A little "How many people were soldiers in ancient Rome" type searches gave me these numbers...

16% of adult males in the Roman mid-republic (https://en.wikipedia.org/wiki/Roman_army_of_the_mid-Republic...), call that 8% of adults of all genders.

Wikipedia says that there's about 1.34 million people in active duty in the US military, out of about 342 million people, 21.5% of which are under 18. (https://en.wikipedia.org/wiki/Demographics_of_the_United_Sta..., https://en.wikipedia.org/wiki/United_States_Armed_Forces)

I think that's 0.5%? Down from 8% in ancient Rome?

That has little to do with technological advances, just the fact that the US is at an imperial peace; ie. it is under zero threat of invasion and is currently only engaged in small-scale imperial adventurism across the globe which does not require a large standing army. ~16% of adult Americans served in WW2, or ~33% of adult men.