How do you convert from base 10 into a different base? or vice versa?

Well, base 10 into a different base would be like 16 into base 3 would be 1s spot, 3s spot, 9s spot, 27s spot, etc. So, 16 would be 121. 1 nine, 2 threes, and 1 one. Tell me if that doesn't make sense. Every time you multiply by the number of the base. As well, you can't put a 3 any of the spots, because 3 threes make a nine, which would put it into the next category. Again, tell me if this doesn't make sense.