# Difference between revisions of "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 1

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 the equation $$10000x=4\cdot\frac{1}{x}$$ This is equivalent to $$x^2=\frac{4}{10000}$$ Since $x$ is positive, it follows that $x=\frac{2}{100}=\boxed{\textbf{(C)}\ 0.02}$

## Solution 2

Alternatively, we could try each solution and see if it fits the problems given statements.

After testing, we find that $\boxed{\textbf{(C)}\ 0.02}$ is the correct answer.

~ljlbox