NCERT Class 10 Solutions: Real Numbers (Chapter 1) Exercise 1.4 –Part 5
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Q3 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:

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

Is non terminating and nonrepeating
So, it is not a rational number
Therefore, the given number is an irrational number

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.