Question

The recurring decimal $1.\overline{263}\dots$ in a fraction form is equal to

• A. $\frac{1262}{90}$
• B. $\frac{1262}{99}$
• C. $\frac{1262}{999}$
• D. none ofthese

Answer 1

The correct option is C $\frac{1262}{999}$

Let $x=1.263263263$[we multiply it by $1000$]
Here $3$ digits are repeated
$1000x=1263.263263$.....
$x=1.263263$...

$999x=1262$
$=>x=\frac{1262}{999}$
The recurring decimal $1.263$ in a fraction form is equal to $\frac{1262}{999}$