NCERT Class 10 Solutions: Real Numbers (Chapter 1) Exercise 1.4 –Part 5

Q-3 The following real numbers have decimal expansions as given below. In each case, decide whether they are rational or not. If they are rational, and of the form, what can you say about the prime factor of q?

Solution:

1. Is terminating

   So, it would be a rational number

   Hence is now in the form of

   And the prime factors of q are in terms of 2 and 5

2. Is non terminating and non-repeating

   So, it is not a rational number

   Therefore, the given number is an irrational number

3. Here is non terminating but repeating decimal

   So, it would be a rational number of the form and q is not of the form

   That is the prime factors of q will also have a factor other than 2 or 5.