Question

1- Dê a fração geratriz das seguintes dizimas periódicas:

a) 1,11111...


b) 0.2323232323232323...


c)4,65656565....


d)12,1212121212....


e)182,898989898989...



f) 0,2222222222222222222222222222222222...

Answer 1

Boa noite!

a)
$1,111\ldots=1,\overline{1}=1\frac{1}{9}=\frac{10}{9}$

b)
$0,232323\ldots=0,\overline{23}=\frac{23}{99}$

c)
$4,656565\ldots=4,\overline{65}=4\frac{65}{99}=\frac{461}{99}$

d)
$12,121212\ldots=12,\overline{12}=12\frac{12}{99}=12\frac{4}{33}=\frac{400}{33}$

e)
$182,898989\ldots=182,\overline{89}=182\frac{89}{99}=\frac{18107}{99}$

f)
$0,222\ldots=0,\overline{2}=\frac{2}{9}$

Espero ter ajudado!