This patch introduces "question-mark style printing" for intervals, where instead of [1.123 .. 1.125] we get 1.124? (the question mark means that the previous digit may be off by +/- 1). (The slightly unfortunate thing is that [1.1238 .. 1.1242] will also print as 1.124?, so the new default printing loses a lot of information about exactly how tight the interval is.)
I'm going to post a preliminary patch first, that actually changes the printing and adds extensive docstrings and doctests for the new/changed methods. This leaves many, many doctests broken throughout the rest of Sage.
If/when this preliminary patch is positively reviewed, I will go ahead and post a follow-on patch that fixes all the doctests.