Question

Como faço para transformar a dizima periodica 1,212121212121212121... em fração geratriz?

Answer 1

$1,212121212121212121... = 1+0,212121212121212121...=1+ \frac{21}{99} \\ \\=1,212121212121212121... =\frac{99}{99} + \frac{21}{99} =\frac{99+21}{99} = \frac{120^{:3}}{99_{:3}}=\frac{40}{33} \\ \\=1,212121212121212121... =\frac{40}{33}$





$-1,212121212121212121... = -(1+0,212121212121212121...)\\ \\-1,212121212121212121... =-(1+ \frac{21}{99} )\\ \\-1,212121212121212121... =-(\frac{99}{99} + \frac{21}{99}) =-\frac{99+21}{99} =- \frac{120^{:3}}{99_{:3}}=-\frac{40}{33} \\ \\-1,212121212121212121... =-\frac{40}{33}$