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I was told that in nuclear reactions, the law of conservation of mass does not hold true. I was wondering is that because the mass lost is in the form of energy?

Yes. That's one example showing there is no law of conservation of mass. In macroscopic systems (atomic/molecular scale and above, really) it's a reasonable approximation, since your level of measurement precision will probably not reveal the discrepancy — 1 eV of energy difference is ~10^-9 amu.

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