Ok time for the exact quote from FotR Shadow of the Past chapter about 3/4 of the way through, Gandalf to Frodo:
Quote:
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It has been said that dragon-fire could melt and consume the Rings of Power, but there is not now any dragon left on earth which the old fire is hot enough; nor was there ever any dragon, not even Ancalagon the Black, who could have harmed the One Ring, the Ruling Ring, for that was made by Sauron himself.
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So no dragon, not even the biggest, baddest dragon had what it would take to melt the One Ring. The quote says that the big, bad ones could melt the Rings of Power, but, there aren't any left now that are able. It doesn't say that there aren't any dragons left -- period.
--Imladrien