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NDA 2016 Maths · Mathematics · Sequences and Series · easy

The recurring decimal 0.272727… expressed as a fraction in lowest terms is

Single correct option

The recurring decimal 0.272727…0.272727\ldots expressed as a fraction in lowest terms is
  1. A. 27100\dfrac{27}{100}
  2. B. 937\dfrac{9}{37}
  3. C. 310\dfrac{3}{10}
  4. D. 311\dfrac{3}{11}
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Answer: (D) 311\dfrac{3}{11}

The decimal is the infinite GP 0.27+0.0027+⋯0.27+0.0027+\cdots with first term 0.270.27 and ratio 0.010.01. Its sum is 0.270.99=2799=311\dfrac{0.27}{0.99}=\dfrac{27}{99}=\dfrac3{11}. Writing 27100\tfrac{27}{100} ignores the repetition, and 937\tfrac{9}{37} results from using 999 instead of 99.
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Original question written in the NDA 2016 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake