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So what we're really concerned about is high-level waste so stuff that was actually inside the reactor. Again, I have just recently discovered that 95% of that is recycled back into nuclear fuel (so called MOX).
This movie from La Hague reprocessing plant (France) goes into great detail on how it works https://www.youtube.com/watch?v=V0UJSlKIy8g
So the remaining amounts are absolutely tiny, especially if you compare with other sources of energy.
