[godelski]

And that's good, because you'll get the wrong answer if you used the number with too many points (nit picking: more decimal points does not mean higher precision).

In fact, this is part of why you'll see physicists do all their reductions with variables and plug in numbers at the very end. This ensures that you doing get (what we could call) floating point errors. You don't have extra numbers hanging around (from real numbers like 1/9 or pi). There are also other benefits to doing this.