Question

Transforme as dízimas períodicas simples em frações geratrizes : a) 0,1111... b) 0,25252525... c) 0,01010101... d) 0,123123123123... e) 0,53535353... f) 0,5555... g) 0,321321321321... h) 0,14141414... i) 0,4210421042104210... j) 0,32323232 Eu preciso urgente quem me ajudar muito obrigado!!!!!

Answer 1

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

Espero ter ajudado ☺️