The default Android calculator app by Hans Boehm (developer of the Boehm Garbage Collector as well) does this by using the computable real numbers.

https://dl.acm.org/doi/10.1145/2911981

Provides a good overview of how it works and perms website has more information.

What’s cool about the computable reals implementation is you can increase the precision after the fact and it will recalculate up to that precision. Basically it memoizes the steps of the calculation and how they affect the precision.

I doubt the modern GNU or BSD versions of it that you are likely using do. Noone uses the original anymore.

Is scale factor the same as error bounds in http://man.openbsd.org/dc ?

I believe it's just the number of digits when the printing cuts off