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

The rational form of a number $1 \cdot \overline{41}$ is
  1. $\frac{154}{99}$
  2. $\frac{55}{99}$
  3. $\frac{140}{99}$
  4. $\frac{41}{99}$

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 $99 x=140$ $x=\frac{140}{99}$ $\therefore 1 . \overline{41}=\frac{140}{99}$

Asked in: MHT CET 2020 (16 Oct Shift 2)

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