> Another way is to think of it as an interval of real numbers between the next lowest and highest intervals. Under this latter interpretation, it makes sense to discuss shortest decimal string within the interval, 0.3 in this case.

Note that the result of 0.1+0.2 does not lie in the interval containing 0.3, which is was confuses most people. The issue is that there is some imprecision in representing 0.1 and 0.2 too, and that compounds when summing, resulting in something that does not actually correspond to 0.3 (hence the classic 0.1+0.2!=0.3)