Question

calcule a fração geratriz para cada dízima periódica abaixo.


a) -0,7777....

b) 5,3888...

c)1,8999....

d)1,20101010

Answer 1

A)

0,777... = x

10x= -7,777...

10x= -7+0,777...

10x= -7+x

10x-x= -7

   9x= -7

     x= -7/9

Resposta → -7/9

B)

5,3888...

100x= 538,88...

100x= 538+0,88...    

100x= 538+8/9

100x= 4842/9 + 8/9

    100x= 4850/9

        x= 4850/9*100

        x= 4850/900

        x= 97/18

Resposta → 97/18

C)

1,8999...

100x= 189,99...

100x= 189+0,99...

100x= 189+ 9/9

100x= 189+1

100x= 190

     x= 190/100

     x= 19/10

Resposta → 19/10

Temos que aceitar isso kkkkkk pois 0,999... = 9/9= 1

D)

1,20101010...

10000x= 12010,1010...

10000x= 12010+0,1010...          → 0,1010= 10/99

10000x= 12010 + 10/99

10000x= 1188990/99 + 10/99

10000x= 1189000/99

         x= 1189000/99*10000

          x= 1189000/990000

           x= 1189/990

Resposta → 1189/990