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  "body": "\n## Summary\n\nMachine epsilon measures the relative precision of a system of [[floating-point arithmetic|RTKRSC3KPH]].\nIt is the gap between $1$ and the next larger floating-point number, or, in another common convention, half of this gap.\nThe half-gap, called the unit roundoff, bounds the relative error of rounding a real number to the nearest floating-point number.\nAlmost every error bound in numerical analysis is stated in terms of it.\n\n## Explanations\n\n### L1 human\n\nA computer stores numbers with a fixed number of binary digits.\nMachine epsilon tells how fine this grid of numbers is near $1$.\nIn double precision it is $2^{-52} \\approx 2.2 \\times 10^{-16}$, so a computer can tell $1$ from $1 + 2^{-52}$ but rounds $1 + 2^{-54}$ back to $1$.\nSince the grid scales with the size of the number, the same relative accuracy of about $16$ decimal digits holds for big and small numbers alike.\n",
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