2001 AMC 10 Problems/Problem 7

Problem

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?

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

Solution

We can write our equation as:

$\frac{x}{10000}=\frac{4}{x}$

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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2001 AMC 10 Problems/Problem 7

Problem

Solution