Question

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...

Answer 1

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