Question

Determine a fração geratriz da dizima periódica 0,25383383383383383...​

Answer 1

$\mathsf{x=0,25383383...\times100}\\\mathsf{100x=25,383383... \times(1000)}\\\mathsf{100000x=25383,383383...}$

$-\underline{\begin{cases}\mathsf{100000x=25383,383383...}\\\mathsf{100x=25,383383... }\end{cases}}$

$\mathsf{99900x=25358}\\\mathsf{x=\dfrac{25358\div2}{99900\div2}}$

$\huge\boxed{\boxed{\boxed{\boxed{\mathsf{x=\dfrac{12679}{49950}}}}}}$