How can I convert repeated decimal to fraction?

Look here and see how it is done: https://web2.0calc.com/questions/what-is-0-273-repeating-as-a-fraction

 

Like, convert 3.33333333...... or 6.123123123123... or 5.478478478478 or 9.25366666..... to fractions. 

 

3.3333333... =3 1/3

6.123123123.... =6  41/333

5.478478478...=5  478/999

9.253666666....=9 761/3000

Here is how I do it:

x=6.123 123 123....

then

1000x = 6123. 123 123 ....

Now do this:

1000x - x = 999x

6123. 123 123....  - 6.123 123... = 999x

6117 = 999x     divide both sides by 999

x = 6117/999    and simplify (if possible)

x = 2039/333                                                                      6117/999 = 6.1231231231231231