Question

find a rational number of from p/q corresponding to the decimal representation 0.222..., where p and q are integers and q not equal 0

Answer 1

Let 0.222... be x.

= x = 0.222.... . 1.

Multiply both sides by 10.

= 10x = 2.222... . 2.

Subtract eq. 1. from 2.

= 10x - x = 2.222... - 0.222...

= 9x = 2

= x = 2/9.

Hope it's helpful to u.