Express the 0.12 and bar on 2 as a fraction in simplest form

1.	Express the 0.12 and bar on 2 as a fraction in simplest form
Answer» Let we have ,{tex}x= 0.1 \\overline { 2 }{/tex}, then{tex}x{/tex}\xa0= 0.12222....{tex}\\implies{/tex}10x\xa0= 1.2222.... ...(i){tex}\\implies{/tex}100x= 12.2222... ...(ii)Subtracting (i) from (ii), we get{tex}\\implies{/tex}100x-10x=11{tex}\\implies90 x = 11 \\quad \\therefore x = \\frac { 11 } { 90 }{/tex}Thus the value of x ={tex}0.1\\overline {2}{/tex} is equal to\xa0{tex}\\frac {11}{90}{/tex}

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