Question

resolva essas geratriz composta a)0,2333... b)2,03131 ... c)1,12111... d)2,0231231 ... e)0,1222...

Answer 1

Resolva essas geratriz composta




a)0,2333...


           x      =      0,2333.. ( 10) multiplica
       10x     =       2,3333.. ( 10) multiplica
    100x      =     23,3333..

100x = 23,3333..
  10x =   2,3333,, ( subtrai)
-----------------------------
90x =  21,0000...

90x = 21
x = 21/90   ( divide AMBOS por 3)
x = 7/30

então

0,2333... = 7/30

  
 b)2,03131 ...
 
        x   =         2,0313131... (10) miltiplica
    10x  =        20,31313131..(100) multiplica
1000x  =    2031,31313131...

1000x = 2031,31313131
    10x  =    20,31313131...  subtrai
---------------------------------- 
 990x   = 2011,0000000...

990x = 2011
x =2011/990

então

0,20313131... = 2011/990


 c)1,12111...
     
                  x         =         1,12111... ( 100)multilica
            100x         =      112,1111... (10) multiplica
          1000x        =      1121,1111...

1000x =  1121,1111...
  100x  =   112,1111 subtrai
--------------------------------
 900x  = 1009,0000....

900x = 1009

x = 1009/900

1,12111... = 1009/900

   
d)2,0231231 ...


               x         =         2,0231231231...   (10)multiplica
           10x         =       20,231231231...  (1000)multiplica
    10.000x        =  20231,231231231...

10.000x = 20231,231231231...
       10x =       20,231231231...(subtrai)
-------------------------------------------------
  9990x =  20.211,00000000...

9990x = 20211

x = 20.211/9990  ( divide AMBOS por 3)
x = 6737/3330 

e)0,1222...
 
               x      =    0,1222...   ( 10) multiplica
           10x      =   1,2222..     (10) multiplica
         100x      =  12,222..

100x = 12,222..
 10x  =   1,222... subtrai
 ------------------------
  90x = 11,000...

90x = 11
x = 11/90

0,1222... = 11/90