Answer:
[tex]\frac{1}{9}[/tex]
Step-by-step explanation:
Create 2 equations with the repeating part after the decimal point. Then by subtracting the repeating part is eliminated
let x = 0.1111.... → (1) ← multiply both sides by 10
10x = 1.1111.... → (2)
Subtract (1) from (2) eliminating the repeater, that is
9x = 1 ( divide both sides by 9 )
x = [tex]\frac{1}{9}[/tex]
That is
0.111111... = [tex]\frac{1}{9}[/tex]
