Question

Fração geratriz das dízimas periódicas simples de 3,21212121

Answer 1

I) x = 3,2121212121...

II) 10x = 32,121212121...

III) 100x = 321,21212121...

III) - I)

$\left \{ {{x = 3,212121...} \atop {100x=321,212121...}} \right.$

Fazendo III) - I), teremos

100x - x = 321,2121.... - 3,2121....

99x = 321 - 3

99x = 318

x = 318/99 = 106/33