Question 5
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 $\frac{2}{7}.$ What is the number of possible values for $r?$