Question

Determine a fração geratriz de cada dízima periódica a seguir:
a)3,0 21 21 21 21...
b)3,2 2 2 2 2 2....

Answer 1

a) 3,021~  =   x

3021,21~ =  1000x

3021,21 - 3,021  =  1000x - x 
3018 = 999x
x = 3018/999   = 1006/333

B)  3,2222

3,2222 = x 
32,222 = 10 x

32,222 - 3,222 = 10x - x
29 = 9x 

x = 29/9

Answer 2

A ) 

$\boxed{3,02121...= \frac{3021-30}{990} = \frac{2991^{\div3}}{990^{\div3}} = \frac{997}{330} }$

B ) 

$\boxed{3,222...= \frac{32-3}{9} = \frac{29}{9} }$