[jacobolus]

That numbers have interesting relationships to each-other is not an “ugly thing”, but rather a beautiful thing. The relationships exist whether we pay attention to them or not, so giving people a way to write and pronounce those relationships is a nice way to improve numeracy.

Writing numbers in multiple possible ways is really not that big a problem for most uses (for record-keeping in business transactions maybe). Personally I recommend becoming familiar with two different normalizations: all same-signed digits (the form we use now) or [–5, 5] with digits before a terminal 5 rounded away from zero. But in general for personal scratch work numbers don’t need to be normalized unless you feel like it. As long as you understand that 20–3 is the same as 10+7, it doesn’t really matter which one you think of as primary.

We use multiple number representations all the time, with e.g. the vulgar fraction 11/8 alternately representable as the “mixed number” 1 + 3/8, or as the decimal fraction 1.375, the simple continued fraction [1; 2, 1, 2], the percentage 137.5%, or the common logarithm ~10^(0.1383). Figuring out that 1.375, 1.385̅, 1.42̅5̅, 1.43̅5, and 2.6̅2̅5̅ are the same number isn’t that hard, with some practice.