Question

Find an irrational number between $0.1$ and $0.19$.

Answer 1

$0.1$ and $0.19$ are two rational numbers, as it is terminating.

We know, between any two rational numbers, there are infinitely many irrational numbers.

An irrational number has non-terminating non-recurring decimal expansions.

Then irrational number between $0.1$ and $0.19$ can be $\mathrm{0.1010010001...}$.

Similarly, $\mathrm{0.13030030003...}$ is also an irrational number between $0.1$ and $0.19$.

NOTE:

These are some of the possible answers. It might have different solution.