Then you calculate the decimal expansion to the desired number of decimal places. This avoids accumulation of roundoff errors in intermediate results.

Note that writing sqrt(2) as 1.41 or 1.41421 or any other decimal expansion you might want to write is incorrect: you will always get some roundoff error. If you want to calculate that sqrt(2)*sqrt(2)=2 then you can’t do so by multiplying the decimal expansions.

You never evaluate symbols until your giving a numerical equivalent.

Sure if a question asks for the escape velocity from Jupiter this has an approximate numerical value, but you don't just start by throwing numbers at a wall, you get the simplest equation which represents the value you're interested in an then evaluate it once you have a single equation for that parameter.

Yes sqrt(2)*pi has a numerical approximation but you don't want that right at the start of taking about something like spin orbitals or momenta of spinning disks. Doing the latter compounds errors.

It's no different to keeping around "i"/"j" until you need to express a phase or angle as it's cleaner and avoids compounding accuracy errors.

If it's a maths problem you just leave it as symbols. If it's a science or engineering problem you expand it to a decimal approximation with the precision needed for the specific problem you are dealing with.

Note that even for an engineering problem, you don't necessarily use a decimal representation. You may well want to represent pi as 3 or 4 or 22/7 or any other approximation that is good for your particular use case. Or you may even have usecases where you do things the opposite way - you may want to approximate 1 as pi/3 or something like that for certain kinds of problems (e.g if you're going to take the sin of your result).