Walking with my son at 3:14pm the other day, I mentioned to him, "Hey, it's Pi Time". My son knows 35 digits of $\pi$ (don't ask), and knows that it's transcendental. He replied, "is it exactly $\pi$ time?"
This led to a discussion about whether there is ever a time each afternoon that is exactly $\pi$, meaning 3:14:15.926535...
This feels like some kind of Zeno's Paradox. I told him that (assuming time is continuous) it had to be $\pi$ time at some point between 3:14:00 and 3:15:00, but the length of that moment was 0. However, this discussion left him confused.
Can anyone suggest a good way to explain this to a child?