Question

encontre a fraçao geratriz (simplificada) das dizimas periodicas a seguir A 0,6666... B 8,555... C ,5252... D 0,2828... E 12,3444... F 15,6222... G 20,7888... H 7,2355...

Answer 1

a) x = 0,666 10x = 6,666
10x - x = 6,66 - 0,66
9x = 6 
x = 6/9 >>> 2/3

b) x = 8,555    10x = 85,555
10x - x = 85,555 - 8,555
9x = 77
x = 77/9

c) x = 0,5252      100x = 52,5252
100x - x = 52,52 - 0,52
99x = 52
x = 52/99

d) x = 0,2828     100x = 28,2828
100x - x = 28,28 - 0,28
99x = 28
x = 28/99

e) x = 12,3444   10x = 123,444    100x = 1234,444
100x - 10x = 1234,44 - 123,44
90x = 1111
x = 1111 / 90

f) x = 15,6222     10x = 156,222      100x = 1562,222
100x - 10x = 1562 - 156
90x = 1406
x = 1406 / 90 >>> 703/45

g) x = 20,7888     10x = 207,888     100x = 2078 ,888
100x - 10x = 2078,88  - 207,88
90x = 1871
x = 1871 / 90

h) x = 7,23555   100x = 723,555   1000x = 7235,555
1000x - 100x = 7235,55 - 723,55
900x = 6512
x = 6512/900  >>> 1628/225