Irregular Numbers Concept

You may be used to quantifying things in terms of whole numbers or fractions most of the time.
I know I am. It seems to make up pretty much all of my everyday maths. And I'm sure we're all aware of 'Pi', a number that helps us relate diameters to circumferences.
I thought it may be interesting to think about the maths that goes on in our lives without much conscious input from us. When you calculate distances (using pretty much any sense) do you work exclusively in rational numbers, or does a number like 'Pi' make an appearance?
Are there a whole load of numbers, having particular purposes to particular senses, that if we looked at them on paper without really thinking about them, we would find they seemed quite random, and perhaps unusual or irregular?

(It just seems weird that my mind could say be using the square root of 2, 'Pi' or other irrational numbers)

It has widely been suggested that all things are simply mathematical equations in a giant plane (being our reality). I think this concept is accurate in its inverse; that is to say, I believe that all actions taken and all things can be expressed mathematically. Mathematics is really the human expression of "How do we translate what's going on around us into terms we can readily understand?" That said, human grasp of mathematics is rather lacking. We obviously can't understand everything in mathematics because everything in physical existence (and possibly further, if some Greek philosophers are to be believed) can be expressed by mathematics. If we don't understand everything that exists, we cannot, by definition fully understand mathematics. Numbers like Pi represent a concept, not an actual number, to my thought. Numbers can continue forever, but the concept of Pi is paradoxically quite finite: infinity. I do not personally believe that the human brain is capable of subconsciously carrying out mathematical operations with infinite numbers millions of times a day. While the actions that our brains do think of can be represented mathematically, mathematics doesn't come naturally to our brains. Naturally, we can assume that if all things that exist can be represented mathematically, then mathematics can define the universe. That assumption is valid, except that things that don't exist, but can still be conceptualized are not represented mathematically, and things that don't exist and can't be conceptualized by humans aren't represented mathematically. The universe of potential existence is probably as important as the universe of actual existence, and if we can't define potentials mathematically, mathematics can't lead us frther in our understanding of the nature of the universe.