NCERT Class 10 Solutions: Real Numbers (Chapter 1) Exercise 1.4 –Part 1
Q1 Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non terminating repeating decimal expansion:
Solution:

We know that if the denominator of a rational number has no prime factors other than 2 or 5

Then it is expressible as a terminating, otherwise it has non terminating repeating decimal representation

Thus, we will have to check the prime factors of the denominators of each of the given rational numbers

Is terminating if

p and q are coprime

And q is of the form Where n and m are nonnegative integers
Checking Coprime
13 and 3125 have no common factors,
So, 13 and 3125 are coprime
For denominator 3125
Hence
So, denominator is of the form
Where
Thus is terminating decimal


Is terminating if

p and q are coprime

And q is of the form Where n and m are nonnegative integers
Checking Coprime
17 and 8 have no common factors,
So, 17 and 8 are coprime
For denominator 8
Hence
So, denominator is of the form
Where
Thus is terminating decimal