Calcule as geratrizes das seguintes dizimas periódicas:
a-0,555...
B-1,030303030303...
C-5,018018018018...
D-0,0060606...
E-3,616666...
F-12,914444444...
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A) 0,555...
x = 0, 555...
(10)x = 0,555... . (10)
10x = 5,555...
10x = 5 + x
10x - x = 5 + x - x
9x = 5
9x/ 9 = 5/9
x = 5/9
B ) 1, 030303...
x = 1,030303... (A)
( 100). x = 1,0303... (100)
100x = 103,0303... (B)
Fazendo B-A
100x - x = 103,03... - 1,03...
99x = 102
99x/99 = 102/99
x = 102/99
C) 5,018018...
x = 5.018... (A)
1000x= 5018,018...(B)
Fazendo B - A
1000x- x = 5018,018... - 5, 018...
999x = 5013
999x/999 = 5013/999
x= 5013/999
D) 0,0060606...
x = 0,0060606... (A)
10x = 00, 0606...
100x = 0006,0606... (B)
Fazendo B - A
100x - x= 0006,0606... - 0,00606...
99x = 0006,0
99x = 06
99x/99 = 06/99
x = 06/99 (÷3)
x = 03/33
E) 3,61666...
x = 3,61666...
100x = 361,666... (A)
1000x = 361666,666... ( B)
Fazendo B - A
1000x - 100x = 361666,666...- 361,666...
900x = 361305
900x/900 = 361305/ 990
x = 361305/990
F) 12, 914444...
x = 12, 91444...
100x = 1291,444... (A)
1000x = 12914,444 (B)
Fazendo B - A
1000x - 100x = 12914,444... - 1291, 444...
900x = 11623
900x/900 = 11623/900
x= 11623/ 900
x = 0, 555...
(10)x = 0,555... . (10)
10x = 5,555...
10x = 5 + x
10x - x = 5 + x - x
9x = 5
9x/ 9 = 5/9
x = 5/9
B ) 1, 030303...
x = 1,030303... (A)
( 100). x = 1,0303... (100)
100x = 103,0303... (B)
Fazendo B-A
100x - x = 103,03... - 1,03...
99x = 102
99x/99 = 102/99
x = 102/99
C) 5,018018...
x = 5.018... (A)
1000x= 5018,018...(B)
Fazendo B - A
1000x- x = 5018,018... - 5, 018...
999x = 5013
999x/999 = 5013/999
x= 5013/999
D) 0,0060606...
x = 0,0060606... (A)
10x = 00, 0606...
100x = 0006,0606... (B)
Fazendo B - A
100x - x= 0006,0606... - 0,00606...
99x = 0006,0
99x = 06
99x/99 = 06/99
x = 06/99 (÷3)
x = 03/33
E) 3,61666...
x = 3,61666...
100x = 361,666... (A)
1000x = 361666,666... ( B)
Fazendo B - A
1000x - 100x = 361666,666...- 361,666...
900x = 361305
900x/900 = 361305/ 990
x = 361305/990
F) 12, 914444...
x = 12, 91444...
100x = 1291,444... (A)
1000x = 12914,444 (B)
Fazendo B - A
1000x - 100x = 12914,444... - 1291, 444...
900x = 11623
900x/900 = 11623/900
x= 11623/ 900
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