Correct expression of \(0.0\overline {18} = ?\)

This question was previously asked in
NTPC Tier I Previous Paper 16 (Held On: 11 Apr 2016 Shift 2)
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  1. 1/55
  2. 18/100
  3. 18/1000
  4. 1/66

Answer (Detailed Solution Below)

Option 1 : 1/55
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Detailed Solution

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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

\(0.\overline {ab} = ab/99\)

⇒ \(0.0\overline {18} = 18/990\)

⇒ 2/110 = 1/55

∴ The fraction of \(0.0\overline {18} \) is 1/55.
ab = ab/99

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