Seems reasonable, but then this is not "exact" precision as you claim, but "very large" or "dynamic precision". Saying that the precision of a real number is exact is very misleading, as it evokes inevitably an automatic theorem-proving context.
By the
# Gauss-Kuzmin theorem [5, 6], a partial quotient in the
# continued fraction expansion of almost every number exceeds
# 1e+31 with probability log2(1+1e-31) =~= 1e-31/ln(2) =~=
# 1.5e-31.Notice that this result does not say that most numbers have bounded partial quotients. In fact, a classical result in diophantine approximation theory, if I recall correctly, says that the set of numbers whose partial fractions are bounded (called badly aproximable numbers) is of Lebesgue measure zero. Thus, if your system represents real numbers by sequences of bounded partial quotients, then it can only represent a negligible (but uncountable) set of real numbers. A "random" number in [0,1] will certainly have an unbounded sequence of partial quotients (i.e., with probability 1).