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2001 AMC 10 Problem 7

Problem 7 of 25EasierAlgebraNumber Theory

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?

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Solution

Moving the decimal four places right multiplies xx by 10000.10000. So 10000x=4⋅1x,10000x=4\cdot\dfrac1x, giving x2=410000.x^2=\dfrac{4}{10000}. Since x>0,x\gt0, x=2100=0.02.x=\dfrac{2}{100}=0.02. Thus, the correct answer is C.

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Concepts: place value · decimal · algebraic manipulation

Problem text and solution from the LIVE past-contest archive. See also the AoPS wiki page for community solutions.