But then you could cut a note in half, and swap it for two new notes.
No, it has to be measurably more than half.
Well, no shit. “>50%” means “more than one half”.
And for the OP, some more information:
[quote]
What is mutilated currency?
Currency notes which are:
[ul]
[li]NOT CLEARLY more than one-half of the original note and/or, [/li][li]in such condition that the value is questionable and special examination is required to determine its value. [/ul][/li]Currency can become mutilated in any number of ways. The most common causes are: fire, water, chemicals, explosives; animal, insect or rodent damage; and petrification or deterioration by burying. Under regulations issued by the Department of the Treasury, mutilated United States currency may be exchanged at face value if:
[ul]
[li]more than 50% of a note identifiable as United States currency is present; or, [/li][li]50% or less of a note identifiable as United States currency is present, and the method of mutilation and supporting evidence demonstrates to the satisfaction of the Treasury that the missing portions have been totally destroyed. [/ul][/li][/quote]
So what happens if I get 3 bills and cut them carefully into 4 pieces such that there is 75% on each bill (The last one is a fragment of 25%'s but its still complete) and then send them to 4 different treasuries?
Each redeemed bill must posess a complete, unique serial number. If you cut up three bills as you describe, you’ll only have three unique serial numbers. Try again.
To finish answering the original question, no such case has ever made it to court (AFAIK, and IANAL) and no one has ever pressured Congress to pass a law that dealt with this at that level of specificity. Basically, you and the restaurant can both do whatever you want, and if either tries to take the other to court, the plaintiff would have to prove that the other party acted with intent to defraud or some such. But in real life, it never gets that far, because somebody in the restaurant will change a torn five for a good one, or something else will be worked out, like Flash 57 says. Frankly, the law doesn’t care, because the law doesn’t deal in trifles.
The word “clearly” in the Treasury guidelines is certainly open to debate. Is 51% clearly more than 50%? Mathematically, yes. Observationally, probably not - 1% of a US bill is about .06". At what point is a bill clearly more than 50%? As with other federal guidelines and regulations that are vaguely worded, the industry must itself establish a standard. Banks have decided, in this case, that 60% can be observed to be clearly more than 50%. Hence the bill template I described in an earlier post.
As futher evidence of vague and contradictory guidelines, the Treasury’s own web site states:
while the Dept of Printing and Engraving’s website says a bill may be redeemed if:
The latter is correct, but you wouldn’t know it by the Treasury’s information.
I gave a real world anwer to the OP. You can declare that 51 is greater than 50 all day long, but to get your bill redeemed at a bank it’s going to have to be 60% with one complete serial number. The rules at any given merchant are up to them.