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Express \(0.\)\(2\overline{54}\) as a fraction in simplest form. |
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Answer» Let x = 0.2bar(54) = 0.2545454... … (1) 100x = 25.45454545…. … (2) Now, Subtracting equation (1) from equation (2), we get 100x – x = (25.454545….) – (0.25454545….) ⇒ 99x = 25.2 = \(\frac{252}{10}\) = \(\frac{126}{5\times 99}\) ⇒ x = \(\frac{126}{5\times 99}\) = \(\frac{14}{5\times 11}\) = \(\frac{14}{55}\). Hence, Simplest form of \(0.2\overline{54}\) is \(\frac{14}{55}\). |
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