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Résultat final Étapes Termes et sujets

0. (530920060331825037707390648567119155354449472096)

0.(530920060331825037707390648567119155354449472096)

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Explication étape par étape

1. Mettre en place la division longue

$\frac{352}{663}$

$\frac{352}{663} = 352 \div 663$ .

$\frac{352}{663}$

$\frac{352}{663} = 352 \div 663$ .

$\frac{352}{663}$

$\frac{352}{663} = 352 \div 663$ .

$352 \div 663$

$\frac{352}{663} = 352 \div 663$ .

$352 \div 663$

$\frac{352}{663} = 352 \div 663$ .

2. Identifier le cycle repetitif

$\frac{352}{663}$

$352 \to 205 \to 61 \to 610 \to 133 \to 4 \to 40 \to 400$ , $530920060331825037707390648567119155354449472096$ .

$\frac{352}{663}$

$\frac{3520}{663} = d i g i t 5, r e m a \in d e r 205$

$352 \to 205 \to 61 \to 610 \to 133 \to 4 \to 40 \to 400$ , $530920060331825037707390648567119155354449472096$ .

$205$

$\frac{2050}{663} = d i g i t 3, r e m a \in d e r 61$

$352 \to 205 \to 61 \to 610 \to 133 \to 4 \to 40 \to 400$ , $530920060331825037707390648567119155354449472096$ .

$61$

$\frac{610}{663} = d i g i t 0, r e m a \in d e r 610$

$352 \to 205 \to 61 \to 610 \to 133 \to 4 \to 40 \to 400$ , $530920060331825037707390648567119155354449472096$ .

$610$

$\frac{6100}{663} = d i g i t 9, r e m a \in d e r 133$

$352 \to 205 \to 61 \to 610 \to 133 \to 4 \to 40 \to 400$ , $530920060331825037707390648567119155354449472096$ .

$133$

$\frac{1330}{663} = d i g i t 2, r e m a \in d e r 4$

$352 \to 205 \to 61 \to 610 \to 133 \to 4 \to 40 \to 400$ , $530920060331825037707390648567119155354449472096$ .

$4$

$\frac{40}{663} = d i g i t 0, r e m a \in d e r 40$

$352 \to 205 \to 61 \to 610 \to 133 \to 4 \to 40 \to 400$ , $530920060331825037707390648567119155354449472096$ .

$40$

$\frac{400}{663} = d i g i t 0, r e m a \in d e r 400$

$352 \to 205 \to 61 \to 610 \to 133 \to 4 \to 40 \to 400$ , $530920060331825037707390648567119155354449472096$ .

$400$

$\frac{4000}{663} = d i g i t 6, r e m a \in d e r 22$

$352 \to 205 \to 61 \to 610 \to 133 \to 4 \to 40 \to 400$ , $530920060331825037707390648567119155354449472096$ .

$22$

$\frac{220}{663} = d i g i t 0, r e m a \in d e r 220$

$352 \to 205 \to 61 \to 610 \to 133 \to 4 \to 40 \to 400$ , $530920060331825037707390648567119155354449472096$ .

$220$

$\frac{2200}{663} = d i g i t 3, r e m a \in d e r 211$

$352 \to 205 \to 61 \to 610 \to 133 \to 4 \to 40 \to 400$ , $530920060331825037707390648567119155354449472096$ .

$211$

$\frac{2110}{663} = d i g i t 3, r e m a \in d e r 121$

$352 \to 205 \to 61 \to 610 \to 133 \to 4 \to 40 \to 400$ , $530920060331825037707390648567119155354449472096$ .

$121$

$\frac{1210}{663} = d i g i t 1, r e m a \in d e r 547$

$352 \to 205 \to 61 \to 610 \to 133 \to 4 \to 40 \to 400$ , $530920060331825037707390648567119155354449472096$ .

$547$

$\frac{5470}{663} = d i g i t 8, r e m a \in d e r 166$

$352 \to 205 \to 61 \to 610 \to 133 \to 4 \to 40 \to 400$ , $530920060331825037707390648567119155354449472096$ .

$166$

$\frac{1660}{663} = d i g i t 2, r e m a \in d e r 334$

$352 \to 205 \to 61 \to 610 \to 133 \to 4 \to 40 \to 400$ , $530920060331825037707390648567119155354449472096$ .

$334$

$352 \to 205 \to 61 \to 610 \to 133 \to 4 \to 40 \to 400$ , $530920060331825037707390648567119155354449472096$ .

$14$

$352 \to 205 \to 61 \to 610 \to 133 \to 4 \to 40 \to 400$ , $530920060331825037707390648567119155354449472096$ .

$0. (530920060331825037707390648567119155354449472096)$

$352 \to 205 \to 61 \to 610 \to 133 \to 4 \to 40 \to 400$ , $530920060331825037707390648567119155354449472096$ .

3. Ecrire le decimal periodique

$352 / 663 = 0. (530920060331825037707390648567119155354449472096)$

$0. (530920060331825037707390648567119155354449472096)$

$(530920060331825037707390648567119155354449472096) = 0. (530920060331825037707390648567119155354449472096)$ .

$0. (530920060331825037707390648567119155354449472096)$

$(530920060331825037707390648567119155354449472096) = 0. (530920060331825037707390648567119155354449472096)$ .

$0. (530920060331825037707390648567119155354449472096)$

$(530920060331825037707390648567119155354449472096) = 0. (530920060331825037707390648567119155354449472096)$ .

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Les décimales périodiques sont courantes en algèbre et en statistiques. Détecter les cycles aide à faire des calculs exacts et à vérifier les réponses.

Termes et sujets

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