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I came across an estimation of the relative error between two representations of the same number, one implemented in C++ and another one via a computer algebra program, that was in units of machine epsilon. My question is trivial, though I wasn't able to find an answer: If I say that the number has 3 machine epsilons relative error, how many digits does it mean that the approximated number looses compared to the true number?

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  • $\begingroup$ You lost at worst 4 epsilon in total, 3 from your number to true number and one from machines representation of your number. $\endgroup$ – user10354138 Feb 23 at 9:10

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