Question

Determine a fração geratriz de:

a) 0,2121...
b) 24,444...
c) 0,4999...

Answer 1

Resposta:

Explicação passo-a-passo:

a) 0,2121...

x = 0,2121...

10x = 2,121...

100x = 21,2121...

100x = 21,2121...

    - x = 0,2121...

 99x = 21 => $x = \frac{21}{99} => x = \frac{21:3}{99:3} => x = \frac{7}{33}$

b) 24,444...

x = 24,444...

10x = 244,444..

10x = 244,444..

  - x = 24,444...

 9x = 220 => $x = \frac{220}{9}$

c) 0,4999..

  x = 0,4999..

10x = 4,999..

100x = 49,999..

100x = 49,999..

-10x    = 4,999..

90x = 45 => $x = \frac{45}{90} => x = \frac{45:45}{90:45} =>x = \frac{1}{2}$