Question

ATIVIDADE 2 - Determine a fração geratriz das dízimas periódicas simples e compostas abaixo:
A) 0,3555...
B) 36, 12666...
C) 1,4444....
D) 36, 12666...​

Answer 1

Resposta:

$A =\frac{35}{99}$     $B =\frac{32514}{900}$     $C =\frac{13}{9}$          $D =\frac{32514}{900}$

Explicação passo-a-passo:

A)  

     x = 0,3535

100x = 35,3535

100x = 35,3535

   - x = 0,3535

99x = 35

$x = \frac{35}{99}$

B)   x = 36,12666

100x = 3612,666

1000x = 36126,66

1000x = 36126,666

-100x =   3612,666

900x = 32514

$x = \frac{32514}{900}$

C)     x= 1,4444

    10x= 14,444

10x= 14,444

- x=   1,4444

9x= 13

$x = \frac{13}{9}$

D) x = 36,12666

100x = 3612,666

1000x = 36126,66

1000x = 36126,666

-100x =   3612,666

900x = 32514

$x = \frac{32514}{900}$