Question

Obtenha as geratrizes das seguintes dízimas periódicas
A. 0,777...
B.0,232323...
C.9,444...
D.12,53262626...

Answer 1

a-) 0,777...
Atribua valor de x para dízima :
x = 0,777... 

Multiplique por 10 ambos os lados :
10x = 7,777...

Resolva :
10x = 7+x
10-x = 7
9x = 7
x = 7/9

b-)0,2323...

x= 0,232323
100x = 23,232323...
100x = 23+x
100x-x = 23
99x = 23
x = 23/99

c-)9,444...
9+0,444...

x = 0,444...
10x = 4,444...
10x = 4+x
9x = 4
x = 4/9

9,444 ... = 9+4/9 = 81+4/9 = 85/9

d-) 12,532626262...
12,532+0,00062...

12,532+ 62/99000 = 1240668+62/99000 = 1240730/99000 = 124073/9900

Bom estudo!