I can't answer that one, Mr Happy, beyond saying it is amazing how much mental clutter we pick up along the way. Airymouses' comment is more subtle. It took mathematicians literally centuries to get a firm grip on infinite series and thinking of a decimal representation of a number as such a series is valid. But it is a mistake to think of the mechanical process of adding digits and hence conclude recurring decimal numbers are in some way in a different class to those we can add up in a finite number of stepps