Decimals require you to check the end of the number to see if you can round up, but there never will be an end.

The character sequence "0.999..." is finite and you know you can round up because you've got those three dots at the end. I agree that decimals are a shit representation to formalise rational numbers in but it's not like using them causes infinite loops. Unless you insist on writing them, that is. You can compute with infinities just fine as long as you keep them symbolic.

That only breaks down with the reals where equality is fundamentally incomputable. Equality of the rationals and approximate equality of reals is perfectly computable though, the latter meaning that you can get equality to arbitrary, but not actually infinite, precision. You can specify a number of digits you want, you can say "don't take longer than ten seconds to compute", any kind of bound. Once the precision goes down to plank lengths I think any reasonable engineer would build a bridge with it.

...sometimes I do think that all those formalists with all those fancy rules about fancy limits are actually way more confused about infinity than freshman CS students.