Question

1)Escreva a fração geratriz das seguintes dízimas periódicas.
A)4,412412412...
B)0,4312312312...
C)1,7444...

Answer 1

A) x = 4,412412412... (.10)
10x = 44,12412412... (.100)
100x = 441,2412412... (.1000)
1000x = 4412,412412...
900x = 3971
x = 3971/900

B) x = 0, 43123123... (.10)
10x = 4,3123123... (.100)
100x = 43,123123... (.1000)
1000x = 431,23123123... (.10000)
10000x = 4312,3123123... (.100000)
100000x = 43123,123123...
90000x = 38811
x = 38811/90000

C) x = 1,7444... (.10)
10x = 17,444... (.100)
100x = 174,444...
90x = 157 
x = 157/90

Desculpa se tiver algum erro. :)