Transforme dízimas periódicas simples em Frações Geratrizes;
A) 0,111...
B) 0, 2333...
C) 0, 252525...
D) 0, 45222...
E) 0, 010101...
F) 0, 123123123...
Respostas
Resposta:
A) 0,111...
10x= 1,111...
10x-x= 1,111... - 0,111...
9x= 1
x= 1/9
B) 0,252525...
100x= 25,252525...
100x-x= 25,252525... - 0,252525...
99x= 25
x= 25/99
C) 0,0101010...
10x= 0,101010...
1000x 10,101010...
1000x-10x= 10,101010... - 0,101010...
9990x= 10
x= 10/9990
D) 0,123123123...
1000x= 123,123123123...
1000x-x= 123,123123123... - 0,123123123...
999x= 123
x= 123/999
E) 0,535353...
100x= 53,535353...
100x-x= 53,535353... - 0,535353...
99x= 53
x= 53/99
F) 0,555...
10x= 5,555...
10x-x= 5,555... - 0,555...
9x= 5
x= 5/9
G) 0,321321321...
1000x= 321,321321321....
1000x-x= 321,321321321... - 0,321321321...
999x= 321
x= 321/999
H) 0,141414...
100x= 14,141414...
100x-x= 14,141414... - 0,141414...
99x= 14
x= 14/99
I) 0,421042104210...
10000x-x= 4210,421042104210... - 0,421042104210...
9999x= 4210
x= 4210/9999
J) 0,323232...
100x= 32,323232...
100x-x= 32,323232... - 0,323232...
99x= 32
x= 32/99