Answer:
[tex]0.\.{2}=\dfrac{2}{9}[/tex]
Step-by-step explanation:
Let x equal the recurring decimal:
[tex]x=0.\.{2}=0.2222\dots[/tex]
Multiply both sides by 10:
[tex]\implies 10x=2.222\dots[/tex]
Eliminate the recurring part of the decimal by subtracting the equation of x from the equation of 10x:
[tex]\begin{array}{ l r c l}& 10x & = & 2.222...\\\\- & x & = & 0.2222...\\\\\cline{1-4}\\& 9x & = & 2\end{array}[/tex]
Divide both sides by 9:
[tex]\implies x=\dfrac{2}{9}[/tex]
