Question

Calcule o valor da expressão:
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Answer 1

Vamos resolver de forma minuciosa para ficar mais claro.

$0,0666...=\frac{10}{10}\cdot0,0666...=\frac{1}{10} \cdot0,6666...=\frac{1}{10} \cdot\frac{6}{9} =\frac{6^{:6}}{90_{:6}} =\frac{1}{15} \\\\0,060606=\frac{06^{:3}}{99_{:3}} =\frac{2}{33}$

$\frac{\frac{2}{9} }{\frac{2}{3}} =\frac{2/9}{2/3} =\frac{2}{9} \cdot\frac{3}{2} =\frac{6^{:6}}{18_{:6}}=\frac{1}{3} \\\\\\0,1=\frac{1}{10}$

$0,0666...:06060606...+3:\frac{\frac{2}{9} }{\frac{2}{3}}\cdot0,1\\ \\=0,0666...:06060606...+\Big[3:\frac{\frac{2}{9}}{\frac{2}{3}}\Big]\cdot0,1\\=\frac{1}{15}\cdot\frac{33}{2}+\Big[3\cdot\frac{3}{1}\Big]\cdot\frac{1}{10}$

$\\=\frac{33^{:3}}{30_{:3}}+\frac{9}{1}\cdot\frac{1}{10}\\\\=\frac{11}{10}+\frac{9}{10}\\\\=\frac{11+9}{10}\\\\=\frac{20}{10}\\=2$