Question

qual é a fraçao geratriz das dizimas periotica..
0,44444....
0,121212...
]0,477777..
?

Answer 1

$a) 0,4444...= \frac{4}{9} \\ b) 0,121212...= \frac{12^{:3}}{99_{:3}}= \frac{4}{33}\\ c) 0,4777...=0,4+0,0777...=0,4+ \frac{10}{10} \cdot 0,0777...\\ \\=0,4+ \frac{1}{10} \cdot 0,777...= \frac{4}{10} + \frac{1}{10} \cdot \frac{7}{9} \\ \\= \frac{4}{10} + \frac{7}{90} = \frac{36}{90} + \frac{7}{90} = \frac{36+7}{90}= \frac{43}{90}$