Question

Determine as frações geratrizes das dízimas periódicas:
A)0,777...
B)0,4222...
C)2,151515...
D)0,9999...
E)1,9898
F)0,231231231

Answer 1

$a)0,777...= \frac{7}{9}\\\\b)0,4222...= \frac{42-4}{90}= \frac{38}{90}= \frac{19}{45}\\\\c)2,151515...=2+ \frac{15}{99}= \frac{198+15}{99}= \frac{213}{99}= \frac{71}{33}\\\\d)0,999...= \frac{9}{9}=1\\\\e)1,9898...=1+ \frac{98}{99}= \frac{99+98}{99}= \frac{197}{99}\\\\f)0,231231231...= \frac{231}{999}= \frac{77}{333}$