What do ya got there... Numbers?

[johnson1010]

http://io9.com/5977095/why-we-should-sw ... ing-system

I've thought about repeating decimals, and irrational numbers before, never with anything like real mathematical rigor, but it did occur to me that maybe the issue with them has to do with our use of a particular number system.

If 1/3 is not a number we can really represent with base ten, doesn't that say something is wrong with base ten?

I'm not convinced we should all drop base ten and start using base 12, but the above is an interesting article discussing the possibilities of a different number system, and it might give people who don't normally think about these things a little something to chew on.

[Dexter]

Interesting, never thought about that before.

I always thought the metric system of measurements made a lot more sense, but would be nearly impossible for the US to switch to. This would probably be even harder to do.

[JamesALindsay]

There are some pretty salient features here about why using a base-12 number system would be more efficient, but as noted, the change would be horrendous to navigate. Most of us that were raised on base-10 would spend our lives thinking in base-10 and have to do a lot of conversions all the time.

The fraction thing gets a crappy treatment here. In reality, we run into repeating decimals with rational numbers in every case where the denominator of the fraction has in it a prime not included in the prime factorization of the base. So, in base 10, if the denominator of the fraction only contains powers of 2 and 5 in its prime factorization, the decimal terminates. If it contains any other prime, the decimal expansion repeats.

If we changed to base-12, fractions like 1/2, 1/3, and 1/4 would be "nice," but fractions like 1/5, 1/7, 1/11, 1/35, 1/10, 1/15, 1/4, etc. would still have repeating decimal expansions. The only way to get around repeating decimal expansions is to have "base-infinity" notation (which functionally would mean that every number gets its own symbol, which would be useless).

Interesting piece, though, I guess. I don't see it as being imminently practical given the enormous investment that would be involved in changing over.