The reason for the repetition is that 22 divided by 7 is not actually pi, it's just the closest you can get with a common fraction. Pi is derived from the ratio of a circle's circumference to its diameter, which is in fact an irrational number and as such you can't accurately get it by dividing two rational numbers.

The 22/7 shortcut is only useful as a rational number substitute for pi if you don't have to care about anything past the second decimal place, and you can see why that is in your image. The actual first few digits of pi are 3.14159, so you've already got some deviation by the third number past the decimal.

So basically you didn't break pi, you found proof as to why 22/7 actually is not equal to pi.

[quote=Raxacoricofallapatorius]
But but… then how does one calculate pi?
[/quote]

Find a circle that you know the circumference and diameter of. Find their ratio. Tah-dah, you've calculated pi.