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

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Q-1 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

1. Is terminating if

• p and q are co-prime

• And q is of the form Where n and m are non-negative integers

Checking Co-prime

13 and 3125 have no common factors,

So, 13 and 3125 are co-prime

For denominator 3125

Hence

So, denominator is of the form

Where

Thus is terminating decimal

2. Is terminating if

• p and q are co-prime

• And q is of the form Where n and m are non-negative integers

Checking Co-prime

17 and 8 have no common factors,

So, 17 and 8 are co-prime

For denominator 8

Hence

So, denominator is of the form

Where

Thus is terminating decimal

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