Question

determine a fração geratriz das seguintes dízima periódica a) 8,434343...;b)0,47777;c)2,3111

Answer 1

Determine a fração geratriz das seguintes dízima periódica

a) 8,434343...
 
            x        =       8,434343... ( 100) multiplica    
      100x        =   843,434343...

100x = 843,434343..
      x =     8,434343... subtrai
-------------------------------------
   99x = 835,00000...

99x = 835
x = 835/99

assim
8,434343... = 835/99


;b)0,47777;
 
               x       =    0.4777...(10)multiplica
           10x       =    4,7777...(10) mulltiplica
         100x       =   47,777...

100x = 47,7777...
  10x =   4,7777... subtrai
--------------------------------
   90x = 43,0000...

90x = 43
x = 43/90

assim
0,4777... = 43/90  


c)2,3111


           x        =    2.3111...(10)multiplica
       10x       =   23,111... (10)multiplica
     100x      =   231,111..

100x = 231,111...
  10x =   23,111... subtrai
-----------------------------------
  90x = 208,000...

90x = 208
x = 208/90

assim

2,3111... = 208/90