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
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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