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0. (181102362204724409448818897637795275590551)

0.(181102362204724409448818897637795275590551)

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Explicação passo a passo

1. Monte a divisao longa

$\frac{46}{254}$

$\frac{46}{254} = 46 \div 254$ .

$\frac{46}{254}$

$\frac{46}{254} = 46 \div 254$ .

$\frac{46}{254}$

$\frac{46}{254} = 46 \div 254$ .

$46 \div 254$

$\frac{46}{254} = 46 \div 254$ .

$46 \div 254$

$\frac{46}{254} = 46 \div 254$ .

2. Identifique o ciclo de repeticao

$\frac{46}{254}$

$46 \to 206 \to 28 \to 26 \to 6 \to 60 \to 92 \to 158$ , $181102362204724409448818897637795275590551$ .

$\frac{46}{254}$

$\frac{460}{254} = d i g i t 1, r e m a \in d e r 206$

$46 \to 206 \to 28 \to 26 \to 6 \to 60 \to 92 \to 158$ , $181102362204724409448818897637795275590551$ .

$206$

$\frac{2060}{254} = d i g i t 8, r e m a \in d e r 28$

$46 \to 206 \to 28 \to 26 \to 6 \to 60 \to 92 \to 158$ , $181102362204724409448818897637795275590551$ .

$28$

$\frac{280}{254} = d i g i t 1, r e m a \in d e r 26$

$46 \to 206 \to 28 \to 26 \to 6 \to 60 \to 92 \to 158$ , $181102362204724409448818897637795275590551$ .

$26$

$\frac{260}{254} = d i g i t 1, r e m a \in d e r 6$

$46 \to 206 \to 28 \to 26 \to 6 \to 60 \to 92 \to 158$ , $181102362204724409448818897637795275590551$ .

$6$

$\frac{60}{254} = d i g i t 0, r e m a \in d e r 60$

$46 \to 206 \to 28 \to 26 \to 6 \to 60 \to 92 \to 158$ , $181102362204724409448818897637795275590551$ .

$60$

$\frac{600}{254} = d i g i t 2, r e m a \in d e r 92$

$46 \to 206 \to 28 \to 26 \to 6 \to 60 \to 92 \to 158$ , $181102362204724409448818897637795275590551$ .

$92$

$\frac{920}{254} = d i g i t 3, r e m a \in d e r 158$

$46 \to 206 \to 28 \to 26 \to 6 \to 60 \to 92 \to 158$ , $181102362204724409448818897637795275590551$ .

$158$

$\frac{1580}{254} = d i g i t 6, r e m a \in d e r 56$

$46 \to 206 \to 28 \to 26 \to 6 \to 60 \to 92 \to 158$ , $181102362204724409448818897637795275590551$ .

$56$

$\frac{560}{254} = d i g i t 2, r e m a \in d e r 52$

$46 \to 206 \to 28 \to 26 \to 6 \to 60 \to 92 \to 158$ , $181102362204724409448818897637795275590551$ .

$52$

$\frac{520}{254} = d i g i t 2, r e m a \in d e r 12$

$46 \to 206 \to 28 \to 26 \to 6 \to 60 \to 92 \to 158$ , $181102362204724409448818897637795275590551$ .

$12$

$\frac{120}{254} = d i g i t 0, r e m a \in d e r 120$

$46 \to 206 \to 28 \to 26 \to 6 \to 60 \to 92 \to 158$ , $181102362204724409448818897637795275590551$ .

$120$

$\frac{1200}{254} = d i g i t 4, r e m a \in d e r 184$

$46 \to 206 \to 28 \to 26 \to 6 \to 60 \to 92 \to 158$ , $181102362204724409448818897637795275590551$ .

$184$

$\frac{1840}{254} = d i g i t 7, r e m a \in d e r 62$

$46 \to 206 \to 28 \to 26 \to 6 \to 60 \to 92 \to 158$ , $181102362204724409448818897637795275590551$ .

$62$

$\frac{620}{254} = d i g i t 2, r e m a \in d e r 112$

$46 \to 206 \to 28 \to 26 \to 6 \to 60 \to 92 \to 158$ , $181102362204724409448818897637795275590551$ .

$112$

$46 \to 206 \to 28 \to 26 \to 6 \to 60 \to 92 \to 158$ , $181102362204724409448818897637795275590551$ .

$14$

$46 \to 206 \to 28 \to 26 \to 6 \to 60 \to 92 \to 158$ , $181102362204724409448818897637795275590551$ .

$0. (181102362204724409448818897637795275590551)$

$46 \to 206 \to 28 \to 26 \to 6 \to 60 \to 92 \to 158$ , $181102362204724409448818897637795275590551$ .

3. Escreva o decimal periodico

$46 / 254 = 0. (181102362204724409448818897637795275590551)$

$0. (181102362204724409448818897637795275590551)$

$(181102362204724409448818897637795275590551) = 0. (181102362204724409448818897637795275590551)$ .

$0. (181102362204724409448818897637795275590551)$

$(181102362204724409448818897637795275590551) = 0. (181102362204724409448818897637795275590551)$ .

$0. (181102362204724409448818897637795275590551)$

$(181102362204724409448818897637795275590551) = 0. (181102362204724409448818897637795275590551)$ .

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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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