If the Milky Way galaxy is as big as planet earth, how big is Earth?
Well, they are different shapes, but we can get a rough answer by doing a ratio calculation based on their radii.

Let $g$ be the radius of the galaxy, about $5\times 10^{20}\ \mathrm m$.
Let $e$ be the radius of the Earth, about $6371\ \mathrm{km}$.
Let $s$ be the radius of the scaled-down Earth. 

Then,
$$\frac e g = \frac s e$$
So $$s = \frac{e^2} g = \frac {(6371\ \mathrm{km})^2} {5\times 10^{20}\ \mathrm m}$$
which is approximately 80 nanometres. So it's about 1000 times the size of an atom.