Question 31
Let $f(n)$ denote the number of $0$’s in the decimal representation of the positive integer $n$. For example, $f(10001123)=3$ and $f(1234567)=0$. Let
$$M=f(1)\times2^{f(1)}+f(2)\times2^{f(2)}+f(3)\times2^{f(3)}+\cdots+f(99999)\times2^{f(99999)}.$$
Find the value of $M-100000$.
$$M=f(1)\times2^{f(1)}+f(2)\times2^{f(2)}+f(3)\times2^{f(3)}+\cdots+f(99999)\times2^{f(99999)}.$$
Find the value of $M-100000$.