The World of Numbers End of Chapter Class 9 Maths NCERT Solutions

This page solves the The World of Numbers End-of-Chapter set from the new Ganita Manjari book of the 2026-27 syllabus. The NCERT Solutions Class 9 Maths Chapter 3 The World of Numbers End-of-Chapter mix integers, fractions, decimals, and short proofs across sixteen questions, each solved in clear steps.

• Questions solved: all 16 End-of-Chapter problems, with full working.
• Main skills: converting decimals, finding numbers between two, and short proofs.
• Chapter link: it revises the whole number-system chapter before your exam.

These solutions are prepared by subject teachers, matched to the 2026-27 NCERT, and checked step by step so a Class 9 student can follow each line.

What Does Class 9 Maths Chapter 3 The World of Numbers End of Chapter Cover?

The End-of-Chapter set is the full revision test for the chapter. It converts decimals to fractions, proves that √5 is irrational, and locates rational numbers on the line. You also find several rational numbers between two given ones and solve short equations. The questions mix every skill from Exercises 3.1 to 3.5.

Because this set pulls from every part of the chapter, it is the best way to judge your readiness for the exam. Some questions ask for a short proof, such as showing that the square root of five is irrational. Others ask you to convert a repeating decimal into a fraction, or to list several rational numbers inside a small gap. A few link numbers to geometry through the length of a hypotenuse. Working through all sixteen questions in order shows you which exercise to revise again before the annual test, so you spend your last days of study where they help the most.

Video Walkthrough

Source: Vedantu CBSE 10th on YouTube

The World of Numbers End of Chapter Question Breakdown

The sixteen questions revise the whole chapter. Here are the main groups they fall into.

• Q1 to Q3: Convert between decimal form and the pq form.
• Q2: Prove that √5 is irrational.
• Q4 to Q7: Locate rationals on the line and find numbers between two given ones.
• Q8 to Q9: Solve short equations involving rational numbers.
• Q10 to Q13: Use the denominator rule for terminating and repeating decimals.
• Q14 to Q16: Handle sum-and-product conditions and a geometry link with hypotenuses.

Sample Solved Question from End of Chapter

Here is Question 5 of the End-of-Chapter set, solved step by step so you can see the method.

Question: Find 6 rational numbers between 3 and 4.

Step 1. Choose a denominator big enough to leave six gaps. Using 7, write 3=217 and 4=287.

Step 2. Take the numerators strictly between 21 and 28, which are 22, 23, 24, 25, 26, 27. That gives exactly six fractions.

Step 3. Check the range. Each numerator lies between 21 and 28, so each fraction lies between 3 and 4.

Final answer. Six such numbers are 227, 237, 247, 257, 267, 277. Many other answers are also correct.

How to Use These The World of Numbers End of Chapter Solutions

Treat this set as a mock revision test. Solve it fully, then open the Collegedunia solution to check each answer and find any weak spot before the annual exam.

• Solve all 16 questions in one sitting to test the whole chapter at once.
• Mark any question you miss, then revisit that exercise for more practice.
• Download the free Collegedunia PDF to revise the End-of-Chapter set offline.

More Class 9 Maths The World of Numbers Solutions

Use the table below to open the full chapter page or any exercise of Class 9 Maths Chapter 3.