The rational form of a number $1 \cdot \overline{41}$ is
The rational form of a number $1 \cdot \overline{41}$ is
$\frac{154}{99}$
$\frac{55}{99}$
$\frac{140}{99}$
$\frac{41}{99}$
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
$99 x=140$
$x=\frac{140}{99}$ $\therefore 1 . \overline{41}=\frac{140}{99}$