Question

Qual é a fração geratriz que representa a seguinte dizima periódica: 2,1121212...​

Answer 1

Considerando que $k=0,1212...$, temos que:

$100k=12,1212...$

$100k=12+0,1212...$

$100k=12+k$

$99k=12$

$k=0,1212...=\frac{12}{99}=\frac{4}{33}$

Daí tiramos que:

$2,11212...=\frac{21,1212...}{10}$

$2,11212...=\frac{21+0,1212...}{10}$

$2,11212...=\frac{21+\frac{4}{33}}{10}$

$2,11212...=\frac{\frac{697}{33}}{10}$

$2,11212...=\frac{697}{330}$