Correct expression of $0.0\overline {18} = ?$

Question

Question

This question was previously asked in

NTPC Tier I Previous Paper 16 (Held On: 11 Apr 2016 Shift 2)

Attempt Online

Answer 1

Calculation:

Let x = 0.0181818....

⇒ 10x = 0.1818.... ----eq (1)

⇒ 1000x = 18.1818.... ----eq (2)

Now, eq (2) - eq (1)

⇒ 1000x - 10x = 18.1818... - 0.1818...

⇒ 990x = 18

⇒ x = 18/990

⇒ x = 1/55

∴ The fraction of $0.0\overline {18} $ is 1/55

Shortcut Trick

$0.\overline {ab} = ab/99$

$\bar{a b}$

⇒ $\bar{a b}$

⇒ 2/110 = 1/55

∴ The fraction of $0.0\overline {18} $ is 1/55.
$\bar{a b}$