NDA 2025 Maths · Mathematics · Sequences and Series · easy

The recurring decimal 0.27=0.272727… equals the rational number

Single correct option

The recurring decimal

0.\overline{27}=0.272727\ldots

equals the rational number

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Answer: (D) $\dfrac3{11}$

It is a GP:

0.27+0.0027+\cdots

with first term

0.27

and ratio

0.01

. The sum is

\frac{0.27}{1-0.01}=\frac{27}{99}=\frac3{11}

. The value

\frac{27}{100}

is only the first term.

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