Question

Encontre a fração geratriz de 2, 232323

Answer 1

$\mathtt{Fra\c{c}\~ao~Geratriz:} \\ \\ \mathtt{x = 2,23232...~~~(10)} \\ \mathtt{10x = 22,3232...~~~(100)} \\ \mathtt{1.000x =2.232,3232 ... ~~subtrair~3^o~linha~com~2^o~'}\\ ----------- \\ \mathtt{990x =2.210 } \\ \mathtt{x = \frac{2.210}{990}} \\ \\ \mathtt{x = \frac{221}{99}} \\ \\ \\ \boxed{\boxed{\mathtt{Resposta: \dfrac{221}{99}}}}$