Why is 0.57 recurring a rational number

0.5757575757... is a rational number because it can be turned into a common fraction.

Let x  =  0.5757575757...   then  100x  =  57.5757575757...

Placing the larger one on top:     100x  =  57.5757575757...

And the smaller one below:               x  =   0.5757575757...

Now, subtract down:                      99x  =  57

Divide by 99:                                   x  =  57/99        a common fraction, a rational number