Give two rational numbers lying between 0.515115111511115…. and 0.5353353335….

Let a = 0.515115111511115….

b = 0.5353353335….

We observe that 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

Then,

a < x < y < b

Hence, x and y are required rational numbers.