[ukoto]

Decimal system (well, numbers in general) is a great way to describe things as they provide infinite accuracy both in positive and in negative directions. But you must describe them relative to something - some kind of unit.

So your balloon, to fully described its length, you have chosen to describe it relative to meters. Here's the kicker - how well you can measure the length of the balloon depends also on how well you can measure a meter. In the real world, if you try to measure both, the decimal number that describes how relative a meter is to your balloon will only be limited by how accurate your methods of measuring are. You can develop better measuring technology that will forever approach but never reach the True value (only God knows). It is if you try to measure an analog signal, you can only get a digital estimation. But extracting knowledge requires energy, so you need greater computing power to measure an analog signal but all the computing power in the universe couldn't acquire the True value. This is the result of the real world being nondiscrete and containing infinite knowledge. You can measure things by proportion (such as tau (2*pi) being the relative constant of circle circumference to radius); these numbers are transcendental and we don't know their True value. Your "indescribable" numbers are as indescribable as transcendentals. So yes the decimal goes on forever, but you can still describe it in terms of itself and just give a constant name (like pi).