The recent discovery of radiocarbon in dinosaur bones at first seems incompatible with an age of millions of years, due to the short half-life of radiocarbon. However, evidence from isotopes other than radiocarbon shows that dinosaur fossils are indeed millions of years old. Fossil bone incorporates new radiocarbon by means of recrystallization and, in some cases, bacterial activity and uranium decay. Because of this, bone mineral -- fossil or otherwise -- is a material that cannot yield an accurate radiocarbon date except under extraordinary circumstances. Mesozoic bone consistently yields a falsely young radiocarbon "date" of a few thousand to a few tens of thousands of years, despite the fact that it is millions of years old. Science educators need to be aware of the details of these phenomena, to be able to advise students whose acceptance of biological evolution has been challenged by young-Earth creationist arguments that are based on radiocarbon in dinosaur fossils.