Find the rational number of the form corresponding to the decimal representation 0.222 ..., where p and q are integers and q ≠ 0.

Step-by-step solution

Let x = 0.222 ... = Here, only one digit is repeating. Multiplying both sides by 10, we get 10 x = 2.2222 ... = 10 x – x = 2 9 x = 2 x =