Question
Download Solution PDFCorrect expression of \(0.0\overline {18} = ?\)
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFCalculation:
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.
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