Undoubtedly Rational

Algebra Level 4

$\large {\begin{aligned} N &=&1 + 0.02 + 0.0003 + 0.000004 + \cdots + \dfrac n{100^{n-1}} + \cdots \\ &=& 1.02030405\ldots\end{aligned}}$

Given that $N$ represents an infinite arithmetic-geometric progression sum and it can be expressed as $\dfrac ab$ , where $a$ and $b$ are coprime positive integers. Find $a-b$ .