These family math project are just for fun. These projects tend to cover either fun math we find around the house – see the paper folding example from all the way back in Family Math 1:

or, if not stuff from around the house, they are intended to be a fun overview of some advanced math. The overview of fractions and decimals in binary was supposed to be in the second category, but it led to a really great surprise this morning.

Today with my younger son we moved on to a new chapter in our book – repeating decimals. A few days ago we had started off talking about decimals and fractions by reviewing why .9999…. = 1, so I was hoping to play off of that to show why 1/3 = 0.33333…. However, when I sat down and asked my son what he thought the decimal expansion for 1/3 would be I got a little surprise:

“I don’t know, but I know what it is in binary.”

So fun that he remembered this talk from the Family Math project from a few weeks ago:

With that, we started down a totally new path – how does knowing what 1/3 is in binary help you understand the decimal expansion?