Question

Ache a fração geratriz das dízimas abaixo:

a) 1,1233333...

b) 0,0232323...

Answer 1

a) x = 1,12333.. 10x = 11,23333..
100x = 112,333... 1000x = 1123,333..

1000x - 100x = 1123,333... - 112,333..
900x = 1011
x = 1011/900


b) 0,02323...
1000x = 23,23 10x = 0,2323...
1000x - 10x = 23,23.. - 0,23..
990x =23
x = 23/990

Answer 2

a) 1,1233333... =  1123-112 =  1011
                                  900            900      

b) 0,0232323...=   23
                            990