Couple things.
1. OR($G2>3000000,$G2<5000000)
This is ALWAYS true for any number in G2
Perhaps you mean that to be
AND($G2>3000000,$G2<5000000)
2. You haven't defined all the ranges, what result is expected for a number between 5000000 and 10000000 ?
Lookup is probably the best way to go here..
Something like
=LOOKUP($G2,{0,3000000,5000000,10000000},{"<3","3-5","5-10",">10"})