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I am taking part in a logic puzzle competition, which is organized by a Fédération Française des Jeux Mathématiques. Translation by a local organiser in my country has some flaws and I need to know exactly what to do in every problem.

In problem 16, there's this phrase: arrondie au plus près. Full sentence:

Quelle est, en cm² et arrondie au plus près, l’aire du dodécagone ?

How should I interpret it, is it just rounding up (e.g. 48,9987 → 49)?

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It's rounding to the closest, which differs from rounding up for e.g. 48,19. –  Nikana Reklawyks Jan 7 '13 at 20:50

2 Answers 2

up vote 14 down vote accepted

The phrase arrondi au plus près is short for “arrondi à la valeur la plus proche”, which means “rounded to nearest”. The expected answer when the distance to the previous value is the same as the distance to the next is left unspecified.

In this case, “arrondi à l'unité la plus proche” would have been less ambiguous. Arrondir à la dixaine (tens), à la centaine (hundreds), au dixième (tenths), etc. are different possibilities.

Note: rounded up is “arrondi par excès” or “arrondi à la valeur supérieure” and rounded down is “arrondi par défaut” or “arrondi à la valeur inférieure”.

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There are three ways to "round up" :

  • ceiling (1,458 -> 1,46): “arrondi à la valeur supérieure”
  • floor (1,458 -> 1,45): “arrondi à la valeur inférieure” or "troncature",
  • nearest (1,458 -> 1,46), (1,452 -> 1,45) “arrondi à la valeur la plus proche” or simply "arrondi".
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La troncature est un arrondi vers 0, et non pas à la valeur inférieure (ce n'est pas la même chose pour les nombres négatifs). De plus, dans le cas de l'arrondi à la valeur la plus proche, il y a l'ambiguïté du nombre 0,5. Il n'y a donc pas que trois méthodes d'arrondi. –  BatchyX Jan 21 '13 at 7:48

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