2001 AMC 10 Problems/Problem 7

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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?

$\textbf{(A) }0.0002\qquad\textbf{(B) }0.002\qquad\textbf{(C) }0.02\qquad\textbf{(D) }0.2\qquad\textbf{(E) }2$


We can write our equation as:


Cross-multiply and solve for x.

$x^2=40000 \implies x=200$.

$ 200/10000=2/100= \boxed{\textbf{(C) }0.02}

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