What do you get if you divide the circumference of a bowl of ice cream by its diameter?

Question

Start with a three-digit number and repeat the digits to make a six-digit number, for instance 379379. Now divide by 7, then divide the answer by 11 and then divide this answer by 13.
What do you notice, does it always happen and what is the explanation?

Answer 1

Pi a'la mode.
Pi Day is near 3.14