Question

Resolva: 1,222.../0,1222... por favor.

Answer 1

$\frac{1.222...}{0.1222...}$
dízima periódica 1:
$1.222... = \frac{12 - 1}{9} = \frac{11}{9}$
dízima periódica 2:
$0.1222... = \frac{12 - 1}{90} = \frac{11}{90}$
$portanto. \\ \frac{1.222...}{0.1222...} = \frac{ \frac{11}{9} }{ \frac{11}{90} } = \frac{11}{9} \times \frac{90}{11} = \frac{1}{1} \times \frac{10}{1} = 10$