Question

encontre a fração geriatria de cada dízima periódica a seguir .
a)8,3333333....
b)4,121212......
c)0,451451451.....
d)2,34222222....​

Answer 1

a) x=8,333...(10)

10x=83,33...

10x=83+0,33..

10x=83+3/9

90x/9=747/9+3/9

90x=750

x=750/90

75/9=8,3333....

b) x=4,121212...(100)

100x=412,1212...

100x=412+0,1212...

100x=412+12/99

9.900x/99=40.788/99+12/99

9.900x=40.800

x=40.800/9.900

408/99=4,121212...

c) x=0,451451451...(1000)

1000x=451,451451...

1000x=451+0,451451...

1000x=451+451/999

999.000x/999=450.549/999+451/999

999.000x=451.000

x=451.000/999.000

451/999=0,451451451...

d) x=2,3422222...(1000)

1000x=2.342,2222...

1000x=2.342+0,2222.....

1000x=2.342+2/9

9000x/9=21.078/9+2/9

9000x=21.080

x=21.080/9000

2.108/900=2,3422222...