Question

Determine a geratriz a/b dos seguintes decimais periódicos.

A)0,333...
B)0,1666...
C)0,242424...
D)0,125777...

Answer 1

a) x = 0,333...
10x = 3,333..
10x = 3 + 0,333...
10x = 3 + x
10x - x = 3
9x = 3
x = 3/9
x = 1/3

b) x = 0,1666...
10x = 1,666...
10x = 1 + 6/9
10x = 15/9
90x = 15
x = 15/90
x = 1/6

c) x = 0,242424...
100x = 24,2424...
100x = 24 + x
100x-x = 24
99x = 24
x = 24/99
x = 8/33

d) x =  0,125777...
1000x = 125,777...
1000x = 125 + 7/9
1000x = 1132/9
9000x = 1132
x = 1132/9000
x = 283/2250