  We consider a class of real numbers, a subset of irrational numbers and
certain mathematical constants, for which the elements in the simple continued
fraction appears to be random. As an illustrative example, one can consider
$\pi = \{x_0, x_1, x_2, \dots x_n\}$, where $x$'s are the continued fraction
elements computed with an exact value of $\pi$ up to $N$ precision. We
numerically compute probability distribution for the elements and observe a
striking power-law behavior $P(x)\sim x^{-2}$. The statistical analysis
indicates that the elements are uncorrelated and the scaling is robust with
respect to the precision. Our arguments reveal that the underlying mechanism
generating such a scaling may be sample space reducing process.
