Last week my younger son read chapter 2 of Jordan Ellenberg’s How not to be Wrong. In that chapter Ellenberg discusses the the nunber 0.999999…. and whether or not it equals 1.

Today I thought it would be fun to approach the idea from the (slightly) different perspective of using fractions and binary.

We started with a review / refresher of how to write integers in binary since we haven’t talked about that in a while:

Then we talked about how you write fractions in binary including fun problem of writing 1/3 in binary:

Now I posed the question of how could we write 1 in binary – this part turned out to be the rare discussion that was as fun as I’d hoped it would be đŸ™‚

Finally, having found an interesting way to write 1 in binary, we moved on to the question of how to write 1 in base 10:

This was a enjoyable project. The discussion of infinite series in How not to be Wrong is fascinating and accessible to a wide audience. Talking through the ideas in that chapter with my younger son has been really fun!