Other things, the Solar System, and even galaxies are similarly sparse. I find it fascinating that two galaxies can pass through each other with probably no stars colliding. (Gas, however, is a different matter, uh...so to speak, and gravitational, tidal forces are really, really a different matter!)
Which led to an interesting question. Which of these is the emptiest? My first intuition was that the average distance between objects, cubed, would give a rough indication of emptiness. Now, as I write this, it's obvious that emptiness is just density. In this case we're talking about particle density (things per cubic-length) and not mass density (grams per cubic-length).
Here's my first, rambling shot at the question.
As a start, the Sun is about 100 Earth's in diameter but the nearest star is four LY away which is about 24e12 miles. The earth's diameter is about 8000 miles, right? (I never can remember, but we are headed east at about 1000 mi/hr meaning the circumference is about 24,000 miles and over pi * d gives 8000 as d).
That make the Sun about 8e5 miles in diameter. So the nearest star distance is 24e12 / 8e5 = 3e7 diameters.
The web page you sent says the proton diameter to atom diameter ratio is about 1e5 so that makes a galaxy maybe 300 times emptier [sic] (3e7 / 1e5 = 3e2), or taking it in a volume sense, (3e2)^3 = 9e6 =~ 10 million times emptier. Wow. I wonder if that's right...
Now take the Solar system. If the Sun is 8e5 miles in diameter, we know the earth-sun distance is about 93e6 miles. 93e6 / 8e5 =~ 12e1 = 120. So the Earth is only about 120 solar diameters away so the solar system isn' t nearly as empty as an H atom. By volume 1e5 / 1.2e2 =~ 8e2. By volume (8e2)^3 =~ 6e8 so the atom is 600 million times more empty!
Neptune is at about 35 AU I think so that makes it about 4000 diameters, still less ``empty'' than an atom.