I calculated $\left(\frac17\right)^2$ and the calculation returned a decimal where a series of numbers going up by an exponent of 2 were all concatenated together at the end of the decimal. the number looked like this:
0.02040816326530612...
It started with 02, 04, 08, 16, 32, and kept going until the hundredth digit inevitably started interfering with previous parts of the pattern. Is there a way to somehow encode all of this into a repeating decimal? because I'm certain that it repeats eventually.