When the decimal point of a certain positive decimal number is moved four places to the right, the new number is four times the reciprocal of the original number. What is the original number?
$\textbf{(A) }0.0002\qquad\textbf{(B) }0.002\qquad\textbf{(C) }0.02\qquad\textbf{(D) }0.2\qquad\textbf{(E) }2$
If $x$ is the number, then moving the decimal point four places to the right is the same as multiplying $x$ by $10000$. This gives us:  
\[10000x=4\cdot\frac{1}{x} \implies x^2=\frac{4}{10000}\] 
Since \[x>0\implies x=\frac{2}{100}=\boxed{\textbf{(C)}\ 0.02}\]