The point of the paper is that is nowhere near enough for common calculator operations like trigonometry or exponentials
The real numbers are notoriously non-equivalent to the rational numbers.
sure, but supporting rational numbers solves for 2/3 of the types of "real" numbers in a dramatically better way than just making less crappy decimal representations.
I haven't read the paper yet, but if I understand the post correctly, this interface represents numbers as the product of a rational and a recursive real, where the latter may be 1.