Question

Resolva: 1,888... • 2/17

Answer 1

Primeiro vamos encontrar a fração geratriz da dízima periódica $1,888\ldots$.

$x=1,888\ldots=1,\overline{8}\\ \\ 10x=18,888\ldots=18,\overline{8}\\ \\ \\ 18,888\ldots=17+1,888\dots\\ \\ 10x=17+x\\ \\ 10x-x=17\\ \\ 9x=17\\ \\ x=\dfrac{17}{9} \Rightarrow \boxed{1,888\ldots=\dfrac{17}{9}}$


Então

$1,888\ldots \times \dfrac{2}{17}\\ \\ =\dfrac{17}{9} \times \dfrac{2}{17}\\ \\ =\dfrac{17 \times 2}{9 \times 17} \rightarrow \boxed{\text{O 17 \'{e} cancelado}}\\ \\ =\dfrac{2}{9}\\ \\ \\ \boxed{1,888\ldots \times \dfrac{2}{17}=\dfrac{2}{9}}$