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Sort of. That's a common explanation for what happens in a nuclear reaction. But technically, both matter and energy are conserved - there is no more or less matter after the reaction, than before the reaction. Therefore, in such cases there is no matter-to-energy conversion. Read the Wikipedia article on "Mass deficit" or "Binding energy" for a more detailed explanation.

There's no sort of about it. The meaning of Einstein's equation (E = mc2) is that matter and energy are interconvertible, and this happens all the time. What is conserved is mass-energy. Mass and energy are not conserved separately.

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