Question

determine as frações geratrizes das seguintes dizimas periódicas
2,3555...​

Answer 1

$2,3555...~=~2+0,3+0,0555...\\\\\\2,3555...~=~2+\frac{3}{10}+\frac{5}{90}\\\\\\2,3555...~=~\frac{90~.~2~+~9~.~3~+~1~.~5}{90}\\\\\\2,3555...~=~\frac{180+27+5}{90}\\\\\\2,3555...~=~\frac{212}{90}\\\\\\\boxed{2,3555...~=~\frac{106}{45}}$