To be a Mathematician is to continue to ask the question of ‘why?’. Long after a normal person would be satisfied.
One lesson towards the end of primary school was taken by our headteacher. In it he decided to teach us all about repeating decimals, he did this using the decimal representations of the seventh fractions. From what I remember the lesson consisted of our headteacher writing out various seventh fractions as decimals and getting us to try and spot the pattern. The details of the rest of the lesson are hazy but I do remember that I was quite slow at spotting the pattern.
In addition to that TED talk, numberphile also posted a video about this number in case you haven't seen it.
If you haven't seen this TED talk, I think you would really like it. It's all about the weird craziness of prime numbers and also includes a healthy dose of the quirkiness of mathematicians.