I think the confusion comes when mathematicians say "a sheet of paper can be 0.333... (0.3_, ie 0.3 recurring) units long" or something because in experienced reality we can always choose a measure that's rational (in the maths sense). That 1/3 of a meter can be measured in one-third-meter units and be precise and easily written.

Now sure, make a square using those measures and measure the diagonal, like an awkward mathematician - "see, see, we need irrationals!" - but then we can just cut another measure that's exactly that length ... stupid mathematicians!

Yeah representation is not reality.

Now, says the ratio of those two measuring sticks ...