Chapter 1 Real Numbers Ex 1.4

Chapter 1 Real Numbers Ex 1.4

Question 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:

Solutions:

Question 2.
Write down the decimal expansions of those rational numbers in Question 1 above which have terminating decimal expansions.
Solutions:
In Question 1, (i), (ii), (iv), (vi), (viii) and (ix) are having terminating decimal expansion.

Question 3.


Here, q = 29 x 59, So prime factorisation of q is of the form 2ⁿ x 5^m.

(ii) 0.120120012000120000…
Since the decimal expansion is neither terminating nor non-terminating repeating, therefore the given real number is not rational.