A positive integer $n$ is known as an interesting number if $n$ satisfies $$ \left\{\frac{n}{10^k}\right\} > \frac{n}{10^{10}} $$ for all $k=1, 2, \ldots, 9$, where $\{x\}=x - \lfloor x \rfloor$.
Find the number of interesting numbers.
A positive integer $n$ is known as an interesting number if $n$ satisfies $$ \left\{\frac{n}{10^k}\right\} > \frac{n}{10^{10}} $$ for all $k=1, 2, \ldots, 9$, where $\{x\}=x - \lfloor x \rfloor$.
Find the number of interesting numbers.