Well, I'm a prude, so I'm on the cashier's side. $0.13 out of what? $0.50? That's a bit of a chunk I'd say. Even if it was over a buck, it's over 10%. I work on the impression that it's meant for 1, 2, 3 cents, no more. Four and up you should cough up the nickel and leave the pennies behind.
Personally I wish they'd do away with pennies anyway. Go to a system based on 5 cents. Round up for 3 and over, down the other way. Not like computer based cash registers can't do that now. I know the argument is that businesses will lose money but if the decision point is set at 3 they'll win on the balance of time.