>If you can stand it, here's one more point on the reading numbers >issue. All of this talk has made me wonder about what those symbols >(a dot, a four, and a five) really mean. The fact that we always assume >base ten jumped unbidden into my head. The real way to say it might be >"radix point 4 5 base ten". Now, I am not suggesting that we teach it to >kids this way, just a) noticing an interesting aspect of this discussion >and b) reiterating that there must be some balance between convenience and >conceptual correctness.
>It also might be a fun thing to think about what .45 is base six, for >example. Maybe some students would get a "bigger picture" of what the >radix point means if they could see what it meant with other bases.
In a computer organization class I took some time ago, we had to build various circuits to do arithmetic (on paper). This included floating point multiplication and division with a binary representation. This was a good exercise in manufacturing headaches (it wasn't really that bad).
I frequently work with hex numbers (analyzing memory and crash dumps) and have lots of opportunities to work in different bases (usually 2, 10 and 16). Perhaps teaching computer organization (real computer science - not computer usage) would help with a math appreciation of working in different number bases.