Question

fração geratriz de 7, 6444​

Answer 1

Existem duas formas de calcular a dízima periódica composta:

1.

$\Rightarrow \ \ \ \ x \ \ = \ \ 7,6444... \\\\ \Rightarrow \ \ \ \ 10x \ \ = \ \ 76,444... \\\\ \Rightarrow \ \ \ 10x \ \ = \ \ 76 \ + \ \frac{4}{9} \\\\ \Rightarrow \ \ \ 10x \ \ = \ \ \frac{688}{9} \\\\ \Rightarrow \ \ \ \boxed{ \ x \ \ = \ \frac{688}{90} \ }$

2.

$7,6444... \ \ \ \iff \ \ \ \frac{764 \ - \ 76}{90} \ \ \ \iff \ \ \ \boxed{ \ \frac{688}{90} \ }$

De qualquer forma,

$\huge\boxed{ \ RESPOSTA \ \ \Rightarrow \ \ 688/90 \ \ }$