Question

Qual a fração geratriz da dízima periódica 0,1121212...?
A)112
1000
B)111
99
C)111
990
D)112
99
E)112
990

Answer 1

Caso tenha problemas para visualizar a resposta experimente abrir pelo navegador https://brainly.com.br/tarefa/34199015?answering=true&answeringSource=feedPublic%2FhomePage%2F5

$\sf x=0,11212121...\cdot100\\\sf100x=11,212121...\cdot100\\\sf 10~000x=1121,212121...\\-\underline{\begin{cases}\sf10~000x=1121,212121...\\\sf100x=11,2121...\end{cases}}\\\sf9900x=1110\\\sf x=\dfrac{111\diagup\!\!\!0}{990\diagup\!\!\!0}\\\huge\boxed{\boxed{\boxed{\boxed{\boxed{\sf x=\dfrac{111}{990}}}}}}$