Question

Determine as geratrizes das seguintes dizimas periodicas:
a= 3,151515 b=0,05222 c=0,007007007 d= -2,4777 e=0,888 f= -0,02333 g=0,1444 h= 1,42131313 i= 2,75252525 j= 0,1333 ...

Answer 1

a) 3,1515... 3 15/99 = (99 x 3 + 15)/99 = 312/99 = 104/33

b) 0,05222... = (052 - 05)/900 = 47/900

c) 0,007007... = 007/999 = 7/999

d) -2,4777.. = 2 (47 - 4)/90 = 2 (43/90) = (90 x 2 + 43)/90 = -223/90 

e) 0,888... = 8/9

f) -0,02333.. = (023 - 02)/900 = 21/900 = -7/300

g) 0,1444... = (14 - 1)/90 = 13/90

h) 1,421313... = 1 (4213 - 42)/9900 = 1 4171/9900 = (9900 x 1 + 4171)/9900 = 14071/9900 

i) 2,752525... = 2 (752 - 7)/990 = 2 745/990 = (990 x 2 + 745)/990 = 2725/990 = 545/198

j) 0,1333.. = (13 - 1)/90 = 12/90 = 2/15

Espero ter ajudado.