The number $$r$$ can be expressed as a four-place decimal $$0.abcd,$$ where $$a, b, c,$$ and $$d$$ represent digits, any of which could be zero. It is desired to approximate $$r$$ by a fraction whose numerator is 1 or 2 and whose denominator is an integer. The closest such fraction to $$r$$ is $$\frac 27.$$ What is the number of possible values for $$r$$?

(第十五届AIME1997 第5题)