Decimal to fraction

1741/333 = 576/333

We don't need to worry about the "5"  part, yet

1)  Take 228  and subtract  the non-repeating part of the decimal  =  228- 22 = 206....this is our numerator

2) In the denominator, write the same number  of 9's as the repeating part  of the decimal= 9

    And write the same  number of 0's as the non-repeating part  of the decimal = 00

So  .228 (8 repeating)  =   206 / 900 =   103 / 450

So we have

5 + 103 / 450   =  2343 / 450

Here is another method :

x   = 5.228

100x = 522.8888.....

1000x = 5228.8888.....

1000x - 100x =  900x =   5228.8888....   - 522.8888....    = 4706

900x = 4706

x = 4706/900   simplify as needed                     (=  5  103/450)