Super Lloyd wrote:

1st I believe you could have never repeating rationale (integer / integer) as well, this is simply an artefact of decimal notation.

I think you cannot have a never repeating rational number. As you do the long division, at each step you either end up with zero as a remainder (and terminate the sequence) or some other finite positive number. After some number of steps you must have a zero remainder or repeat a previous remainder, at which point you now have a repeating sequence. Robert