Express 0.2545454............. As a fraction in simplest form

1.	Express 0.2545454............. As a fraction in simplest form
Answer» Let {tex}x = 0.2 \\overline { 54 }{/tex} .Then, x = 0.2545454... ...(i) ( multiply 10 on both sides){tex}\\therefore{/tex} 10x = 2.545454... ...(ii)and 1000x = 254.545454... ... (iii)Subtract\xa0(ii) from (iii), we get990x = 252 {tex}\\Rightarrow x = \\frac { 252 } { 990 } = \\frac { 126 } { 495 } = \\frac { 42 } { 165 } = \\frac { 14 } { 55 }{/tex}.{tex}\\therefore \\quad 0.2 \\overline { 54 } = \\frac { 14 } { 55 }{/tex}

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