Question

Calcule o valor numérico da expressão = 3,212121…+ 1,3666…

Answer 1

Resposta:

4,5787878...

Explicação passo-a-passo:

Ha dois modos:

1)

$\begin{array}{cccccccc}\\\\ &3,&2&1&2&1&2&1\\+&1,&3&6&6&6&6&6\\=&4,&5&7&8&7&8&7\\\end{array}\right]$

2)

$\dfrac{p}{q} = 3,212121...$

$100\frac{p}{q} - \frac{p}{q} = 99 \frac{p}{q}$

$\begin{array}{ccc ccc c} 3&2&1,&2&1&2&1\\-&&3,&2&1&2&1\\\end{array}\\\line(1,0){110}\\\begin{array}{ccc } 3&2&1\\-&&3\\\end{array}\\\line(1,0){50}\\\begin{array}{ccc } 3&1&8\\\end{array}$

$99\frac{p}{q} = 318 \therefore \frac{p}{q} = \frac{318}{99} = \frac{106}{33}$

Do mesmo jeito:

$\dfrac{r}{s} = 1,36666...$

$10\frac{r}{s} - \frac{r}{s} = 13,6666... - 1,3666...\\\therefore 9\frac{r}{s} = 13,6 - 1,3 = 12,3\\\therefore \dfrac{r}{s} = \dfrac{12,3}{9} = \dfrac{41}{30}$

Logo

$3,212121...+ 1,3666... = \dfrac{p}{q} + \dfrac{r}{s} = \dfrac{106}{33} + \dfrac{41}{30} = \dfrac{106\times 10 + 41 \times 11}{330} = \dfrac{1060 + 451}{330} =\\ =\dfrac{1511}{330} = 4,5787878...$