Question

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...

Answer 1

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