Question

1- determine as frações geratrizes das dízimas periódicas:(com a conta)
a- 0,666... b-0,888... c-0,121212... d-2,444... e-1,5555... f-1,16666...
2- resolva a expressão:
(0,333...) X (0,1111....)

Answer 1

Ola Mariana

a) 

x = 0.666...
10x = 6.666...

9x = 6

x = 2/3 

b) 

x = 0.888...
10x = 8.888...

9x = 8

x = 8/9 

c)

x = 0.121212...
100x = 12.121212...

99x = 12

x = 4/33 

d)

2.444... = 2 + 0.444...

x = 0.444...
10x = 4.444..
9x = 4
x = 4/9

2 + 4/9 = (18 + 4)/9 = 22/9 

1.555... = 1 + 0.555..

x = 0.555...
10x = 5.555...
9x = 5
x = 5/9 

1 + 5/9 = 14/9 

1.1666... = 1 + 1/10 + 0.0666...

x = 0.0666...
100x = 6.666..
10x = 0.666..

90x = 6

x = 1/15 

1 + 1/10 + 1/15 = (150 + 15 + 10)/150 = 175/150 = 7/6 

0.333... = 1/3

0.111... = 1/9

(1/3)*(1/9) = 1/27