How can I convert a repeating decimal into a fraction in simplest form?

Question

Example :       .4444444444 (repeating) in fraction with simplest form

Answer 1

0.4444=4/9

me ges yu get speerans after yu see such stuf 50 yeers

other kommon stuf=x/11, such as 2/11=0.1818181818

big-braen boys sae: take 18/99, then see hav kommon fakter=9

so 18/99 =2/11

sum others: 1/6=0.166666

1/7=0.1428571

Answer 2

Let x=0.4444444………   -1

10x=4.4444444…………. -2

eq 2-eq1 we get 9x=4

therefore x=4/9