QUESTION

CSAT

Hard

Maths

Prelims 2020

The recurring decimal representation 1.272727 … is equivalent to

Select an option to attempt

Explanation

  1. Define the decimal (x)(x), x=1.272727…x = 1.272727…, x=1.272727...x = 1.272727...
  2. Separate repeating part, x=1+0.272727...x = 1 + 0.272727..., y=0.272727...y = 0.272727...
  3. Eliminate repeating part, Multiply by 100: 100y=27.272727...100y = 27.272727..., 100y−y=27100y - y = 27
  4. Solve for yy, 99y=27→y=27/99→99y = 27 \rightarrow y = 27/99 \rightarrow Simplify →y=3/11\rightarrow y = 3/11, y=3/11y = 3/11
  5. Combine results, x=1+3/11→x=11/11+3/11x = 1 + 3/11 \rightarrow x = 11/11 + 3/11, x=14/11x = 14/11
  6. Final Answer, Correct Option: (B), 14/1114/11

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