Q. 1

# A number having non-terminating and recurring decimal expansion is –

A. an integer

B. a rational number

C. an irrational number

D. a whole number

Answer :

By definition, a rational number is one which follows either of the following 2 conditions:

1. __It can be expressed in__ __form where p and q are integers (q__ __≠__ __0).__

2. __Its decimal expansion is either terminating or non-terminating recurring.__

Ex. – 0.35 (terminating decimal expansion) → Rational number

0.7777…. = (non-terminating but recurring i.e. the number does not terminate but its digits follow a pattern.) → Rational number

π = 3.14…… (Non-terminating non recurring) → Irrational number

Hence, the answer.

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