= Solution
With the gap-at-one convention, <machine epsilon> is the difference between $1$ and the next larger representable <floating-point number>. The <double-precision floating-point format> has 53 significant binary digits, including the implicit leading digit, so
$$
\boxed{\varepsilon_{\rm mach}=2^{-52}\approx2.22\times10^{-16}.}
$$
A related convention uses <unit roundoff>, the worst relative rounding scale for round-to-nearest: $u=2^{-53}\approx1.11\times10^{-16}$. Stating the convention distinguishes these two common values.<IEEE arithmetic in Oracle's Numerical Computation Guide>[Chapter 2, IEEE Arithmetic Model; Double Format and Table 2-5]{ref}
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