How do I convert repeating decimals to fractions

As a couple of examples:

 

.33333.......

let 'x' = .3333333.....

then 10x = 3.33333.....

 

subtract 'x' fro 10x        3.3333.....

                                   -   .3333....

                                  ____________

 

9x     =                          3.0     Solve for 'x'

x = 3/9 = 1/3

 

 

Another one:

.8989898989.......

let 'x' = .8989.....

then 100x = 89.8989.....         (not that we have to use 100x in this example because there are TWO repeating digits)

 

then 100x - x        

                           89.8989........

                         -     .8989.......

                        ____________

99x =                  89.                            Solve for 'x'

x = 89/99

 

 

Do you have SPECIFIC examples of which you need help ???