A floating point can only represent a rational number. Why do you want to include irrational numbers?
Discussion
I'm talking about a concept, and an accurate and correct word that describes the concept. I'm not sure why you are derailing the train to try to get me to talk about a different concept.
There IS A CONCEPT of all the numbers from 0 to 1, a very special interval with special properties. And we have no word for it, even though it comes up again and again. People have locked into divisions-of-100 (which is antiquated and should be retired entirely), people have locked into rational vs irrational (which is totally unrelated to the concept of this interval). I'm entirely unconvinced that your line of reasoning is moving towards the answer to my question.
I was under the impression you wanted to know what to name a variable. I happen to have the same question if that is the case.
I always want to name a variable (or type) accurately after it's actual purpose, so that I don't confuse myself when I read it back later. I would be confused if the variable name lead me to think about irrational numbers.
But I'm not writing the game now. I was just reminded of this by PABLO's post when he mentioned "FRACTIONS".
An irrational number can only be represented by a computer in an abstract form (obviously) so if all youre doing is multiplication, division, addition and subtraction and nothing to do with logarithms, roots, or an operation with pi or e, theres no reason to consider irrational numbers. I understand you want a name that represents any number from 0 to 1, which technically is an infinite set including irrational and infinitesimals, but it appears this name doesent exist. I would call it something like a positive subunitary proportion.
It appears there is a new SI unit to deal with this problem. The unit is called "Uno". Not sure if this is something that is compatible with your issue.
https://archive.iupap.org/commissions/interunion/iu14/ga-99.html