Kind of, but you're not just picking rationals, you're picking rationals that are known to converge to a real number with some continuous property.
You might be interested in this paper [1] which builds on top of this approach to simulate arbitrarily precise samples from the continuous normal distribution.
You might be interested in this paper [1] which builds on top of this approach to simulate arbitrarily precise samples from the continuous normal distribution.
[1] https://dl.acm.org/doi/10.1145/2710016