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  "body": "\n## Summary\n\nRounding replaces a number by a nearby number from a fixed set, such as the integers, the numbers with two decimals, or the [[floating-point numbers|RTKRSC3KPH]].\nRounding to nearest picks the closest element and needs a rule for ties, such as rounding half to even.\nDirected rounding always goes down, up or toward zero; the [[floor function|08GR54CKEA]] is rounding down to an integer.\nIn a computer every arithmetic result is rounded, and the difference is the [[round-off error|CPN6SD3BTV]].\n\n## Explanations\n\n### L1 human\n\nRounding makes a number shorter and simpler, at the price of a small error.\nA price of $3.47$ euros rounded to whole euros is $3$; rounded to one decimal it is $3.5$.\nThe number $2.5$ is exactly halfway between $2$ and $3$, so one needs a tie rule: \"half up\" gives $3$, \"half to even\" gives $2$.\nRounding half to even avoids a systematic upward drift when many rounded numbers are added.\n",
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