Question

Calcule a fração geratriz das dízimas periódicas compostas: a)0,4888… b)4,9555... c)8,1626262

Answer 1

Resposta:

a)

0,4888… = x . (10)

04,888.. = 10 x . (10)

48,888.. = 100x

100x - 10x = 48,888.. - 4,888...

90x = 44

x = $\frac{44}{90} = \frac{22}{45}$

b)

4,9555...   = x . (10)

49,555.. = 10x . (10)

495,555.. = 100x

100x - 10x = 495,55... - 49,55..

90x = 446

x= $\frac{446}{90} = \frac{223}{45}$

c)

   8,16262... = x . (10)

 81,6262... = 10x . (100)

8162,6262.. =  1000x

1000x - 10x = 8162 - 81

990x = 8081

x= $\frac{8081}{990}$

Se quiser entender como calculei assista o vídeo:

https://youtu.be/r-X8QIrlQ3k