Question

calculando o valor da expressão
$\frac{0.2727..... + \frac{1}{3} }{4 - 0.2222....}$
obtmos:
a)30
187

b)3
20

c)15
17

d)4
15

e)19
200​

Answer 1

Explicação passo-a-passo:

${0,2727,,+{1\over3}\over4-0,222...}=\\ \\ 0,2727..={27\over99}={3\over11}\\ \\ 0,222...={2\over9}\\ \\ Logo\\ \\{ {3\over11}+{1\over3}\over4-{2\over9}}=\\ \\ {{9+11\over33}\over{36-2\over9}}=\\ \\ {{20\over33}\over{34\over9}}=\\ \\ {20\over33}\div{34\over9}={20\over33}\times{9\over34}=\\ \\ simplificando\\ \\ {\not20^{10}\over\not33_{11}}\times{\not9^3\over\not34_{17}}=\\ \\ {10\over11}\times{3\over17}={30\over187}~\mapsto letra~~A$