Question

Express the decimal number 2.̅218 ̅̅̅̅ in the form of

where p and q are integers and q≠0.

Answer 1

$let \: x = 2.218 \: where \: 8 \: is \: recurring$
$x = 2.2188....$
$100x = 218.88... (i)$
$1000x = 2218.88.....(ii)$
$now \: (ii) - (i)$
$1000x - 100x = 2218.88 - 218.88$
$900x = 2000$
$x = \frac{2000}{900} = \frac{20}{9}$