The decimal representation of 71 150 is : - Vidyadip

MCQ

The decimal representation of $\frac{71}{150}$ is :

A
A terminating decimal.
✓
A non-terminating, repeating decimal.
C
A non-terminating and non-repeating decimal.
D
None of these.

✓

Answer

Correct option: B.

A non-terminating, repeating decimal.

A number is a terminating decimal, if the denominator is of the form $2^m \times 5^n,$
where $m$ and $n$ are non $-$ negative integers.
The prime factorisation of the denominator is $2 \times 3 \times 50^2$
So, the denominator will be non $-$ terminating.
Since $\frac{71}{150}$ is a rational number, it will surely be repeating.

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