Question

Qual a fração que gerou a seguinte dízima periódica composta: 9,18222... ?

Answer 1

Resposta:

9,182 22...

9182 - 918 / 900
8264/900 ✓

Answer 2

Hi !

Resolução

Acompanhe a conta abaixo:

$\sf x=9,18222\cdots \\\\\\\sf 100x=918,222\cdots\\\\\\\sf 100x-x=918,222\cdots-9,18222\\\\\\\sf 909,03978\cdots$

Portanto:

$\sf 99x=909,03978\cdots\Rightarrow \boxed{\sf \frac{909,03978}{99} }$

Prova:

$\sf \dfrac{909,\:03978}{99}=918222\cdots$