2001 AMC 10 Problem 7

Question

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?

0.0002

0.002

0.02

0.2

2

Answer: C

Concepts:place value decimal algebraic manipulation

Difficulty rating: 1170

Small hint:

Moving the decimal point four places right multiplies by

10000

Big hint:

So

10000x=\dfrac{4}{x},

giving

x^2=\dfrac{4}{10000}

Solution:

Moving the decimal four places right multiplies

x

by

10000.

So

10000x=4\cdot\dfrac1x,