Question

Transforme as dizimas periódicas em geratrizes: a)3,444... b)-2,5 c)0,45 d)-0,31222...

Answer 1

A) 31/9
B ) 22,5/ 9 = 225/90 = 25 / 10
C) 45/10
D) 2,81/9 = 281/900

Answer 2

a) 3,444...

10x = 34,444...
    x =   3,444...
⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻
   9x = 31
     x = 31/9

b) - 2,555...

10x = - 25,555...
    x =   - 2,555...
⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻
  9x = - 23
    x = - 23/9

c) 0,4545...

100x = 45,4545...
      x =   0,4545...
⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻
  99x = 45
      x = 45/99
      x = 5/11

d) - 0,31222...

1000x = - 312,222...
  100x =    - 31,222...
⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻
   900x = - 281
         x = - 281/900