jmc

There are $9$ one-digit positive integers ($1$ through $9$). There are $900$ three-digit positive integers, since there are $100$ three-digit numbers with each hundreds digit from $1$ to $9$. So far, we've counted $909$ positive integers with an odd number of digits. Next are five-digit numbers. Since $909+91=1000$, we're looking for the $91^{\mathrm{st}}$ five-digit number.

The $1^{\mathrm{st}}$ five-digit number is $10000$, so the $91^{\mathrm{st}}$ five-digit number is $10000+90$, or $\boxed{10090}$.