A point is chosen at random within the square in the coordinate plane whose vertices are $(0,0)$, $(3000,0)$, $(3000,3000)$, and $(0,3000)$. The probability that the point is within $d$ units of the center of any unit square (a point of the form $(n+0.5,m+0.5)$ for integers $n,m$) is $\frac{3}{4}$. What is $d$ to the nearest hundredth?