Question

escreva a fração geratriz das dízimas periódicas: a) 0, 128128128 d) 0, 19444...​

Answer 1

$\large\boxed{\begin{array}{l}\rm a)\\\sf x=0,128128...\cdot1000\\\sf 1000x=128,128128...\\-\underline{\begin{cases}\sf 1000x=128,128128...\\\sf x=0,128128...\end{cases}}\\\sf 999x=128\\\sf x=\dfrac{128}{999}\end{array}}$

$\large\boxed{\begin{array}{l}\rm d)\\\sf x=0,19444...\cdot100\\\sf 100x=19,444...\cdot10\\\sf 1000x=194,444....\\-\underline{\begin{cases}\sf1000x=194,444....\\\sf 100x=19,444...\end{cases}}\\\sf 900x=175\\\sf x=\dfrac{175\div25}{900\div25}\\\\\sf x=\dfrac{7}{36}\end{array}}$