Are the positive reals (R+) a subset of the positive hyperreals (*R+)?

I've never dove into non-standard analysis, but I'm wondering, on the Hyperreal line, there are supposedly infinitesimal quantities (smaller than any R+) and infinite numbers (larger than any R+). On any number line, every number has a location, which we call a point. My question is ... Although (a real + an infinitesimal) is considered an infinitesimal number, the 'infinitesimals' (by themselves) must take up space (length) between 0 and R+. At what location does (infinitesimals by themselves) end and R+ start? What value is this?... The whole point of a number system is to create a number line with "no undefined" locations. In the reals, there are no undefined locations. If the hyperreal line has 'undefined locations,' that seems self-contradictory to its purpose.