The repeating decimal, 0.27..., is converted to the fraction 0.27..=3/xwhat is the value for x in the fraction

Answer:The value of x is 11.Step-by-step explanation:The given number is 0.27272727..., and it is converted to the fraction as[tex]0.272727...=\frac{3}{x}[/tex]                 ..... (1)Multiply both sides by 100.[tex]0.272727...\times 100=\frac{3}{x}\times 100[/tex][tex]27.272727=\frac{300}{x}[/tex]            .... (2)Subtract equation (1) from equation (2),[tex]27.272727-0.272727...=\frac{300}{x}-\frac{3}{x}[/tex][tex]27=\frac{300-3}{x}[/tex]Multiply both sides by x.[tex]27x=297[/tex]Divide both sides by 27.[tex]x=\frac{297}{27}[/tex][tex]x=11[/tex]Therefore the value of x is 11.