To call something big you would certainly have to compare it to something.
for example:
compared to an ant, i am big,
however compared to an elephant, i am small.
From how we view space, our galaxy to us may look enormous.
However in the grand scheme of things and our thoughts on the universe, it is not so big.
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Huge.
Our solar system is mind-boggling big; it's about 7 *billion* miles across (at Pluto's orbit)... next year, a probe we launched in 2005 will *finally* arrive at Pluto - and it left Earth the fastest of any probe we've sent into space - 10 *years* to go halfway across the solar system - that's so far, it takes light about 5 hours to reach us from Pluto - it's 5 'light hours' away.
Now... our Galaxy is 100,000 light *years* across - it would take something moving at the speed of light 100,000 years to travel the diameter of our galaxy.
And, our galaxy is far from the largest; ours holds about 250 billion stars; Andromeda, our large neighbor is about 1 1/2 to twice as big as the Milkyway - perhaps 600 billion stars, and 140,000 light years across. And, there are larger galaxies yet - some Elliptical galaxies can hold a *trillion* stars, and be nearly 500,000 light years across.
So, I repeat.... They're *huge* - beyond what most people's mind can grasp. (Certainly beyond mine!)
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Depends on your definition of "big".
Galaxies are certainly much larger than the Earth.
They are much larger than our solar system.
Some are even larger than our own galaxy.
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They can be massive, even between each other -
http://www.rhysy.net/galaxy-sizes.html
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In relative to Earth, gargantuan.