RFID size is normally determined by the size and configuration of the antenna, not the actual RFID integrated circuit.
Hitachi sells chips with low-performance internal antennas that are the size of a table salt crystal. Most RFID tags are between 20 and 100 mm in length/width and very thin.
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Both RFID tags and barcodes are used to tag products, but RFID has many advantages. An RFID tag can be read at a distance. That helps with inventorying stock, and also helps to catch shoplifters. Retailers have a problem with shoplifters putting an expensive item in a cheap item's box; because the RFID tag would be on the product itself it wouldn't matter what box it was in.
By using an antenna
Usually RFID tags would get the power from the reader.
RFID tags are incredibly easy to purchase. There are many websites and businesses devoted to the increasingly popular RFID technology. A simple search will show you plenty of places that will work with you to create an RFID tag.
The type of RFID tag you are referring to is likely a passive device. It gets read by stimulating it with a certain RF frequency and then looks for a unique return. Hence the tag life is essentially forever.