The invention of paper currency is one of the things that has lifted us from the economics of the Middle Ages to a modern industrial society. However, with paper currency has come other concerns. Some of these are significant, such as the need to prevent counterfeiting, while others are less so, such as determining what to do with bills that have been damaged. If you have a bill or a number of bills that are torn, you will want to find some way to redeem them for their value. There are several ways to go about this.
Tape the pieces back together as best you can using transparent tape. Make sure you line the edges up correctly, and try not to cover up the serial numbers of the bill. You can now try to make use of the currency at the store of your choice. This may not always work.
Go to your nearest bank and ask them to replace the bill for you. If the serial number is intact, they will probably do this for you. Should they not, you have yet another option.
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Mail the entire bill to the Treasury Department's Bureau of Engraving and Printing. They will send you a check for the value of the bill. Of course, it is best to do this with only larger denominations or for a large number of damaged bills, since it would make little sense to go through this much effort over a single dollar.