Question

fração geratriz das seguintes dízimas periódicas, com contas
a) 0,55555...
b) 1,3838...
c) 2,324324...
d) 1,0833...

Answer 1

a) 0,5555...

x=0,5555...
10x=5,555...
__________
10x-x = 5,555...- 0,5555...
9x=5
x= 5/9


b) 1,3838...

x = 1,3838...
10x = 13,838383...
100x = 138,383838...
_______________
100x - x = 138,3838...- 1,3838...
99x = 137
x = 137/99


c) 2,3243...

x = 2,324324...
10x = 23,243243...
100x = 232,4324...
1000x = 2324,324...
________________
1000x - x = 2324,324...- 2,324324...
999x = 2322
x = 2322/999 ÷ 3
x = 774/333 ÷ 3
x = 258/111


d) 1,08333...

x = 1,08333...
10x = 10,8333...
100x = 108,3333...
1000x = 1083,3333...
_________________
1000x - 100x = 1083,33...- 108,333...
900x = 975
x = 975/900 ÷3
x = 325/ 300 ÷ 5
x = 65/60 ÷ 5
x = 13/12