Chopping vs Rounding

Updated 15 Sep 2026

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What it is
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  two methods for representing a number with fewer significant digits: chopping (truncating) simply drops extra digits; rounding rounds to the nearest representable value
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Accuracy comparison
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  rounding's maximum error bound is half that of chopping ( $\frac{1}{2} \times 10^{1-n}$ vs $10^{1-n}$ )
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Worked example
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  $x = 2/3 = 0.666667...$ : chopped to 3 digits gives $0.666$ (error $0.100\%$ ); rounded gives $0.667$ (error $0.050\%$ )
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Cumulative rounding error example
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  repeatedly summing $0.1$ (which cannot be represented exactly in binary — see Patriot Missile Failure) 100,000 times, with each term carrying a rounding error of $+9.5367 \times 10^{-8}$ , accumulates a total error of about $0.009537$ — the sum reads $10000.009537$ instead of the true $10000$
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  lesson: repeated summation of small binary-imprecise fractions accumulates bias linearly with the number of iterations, $O(N)$
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Related
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  Error Taxonomy (Numerical Methods)
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  Machine Epsilon

What it is