**Question:**

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

**Solution:**

Let $a=0.515115111511115 \ldots$ and $b=0.535335333533335 \ldots$

Here the decimal representation of *a* and *b *are non-terminating and non-repeating. So we observe that in first decimal place *a* and *b* have the same digit but digit in the second place of their decimal representation are distinct. And the number *a* has 1 and *b* has 3. So *a* < *b*.

Hence two rational numbers are $0.5152,0.532$ lying between $0.515115111511115 \ldots$ and $0.535335333533335 \ldots$