Do you mean the computable numbers? (there's an algorithm to compute them to arbitrary precision)
The irrational numbers used outside of college math, like pi or e or sqrt(2), are computable, though almost all are not.
You can do a lot of productive math using just computable numbers since they form a real closed field [1]. I believe they're a little harder to work with though.
Computable numbers are those that are described by computable functions. Irrationals like pi can be described by computable functions that take a precision as input.
The irrational numbers used outside of college math, like pi or e or sqrt(2), are computable, though almost all are not.
You can do a lot of productive math using just computable numbers since they form a real closed field [1]. I believe they're a little harder to work with though.
[1] https://en.wikipedia.org/wiki/Real_closed_field