Question

transforme cada número decimal em uma fração geratriz
a)0,444444444...

b)1,23232323...

c)2,21111111...

d)0,123123123123...​

Answer 1

Resposta:

a) $x = \frac{4}{9}$     b) $x = \frac{122}{99}$    c) $x = \frac{199}{90}$   d) $x = \frac{123}{999}$

Explicação passo-a-passo:

a)0,444444444...

   x = 0,4444444

10x = 4,4444444

10x = 4,4444444

  -x = 0,4444444

9x = 4 => $x = \frac{4}{9}$

b)

    x = 1,23232323

100x = 123,123123

100x = 123,123123

   -  x =     1,23232323

  99x = 122 => $x = \frac{122}{99}$

c)

    x = 2,211111

10 x = 22,11111

100 x = 221,1111

100 x = 221,1111

 -10 x =   22,11111

  90x = 199 => $x = \frac{199}{90}$

d)

x = 0,123123123123..

10x = 1,23123123123..

100x = 12,3123123123..

1000x = 123,123123123..

1000x = 123,123123123..

     - x =     0,123123123123..

999x = 123 => $x = \frac{123}{999}$