Decimal expansion of 23 (2^3 5^2 ) will be: - Vidyadip

MCQ

Decimal expansion of $\frac{23}{\left(2^3 5^2\right)}$ will be:

✓
Terminating
B
Non-terminating
C
Non terminating and repeating.
D
Non-terminating and non-repeating

✓

Answer

Correct option: A.

Terminating

(a)
We know by a theorem that, If $x=\frac{p}{q}$ be a rational number, such that the prime factorization of $q$ is in the form $2^n 5^m$, where $n, m$ are non-negative integers. Then $x$ has a decimal expansion which terminates.
Hence, Decimal expansion of $\frac{23}{2^3 5^2}$ will be terminating
So, the correct option is (a).

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