Hils, I am not in CA and don't know anything about STAR testing - the only caution I'd have about STAR testing is if it's like our state testing, it does not test above grade level and you can usually find a summary online for each school re how many students tested "proficient" vs "advanced proficient" etc. Again, I don't know anything about STAR except that I *think* STAR is the CA NCLB state test.
One of my dds has gone to a school that uses AR testing to give a reading level - the way it's used here is what you've mentioned - a 4.7 would mean the student is currently reading (according to the AR test) at the level of a typical student who is in the 7th month of 4th grade. I don't put a *ton* of weight on the AR results - it's a brief test that is meant to test comprehension. My dd who has a reading (2e) challenge has bopped around on results on it quite a bit - sometimes she's behind grade level (slightly), but she's also tested ahead of grade level in spite of clearly being challenged with reading skills.
Re what your ds needs re acceleration - I would always follow your gut and listen to your child. OTOH, I wouldn't think acceleration was necessary based on a few grades out of level reading at your ds' age - reading scores are all over the place in early elementary, and being a few grades above level isn't all that unusual (it's not typical but it's also not out-of-the-box unusual). Re reading, I'd pay more attention to the types and levels of books your child reads at home and the kinds of information he's retaining from them and the kinds of questions he asks based on them.
Best wishes,
polarbear