In Progress

1 over 17 isn't exactly equal to 0.05882323. They are different by about one over seventeen hundred million.

Nearly Done

Seventeen is prime. The repeating string in the decimal representation of it's reciprocal has 16 digits, one less than 17. Subtracting 17 from 100 leaves 83. Powers of 83 can be added in a certain way to create the same repeating string.

Done

The numbers 31 and 41 are prime numbers. The repeating string for 31 is half as long as one less than 31. The repeating string for 41 is an eighth as long as one less than 41.