That doesn't make one set "larger" than the other. You need to define "larger". And you need to make that definition as weird as needed to justify that comparison.
I don't think this definition is that weird, for example by 'larger' I might say I can easily 'fit' all the rational numbers in the real numbers, but cannot fit the real numbers in the rational numbers.
So, let's inspect pi. It's a fraction, precision of which depends on how much you zoom in on it. You can take it as a constant just for having a name for it.
The zooming is finite for every fraction.
How?
> Problem is with the assumption that some numbers such as pi or sqrt(2) can have absolute and full precision.
That's the least of your problems, I couldn't even draw different sized splodges per real number.