equal to 22/7?

Your childNo, that’s only close.

A game for this week: Number sorter

  1. Write 15 numbers on cards.
  2. Players sort them into sets.
  3. Explain each choice.
  4. Most correct explanations wins.

A 5-day plan, 30 minutes a day

  1. Day 1Repeating decimals.
  2. Day 2√2 on the number line.
  3. Day 3Sorting number types.
  4. Day 4Decimals to fractions.
  5. Day 5Number sorter.

Everyday moments to practise

  • Measurements with √2 (A4 paper ratio).
  • Circles and π.
  • Repeating decimals in prices.
  • Calculator limits.

Quick check

Ask these at the end of the week. Tap to see the answer.

Is √5 rational?

No.

0.333… as a fraction?

1/3.

Is 0.75 rational?

Yes, 3/4.

Ready for the next chapter when your child…

  • Classifies numbers.
  • Converts recurring decimals to fractions.
  • Locates √2 on a number line.

Activities, wording and illustrations are Mathify Kids’ own, following the topics of NCERT’s Ganita Manjari (Class 9). See the full Class 9 parent guide for every chapter.

Questions parents ask

What is an irrational number?

A number that can’t be written as p/q; its decimal never ends or repeats.

Why is √2 irrational?

Assuming √2 = p/q in lowest terms leads to both being even, a contradiction.

Are all square roots irrational?

No: √9 = 3 and √16 = 4 are rational.