16. In the Cartesian coordinate system, the four vertices of a square have coordinates $(0,0),(2020,0),(2020,2020),(0,2020)$. A lattice point (i.e., a point with integer coordinates) is randomly selected from within the square. The probability that this point lies within one of the four sectors with the square's vertices as centers and $d$ as the radius is $\frac{1}{2}$. Then the ratio of $d$ to the side length is approximately ( ).
(A) 0.3
(B) 0.4
(C) 0.5
(D) 0.6
(E) 0.7
16. B.

From the problem, we know
$$
\begin{array}{l}
4 \times \frac{1}{4} \pi d^{2}=\frac{1}{2} \\
\Rightarrow d=\sqrt{\frac{1}{2 \pi}} \approx \sqrt{\frac{1}{6.28}} \approx \sqrt{\frac{1}{6.25}}=\frac{1}{2.5}=\frac{2}{5} .
\end{array}
$$