Question

Dada a dízima periódica calcule a fração geratriz :
a - 0,44444...
b - 0,12525...
c - 0,54545...
d - 0,04777...
e - 1,92727...
f - 0,585858...

Answer 1

a)  0,4444...
X=0,4444...    .(10)
10X=4,444

10X=4,444
-X=   0,444
---------------------
9X=   4,000

X=4/9 

B) 0,12525
x=0,12525..     .(10)
10x=1,2525     .(100)
1000x=125,2525

1000x=125,2525
-10x=       1,2525
--------------------------
990x=  124,0000

x=124/990

C) 0,545454...
x=0,54545...     .(100)
10x=54,5454....     
 
100x=54,5454
-x=       0,5454
-----------------------
99x=  54,0000

x=54/99  ai vc dividi os dois por 9

x=6/11

D)0,04777...
x=0,04777    .(100)
100x=4,777  .(10)
1000x=47,777

1000x=47,777
-100x=   4,777
-----------------------
900x=   43,000

x=43/900

E)1,92727
x=1,92727       .(10)
10x=19,2727   .(100)
1000x=1927,2727

1000x=1927,2727
-10x=      19,2727
--------------------------
990x= 1908,0000

x=1908/990 dividi por 18        x=16/55

F)0,585858
x=0,585858      .(100)
100x=58,5858

100x=58,5858
-x=       0,5858
----------------------
99x=  58,0000

x=99/58

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