Question

Encontre a fração geratriz do decimal exato 0,12 e da dízima periódica 0,777...

a) 3/25 e 7/9
b) 3/15 e 7/9
c) 3/25 e 7/999
d) 1/2 e 7/999

Answer 1

$\boxed{\begin{array}{l}\sf 0,12=\dfrac{12\div4}{100\div4}=\dfrac{3}{25}\\\sf x=0,777...\cdot10\\\sf 10x=7,777...\\-\underline{\begin{cases}\sf10x=7,777\\\sf x=0,777....\end{cases}}\\\sf 9x=7\\\sf x=\dfrac{7}{9}\\\huge\boxed{\boxed{\boxed{\boxed{\sf\maltese~alternativa~a}}}}\end{array}}$