This behaviour is what you get in say a cheap 1980s digital calculator, but it's not what we actually want. We want correct answers and to do that you need to be smarter. Ideally impossibly smart, but if the calculator is smarter than the person operating it that's a good start.

You're correct that the use of the calculator means we're talking about computable numbers, so that's nice - almost all Reals are non-computable but we ruled those out because we're using a calculator. However just because our results are Computable doesn't let us off the hook. There's a difference between knowing the answer is exactly 40 and knowing only that you've computed a few hundred decimal places after 40 and so far they're all zero, maybe the next one won't be.