The book “Mathematics for high-school teachers” by Usiskin et al. has what I find a hideously over-complicated approach, at the nutshell of which is a nice idea: How does the notion of the collection of real numbers as a geometric object (a line) mesh up with its realisation as an algebraic object (at the middle-school level, decimal expansions)?
Some things to think about in this connection: If real numbers are directed lengths, how do we add and subtract them? OK, that's not so bad; how about multiplication and division? Now how about square roots? One can draw a nice picture to show $\sqrt2$ as the length of the diagonal of a unit square (constructed on a unit length by ruler and compass) being ‘unfolded’ (by a compass) down to the real line; now we've taken square roots geometrically. Can we do the same thing with the circumference of a circle?
If one wants to think purely in terms of decimals, there's the age-old “Are $1$ and $0.\overline9$ really the same number (and why)?”. It's easy for middle schoolers, and good practice in long division, to find decimal expansions of some unfamiliar (for them) fractions, like $1/7$ and $1/13$; which ones terminate? Which ones repeat? Will one of these always happen? Can you predict in advance which is which, and how long it'll take before it terminates or repeats?