Question 71318
Let y = .444444444(and so on)
so, 10y = 4.4444444(and so on)
so, 10y - y = 4.444444(and so on) - .4444444(and so on)

Now as we assume that 4 is repeating after the decimal place indefinitely so we can easily approximate the decimal parts of 4.44444444 & .44444444 to be equal so ,   
10y - y = 4
9y = 4
y = 4/9   Answer.