0.572 where 7 and 2 are recurring as a fraction

Let x = 0.572727272.....     (1)

 

Multiply (1) by 1000:

1000x = 572.727272.....     (2)

 

Multiply (1) by 10:

10x = 5.72727272.....         (3)

 

Subtract (3) from (2)

990x = 567          (4)

 

Divide both sides of (4) by 990;

x = 567/990

or x = 63/110

.