The old HP calculators, and their emulators, have a computer algebra system, for symbolic maths, that supported this. The user interfaces leave much to be desired, but some also have reverse Polish notation!
> that doesn’t round at all. It computes with constructive real numbers: every result is exact, and you can scroll any answer for as many correct digits as you want.
A CAS is a practical way to achieve this, where everything is stored symbolically, with no rounding, until final calculation. Unlimited precision was through Erable [1]. This was included with/as HP49 CAS, but was an add-on with HP48. Many HP48 are on the iOS app store. The one I tried about a decade ago had the add-on, and I see many still there (but not sure if they have the add-on).
The "S" in CAS is "system", so it's a bit open.