Question

Determine as geratrizes dos números decimais a seguir

A) 8,57222
B) 9,9888
C) 0,15834949
D) 1,152333


(me ajudem por favor)

Answer 1

a) x = 8,57222...
100x = 857,222...
100x = 857 + 2/9
100x = 7715 / 9
900x = 7715
x = 7715/900
x = 1543 / 180

b) x = 9,9888...
10x = 99,888...
10x = 99 + 8/9
10x = 899/9
90x = 899
x = 899/90

c) x = 0,15834949...
10 000x = 1583,4949...
10 000x = 1583 + 49/99
10 000x =156 766 / 99
990 000x = 156 766 
x = 156 766 / 990 000
x = 78 383 / 495 000

d) x = 1,152333...
1000x = 1152,333...
1000x = 1152 + 3/9
1000x = 10371 / 9
9000x = 10371
x = 10371 / 9000
x = 3457 / 3000