[pron]

> who reads that without thinking of irrational numbers?

Not directly related to the article, but many [1] irrational numbers (π for example, or sqrt(2)) can be represented in a computer in their entirety, i.e. "accurate to the last digit." Not all digits are stored at once in RAM, of course, but you can obtain an arbitrary digit (given sufficient time). That's precisely how computable numbers are defined (first by Turing in his 1936 paper that first defined the notion of computation, and was called On Computable Numbers, where the "numbers" in the title refer to real numbers, including irrational ones).

[1]: Relative to the irrational numbers that "we know", not to all uncountable ones, of course.