“Concentrations are tiny, on the order of a single grain of salt dissolved in a liter of water,” said Yi Cui, a materials scientist and co-author of a paper in Nature Energy. “But the oceans are so vast that if we can extract these trace amounts cost effectively, the supply would be endless.”

That's a lot more uranium than I would have guessed. According to the top few google results, it's about 3 milligrams per cubic meter.