Question

Determine a geratriz de cada uma destas dizimas periodicas a- 0,888 b-0,212121
c-0,517517517
d-0,23131313

Answer 1

a-
0,888.. = 8/9

b-
0,212121... = 21/99 = 7/33

c-
0,517517517... = 517/999

d-
0,2313131... = 229/990

Answer 2

Vamos lá :

a) 0,888...

a = 0,888...
10a = 8,888...
____________+
10a - a = 8 - 0
9a = 8
a = 8/9

__________________________
b) 0,212121...

b = 0,212121..
100b = 21,212121...
_________________+
100b - b = 21 - 0
99b = 21
b = 21÷3/99 ÷3 = 7/33

________________________
c) 0,517517517 ...

c = 0,517517517...
1000c = 517,517517517..
_____________________+
1000c - c = 517 - 0
999c = 517
c = 517/999

__________________________
d) 0,2313131...

10d = 2,313131...
1000d = 231,313131...
__________________+
1000d - 10d = 231 - 2
990d = 229
d = 229/990

Espero ter ajudado !!!