Question

determine as frações geratriz dos números racionais.
a) 0,222...
b) 0,321321
c) 0,34545
d) 0,1212
e) 0,333
f) 0,23131

Answer 1

0,222.... 2/9
0,321321....  321/999
03 4545.....  = ( 345-3 )/ 990  = 342 = 990  = 38/110
0,1212..... 12/99  = 4/33
0,333.....  3/9 = 1/3
0,2 3131... = ( 231 - 2)/990 = 229/990

Answer 2

a) X= 0,222... (10)
10X= 2,222...
-  X = 0,222...
 9X = 2
  X = 2/9

b) X= 0,323232... (100)
100X= 32,323232...
      X=   0,323232...
  99X= 32
 X= 32/99

c) X= 0,34545... (10)
10X = 3,454545... (100)
100X = 345,454545...
  10X =     3,454545...
  99X = 342
X= 342/99

d)X= 0,121212...(100)
100X = 12,121212...
      X =   0,121212...
 99X  = 12
X= 12/99

e)X= 0,333...(10)
10X = 3,333...
 - X  = 0,333...
 9X  = 3
X= 3/9

f)X= 0,23131...(10)
10X = 2,313131...(100)
100X = 231,313131...
  10X =     2,313131...
  90X = 229
X=229/90