The World of Numbers Exercise 3.5 Class 9 Maths NCERT Solutions

This page solves The World of Numbers Exercise 3.5 from the new Ganita Manjari book of the 2026-27 syllabus. The NCERT Solutions Class 9 Maths Chapter 3 The World of Numbers Exercise 3.5 sort terminating and repeating decimals and classify numbers as rational or irrational, all in clear steps.

• Questions solved: all 5 problems of Exercise 3.5, with full working.
• Main skills: reading terminating or repeating decimals from the denominator.
• Chapter link: it completes the number line from integers to decimals.

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 Exercise 3.5 Cover?

Exercise 3.5 is about decimal expansions of rational numbers. You decide whether a fraction gives a terminating or a repeating decimal by looking at its denominator. You also do a long division for 113 and classify numbers as rational or irrational. The set even looks at the surprising equality 0.9̄=1.

Decimals are just another way to write rational numbers, and this exercise shows the link clearly. The whole set rests on one neat rule about the denominator. If the bottom of a reduced fraction is built only from twos and fives, the decimal stops. If any other prime is left, the decimal repeats for ever. This rule saves you from long division in most questions. It also explains why some fractions, such as one seventh, produce a repeating block that cycles in a fixed order. Understanding this pattern now prepares you for irrational numbers and real numbers in Class 10, which build directly on the same idea.

Video Walkthrough

Source: Vedantu CBSE 10th on YouTube

The World of Numbers Exercise 3.5 Question Breakdown

The five questions test the decimal-expansion rule from every angle. Here is what each one asks.

• Q1: Decide, without long division, which fractions give terminating decimals.
• Q2: Perform the long division for 113 and find its repeating block.
• Q3: Classify given numbers as rational or irrational and find their decimals.
• Q4: Study the number 0.9̄ and what it equals.
• Q5: Explore the cyclic repeating block of 17.

Sample Solved Question from Exercise 3.5

Here is Question 1 of Exercise 3.5, solved step by step so you can see the denominator test.

Question: Without performing long division, decide which of 720, 415, and 13250 give terminating decimals and which repeat.

Step 1. Use the rule: a fraction in lowest form terminates only when its denominator has no prime factor other than 2 or 5. So factorise each denominator.

Step 2. For 720, the denominator is 20=2²× 5. Only 2 and 5 appear, so this decimal terminates.

Step 3. For 415, the denominator is 15=3× 5. The prime 3 is present, so this decimal repeats.

Step 4. For 13250, the denominator is 250=2× 5³. Only 2 and 5 appear, so this decimal terminates as well.

Final answer. 720 and 13250 terminate, while 415 repeats.

How to Use These The World of Numbers Exercise 3.5 Solutions

Test each denominator yourself first, then open the Collegedunia solution to confirm the decimal type. Checking the prime factors is faster than long division.

• Reduce the fraction, then look for any prime other than 2 or 5 in the denominator.
• If only 2 and 5 remain, the decimal terminates, otherwise it repeats.
• Download the free Collegedunia PDF to revise Exercise 3.5 offline.

More Class 9 Maths The World of Numbers Solutions

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