If you pick a random real number from 0 to 1, there is 0% chance of it being a rational number. Essentially, simplifying greatly, this is true because there are uncountably infinite irrational numbers but the rational ones are countably infinite.
If you want to understand more about this, take a look at measure theory and Cantor’s diagonal argument.
Yes, I am bad at math but I like understanding the math that actually matters and that can’t be done by some stupid brainless calculator.
About the above, I only sort of understand the formal proof, but imagine that there is our universe. Than imagine that there is an infinity of universes like ours. Then imagine that in that infinity of universes there is one gem hidden that you must find.
How long will you have to look for that gem? Well, infinitely long because there are infinite universes.
That gem is all of the rational numbers. You can never find even one of them because the search time required is infinite in duration.
That’s a fair summation of the proof.
(And if you think the above is just irrelevant academic points, this matters a great deal to how computers work and what we can and cannot do with them, among other things.)