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0, 12 (53581661891117478510028653295128939828080229226361031518624641833810888252148997134670487106017191977077363896848137)

0,12(53581661891117478510028653295128939828080229226361031518624641833810888252148997134670487106017191977077363896848137)

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Explicação passo a passo

1. Monte a divisao longa

$\frac{2450}{19544}$

$\frac{2450}{19544} = 2450 \div 19544$ .

$\frac{2450}{19544}$

$\frac{2450}{19544} = 2450 \div 19544$ .

$\frac{2450}{19544}$

$\frac{2450}{19544} = 2450 \div 19544$ .

$2450 \div 19544$

$\frac{2450}{19544} = 2450 \div 19544$ .

$2450 \div 19544$

$\frac{2450}{19544} = 2450 \div 19544$ .

2. Identifique o ciclo de repeticao

$\frac{2450}{19544}$

$2450 \to 4956 \to 10472 \to 7000 \to 11368 \to 15960 \to 3248 \to 12936$ , $53581661891117478510028653295128939828080229226361031518624641833810888252148997134670487106017191977077363896848137$ .

$\frac{2450}{19544}$

$\frac{24500}{19544} = d i g i t 1, r e m a \in d e r 4956$

$2450 \to 4956 \to 10472 \to 7000 \to 11368 \to 15960 \to 3248 \to 12936$ , $53581661891117478510028653295128939828080229226361031518624641833810888252148997134670487106017191977077363896848137$ .

$4956$

$\frac{49560}{19544} = d i g i t 2, r e m a \in d e r 10472$

$2450 \to 4956 \to 10472 \to 7000 \to 11368 \to 15960 \to 3248 \to 12936$ , $53581661891117478510028653295128939828080229226361031518624641833810888252148997134670487106017191977077363896848137$ .

$10472$

$\frac{104720}{19544} = d i g i t 5, r e m a \in d e r 7000$

$2450 \to 4956 \to 10472 \to 7000 \to 11368 \to 15960 \to 3248 \to 12936$ , $53581661891117478510028653295128939828080229226361031518624641833810888252148997134670487106017191977077363896848137$ .

$7000$

$\frac{70000}{19544} = d i g i t 3, r e m a \in d e r 11368$

$2450 \to 4956 \to 10472 \to 7000 \to 11368 \to 15960 \to 3248 \to 12936$ , $53581661891117478510028653295128939828080229226361031518624641833810888252148997134670487106017191977077363896848137$ .

$11368$

$\frac{113680}{19544} = d i g i t 5, r e m a \in d e r 15960$

$2450 \to 4956 \to 10472 \to 7000 \to 11368 \to 15960 \to 3248 \to 12936$ , $53581661891117478510028653295128939828080229226361031518624641833810888252148997134670487106017191977077363896848137$ .

$15960$

$\frac{159600}{19544} = d i g i t 8, r e m a \in d e r 3248$

$2450 \to 4956 \to 10472 \to 7000 \to 11368 \to 15960 \to 3248 \to 12936$ , $53581661891117478510028653295128939828080229226361031518624641833810888252148997134670487106017191977077363896848137$ .

$3248$

$\frac{32480}{19544} = d i g i t 1, r e m a \in d e r 12936$

$2450 \to 4956 \to 10472 \to 7000 \to 11368 \to 15960 \to 3248 \to 12936$ , $53581661891117478510028653295128939828080229226361031518624641833810888252148997134670487106017191977077363896848137$ .

$12936$

$\frac{129360}{19544} = d i g i t 6, r e m a \in d e r 12096$

$2450 \to 4956 \to 10472 \to 7000 \to 11368 \to 15960 \to 3248 \to 12936$ , $53581661891117478510028653295128939828080229226361031518624641833810888252148997134670487106017191977077363896848137$ .

$12096$

$\frac{120960}{19544} = d i g i t 6, r e m a \in d e r 3696$

$2450 \to 4956 \to 10472 \to 7000 \to 11368 \to 15960 \to 3248 \to 12936$ , $53581661891117478510028653295128939828080229226361031518624641833810888252148997134670487106017191977077363896848137$ .

$3696$

$\frac{36960}{19544} = d i g i t 1, r e m a \in d e r 17416$

$2450 \to 4956 \to 10472 \to 7000 \to 11368 \to 15960 \to 3248 \to 12936$ , $53581661891117478510028653295128939828080229226361031518624641833810888252148997134670487106017191977077363896848137$ .

$17416$

$\frac{174160}{19544} = d i g i t 8, r e m a \in d e r 17808$

$2450 \to 4956 \to 10472 \to 7000 \to 11368 \to 15960 \to 3248 \to 12936$ , $53581661891117478510028653295128939828080229226361031518624641833810888252148997134670487106017191977077363896848137$ .

$17808$

$\frac{178080}{19544} = d i g i t 9, r e m a \in d e r 2184$

$2450 \to 4956 \to 10472 \to 7000 \to 11368 \to 15960 \to 3248 \to 12936$ , $53581661891117478510028653295128939828080229226361031518624641833810888252148997134670487106017191977077363896848137$ .

$2184$

$\frac{21840}{19544} = d i g i t 1, r e m a \in d e r 2296$

$2450 \to 4956 \to 10472 \to 7000 \to 11368 \to 15960 \to 3248 \to 12936$ , $53581661891117478510028653295128939828080229226361031518624641833810888252148997134670487106017191977077363896848137$ .

$2296$

$\frac{22960}{19544} = d i g i t 1, r e m a \in d e r 3416$

$2450 \to 4956 \to 10472 \to 7000 \to 11368 \to 15960 \to 3248 \to 12936$ , $53581661891117478510028653295128939828080229226361031518624641833810888252148997134670487106017191977077363896848137$ .

$3416$

$2450 \to 4956 \to 10472 \to 7000 \to 11368 \to 15960 \to 3248 \to 12936$ , $53581661891117478510028653295128939828080229226361031518624641833810888252148997134670487106017191977077363896848137$ .

$14$

$2450 \to 4956 \to 10472 \to 7000 \to 11368 \to 15960 \to 3248 \to 12936$ , $53581661891117478510028653295128939828080229226361031518624641833810888252148997134670487106017191977077363896848137$ .

$0, 12 (53581661891117478510028653295128939828080229226361031518624641833810888252148997134670487106017191977077363896848137)$

$2450 \to 4956 \to 10472 \to 7000 \to 11368 \to 15960 \to 3248 \to 12936$ , $53581661891117478510028653295128939828080229226361031518624641833810888252148997134670487106017191977077363896848137$ .

3. Escreva o decimal periodico

$2450 / 19544 = 0, 12 (53581661891117478510028653295128939828080229226361031518624641833810888252148997134670487106017191977077363896848137)$

$0, 12 (53581661891117478510028653295128939828080229226361031518624641833810888252148997134670487106017191977077363896848137)$

$12 (53581661891117478510028653295128939828080229226361031518624641833810888252148997134670487106017191977077363896848137) = 0.12 (53581661891117478510028653295128939828080229226361031518624641833810888252148997134670487106017191977077363896848137)$ .

$0, 12 (53581661891117478510028653295128939828080229226361031518624641833810888252148997134670487106017191977077363896848137)$

$12 (53581661891117478510028653295128939828080229226361031518624641833810888252148997134670487106017191977077363896848137) = 0.12 (53581661891117478510028653295128939828080229226361031518624641833810888252148997134670487106017191977077363896848137)$ .

$0, 12 (53581661891117478510028653295128939828080229226361031518624641833810888252148997134670487106017191977077363896848137)$

$12 (53581661891117478510028653295128939828080229226361031518624641833810888252148997134670487106017191977077363896848137) = 0, 12 (53581661891117478510028653295128939828080229226361031518624641833810888252148997134670487106017191977077363896848137)$ .

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Decimais periódicos são comuns em álgebra e estatística. Detectar ciclos ajuda na aritmética exata e na verificação de respostas.

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