Question

Fração geratriz da dízima periodica
A) 3,7777777...
B) 7,3444444...
C) 5,1266666...

Answer 1

3,7777..
x=3,777...
10x=37,7777...
10x-x=37,777...-3,777...
9x=34
x=34/9

7,344444...
x=7,34444...
10x=73,4444...
100x=734,4444...
100x-10x=734,444...-73,444...
90x=661
x=661/90

5,12666...
x=5,12666...
100x=512,666....
1000x=5126,666...
1000x-100x=5126,666...-512,666...
900x=4614
x=4614/900 (simplifica por 6)
x=769/150