Question

Transforme a dizima periódica 1,09090... em fração

Answer 1

1,09 090...

109 -1/99

108/99 ==> : (9/9)

12/11

Answer 2

$\mathsf{x=1,090909...\times100}\\\mathsf{100x=109,090909...}$

$\mathsf{-\underline{\begin{cases}100x=109,090909...\\x=1,090909...\end{cases}}}$

$\mathsf{99x=108}\\\mathsf{x=\dfrac{108\div9}{99\div9}}$

$\boxed{\boxed{\mathsf{x=\dfrac{12}{11}}}}$