Question

Determine a geratriz a/b dos seguinte decimal periódico 0,2424....​

Answer 1

$\sf{x=0,242424...\cdot100}\\\sf{100x=24,242424...}$

$-\underline{\begin{cases}\sf{100x=24,242424...}\\\sf{x=0,242424...}\end{cases}}$

$\sf{99x=24}\\\sf{\dfrac{24}{99}=\dfrac{8\cdot\diagup\!\!\!\!3}{\diagup\!\!\!\!3\cdot33}}\\\huge\boxed{\boxed{\boxed{\boxed{\sf{x=\dfrac{8}{33}}}}}}$