Ringo writes:
"Better" approximations are more precise approximations, not necessarily more accurate approximations.
My desk is 1.7543698765423410981666 centimeters long
My desk is about a meter and a half long.
One of these statements is highly precise but a very poor approximation. The other statement is very approximate but far more accurate.
Which of the two statements is the better approximation?
Being roughly accurate trumps being precisely wrong.
It's accuracy that we should be aiming for. Without it precision is really rather worthless.