Answer:
[tex]0.\bar2=\frac{2}{9}[/tex]
Step-by-step explanation:
We want to find the rational number which is equal to [tex]0.\bar2[/tex].
Let [tex]y=0.\bar2[/tex]....eqn(1)
Multiply both sides by 10
[tex]10y=2.\bar2[/tex].....eqn (2)
Subtract eqn (1) from eqn (2)
[tex]10y-y=2.\bar2-0.\bar2[/tex]
[tex]\implies 9y=2[/tex]
Divide both sides by 9.
[tex]\implies y=\frac{2}{9}[/tex]
