Question

Determine as frações geratrizes das seguintes dízimas periódicas



a)0,23333…
b)1,244...
c)0,1717...​

Answer 1

a)

x = 0,2333...

10x = 10 . 0,2333... --> 10x = 2,333...

100x = 100 . 0,2333...  -->  100x = 23,333...

100x - 10x = 23,333... - 2,333...

90x = 21

x = 21/90

x = 7/30

Logo, 0,2333... = 7/30

b)

x = 1,244...

10x = 10 . 1,244... --> 10x = 12,444...

100x = 100 . 1,244...  -->  100x = 124,444...

100x - 10x = 124,444... - 12,444...

90x = 112

x = 112/90

x = 56/45

Logo, 1,244... = 56/45

c)

x = 0,1717...​

10x = 10 . 0,1717...​  --> 10x = 1,7171...

100x = 100 . 0,1717...​  --> 100x = 17,1717...

100x - x = 17,1717... - 0,1717...

99x = 17

x = 17/99

Logo, 0,1717... = 17/99