1.

Express \(0.\)\(2\overline{54}\) as a fraction in simplest form.

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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