Let, a = 0.515115111511115...

And, b = 0.5353353335...

We observe that in the second decimal place a has digit 1 and b has digit 3, therefore,

a < b . So if we consider rational numbers

x = 0.52

y = 0.52052052...

We find that,

a < x < y < b

Hence x, and y are required rational numbers