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
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
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