We are nearly to the end of our Introduction to Number Theory book. In addition to providing us with many math project that are fun all on their own, I’ve been really happy to find so many great and unusual ways to secretly work number sense. The topic today was writing “decimals” in other bases which gave us lots of time to play with fractions, decimals, and place value.
When I got home from work tonight we reviewed a few of the homework problems and then I gave my son a shot at writing out 1/3 in binary. It was neat to watch him work through this problem, and so cool to see him smile at the analogy to 0.99999…. = 1 in binary at the end of the video. I think the fun of topics like this can draw kids into math while also providing lots of opportunities to build on their basic understanding of arithmetic and numbers.
Mike's Math Page 
Having worked on these infinite series, your son might like this storybook about decimal expansions: A strange neighbor, from the CSMP project. http://stern.buffalostate.edu/~csmp/CSMPProgram/Storybooks/AStrangeNeighbor.pdf
Other than this, I recall very few instances of decimal presentations of irrational number in all of standard school math and no others from elementary school. Unfair, of course, relative to their overwhelming majority within the reals.
Probably the other books from CSMP are too basic now. I’d be curious to know what he thinks of this one.
The link from @Joshua above no longer works, but you can find that PDF here:
Click to access AStrangeNeighbor.pdf