2004
Problem - 3274
Find the length of the leading non-repeating block in the decimal expansion of $\frac{2004}{7\times 5^{2003}}$. For example the length of the leading non-repeating block of $\frac{5}{12}=0.41\overline{6}$ is $2$.
Because $\frac{2004}{7\times 5^{2003}}$ can be rewritten as $\frac{A}{7} + \frac{B}{5^{2003}}$. The formal is a repeating decimal and the latter is a string of 2003 digits without repeating. Therefore, the answer is $\boxed{2003}$.
Note: the reason that $\frac{2004}{7\times 5^{2003}}$ can be rewritten as $\frac{A}{7} + \frac{B}{5^{2003}}$ is explained in the book Power Calculation .