I'm Not a Robot - Prove Are You Human

This is depicting a fairly well known problem involving floating point numbers. Certain numbers, like the ones shown in the picture can only be approximated in a binary floating point form of finite precision because, unlike in the decimal system, they are actually periodic continued fractions. So since they cannot be perfectly represented, they are just rounded to the nearest possible value, which causes the bahaviour seen in the picture.

Computers have a hard time calculating stuff when floats are involved.