Question

Exercicio de Dizima Periodica:
A)0,888...
B)0,287...
C)0,1515...
D)0,999...
E)0,121121...
F)0,3434...
G)0,555...
H)0,7878...
PFV E PRA AMANHA ;-;

Answer 1

A)0,888...

:>: 8/9

B)0,287...

:>: 287/999

C)0,1515...

:>: 15/99

D)0,999...

:>: 9/9 = 1

E)0,121121...

:>: 121/999

F)0,3434...

:>: 34/99

G)0,555...

:>: 5/9

H)0,7878...

:>: 78/99

Answer 2

A)
x = 0,888 ...  (10)
10x = 8,888 ...
----------------------
9x = 8
x = 8/9

B)
x = 0,287287 ...  (1.000)
1.000x = 287,287287 ....
-----------------------------------
999x = 287
x = 287/999  

C)
x = 0,1515 ....   (100)
100x = 15,1515...
------------------------
99x = 15
x = 15/99     ÷3
x = 5/33

D)
x = 0,999 ...  (10)
10x = 9,999 ...
-------------------
9x = 9
x = 9/9
x = 1   " 0,99 é muito próximo de 1"
E
x = 0,1211212 ....   (1.000)
1.000x = 121,121121...
----------------------------------
999x = 121
x = 121/999

F) x = 0,3434 ...  (100)
100x = 34,3434...
--------------------------
99x = 34
x = 34/99

G)
x =  0,555...   (10)
10x = 5,555...
-------------------
9x = 5
x = 5/9

H)
x = 0,7878 ...    (100)
100x = 78,7878...
------------------------
99x = 78
x = 78/99   ÷3
x = 26/33