Question

determine a geratriz dos seguintes decimais 0,6666..., 1,353535..., 0,12222

Answer 1

0,666..=6/9
1,353535...=1+35/99=99/99+35/99=134/99
0,12222...=(122-1)/90=121/90

Answer 2

10x = 6,6666...
 - x  = 0,6666...
   9x = 6,0000...
      x = $\frac{6}{9}$
      x = $\frac{2}{3}$

100x = 135,353535...
    - x =      1,353535...
  99x = 134,000000...
      x = $\frac{134}{99}$

100x = 12,22222...
    - x =   0,12222...
  99x =  12,10000...
      x =  $\frac{121}{99}$