Question

Obtenha as geratrizes das dizimas periódicas.

a) 0,444...

b) 3,888...

c) 9,151515...

d) 5,4317878...

Answer 1

a) x = 0,444      10x = 4,444
10x - x = 4,444 - 0,444
9x = 4
x = 4/9

b) x = 3,888        10x = 38,888
10x - x = 38,888 - 3,888
9x = 35
x = 35/9

c) x = 9,151515       100x = 915,151515
100x - x = 915,15 - 9,15
99x = 906
x = 906/99 >>>302/33

d) x = 5,4317878        1000x = 5431,7878       100000x = 543178,7878
100.000x - 1.000x = 543178,78 - 5431,78
99.000x = 537.747
x = 537.747 / 99.000  >>> 179.249 / 33.000