Q96 / 150 · MHT CET 2020 (16 Oct Shift 2) · Mathematics

The rational form of a number $1 \cdot \overline{41}$ is

  • A
    $\frac{154}{99}$
  • B
    $\frac{55}{99}$
  • Correct answer
    C
    $\frac{140}{99}$
  • D
    $\frac{41}{99}$

Solution

The rational form of a number $1.41$ is $\frac{140}{99}$. Let $x=1.414141 \quad$...(i) $100 x=141.414141 \quad$...(ii) Subtract Eq. (i) from Eq. (ii), we get $99 x=140$ $x=\frac{140}{99}$ $\therefore 1 . \overline{41}=\frac{140}{99}$

Hence, the correct answer is option: 'C'.

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