Dear Number Mavens,

Yesterday we talked about repeating and terminating decimals. In looking at whether unit fractions repeated or terminated, we found some interesting patterns. We found that having primes (except 2 or 5) as the denominator led to repeating fractions, and we saw something neat about multiples of 3. Today, we’ll look closer at the amazing repeating patterns that occur when we’re dealing with sevenths.

142857 is one of many magical numbers in our number system. When we stretch that number or cut it up into pieces, it does some mind-boggling things. If you’re still of the belief that numbers are just numbers–dry, boring things that have no relevance to your real life–142,857 is probably enough to convince you that our number system has a deep order to it, and it can model the deep order of the real world.

Sincerely,

Mr. Heimbuck