Respuesta :
[tex]\bf 6.25\overline{25}\qquad x=6.25\overline{25}[/tex]
now... .let's multiply "x" by some power of 10, that will move the "recurring decimal" over to the left-hand-side of the decimal dot.... since is two decimals, then we'll use 100, thus
[tex]\bf x=6.25\overline{25} \\\\\\ \begin{array}{llll} 100x&=&625.25\overline{25}\\ &&619+6.25\overline{25}\\ &&619+x \end{array}\implies 100x=619+x\implies 99x=619 \\\\\\ x=\cfrac{619}{99}\implies x=6\frac{25}{99}[/tex]
now... .let's multiply "x" by some power of 10, that will move the "recurring decimal" over to the left-hand-side of the decimal dot.... since is two decimals, then we'll use 100, thus
[tex]\bf x=6.25\overline{25} \\\\\\ \begin{array}{llll} 100x&=&625.25\overline{25}\\ &&619+6.25\overline{25}\\ &&619+x \end{array}\implies 100x=619+x\implies 99x=619 \\\\\\ x=\cfrac{619}{99}\implies x=6\frac{25}{99}[/tex]
