Question

Obtenha as geratrizes das seguintes dízimas periódicas:

a) 2,666...
b) 3,4848...
c) 1,7555...
d) 0,352121...
e) 0,35444...
f) 2,5424242...​

Answer 1

a) 2,666...

$\frac{26 - 6}{9} = \frac{20}{9}$

b) 3,4848...

$\frac{348 - 3}{99} = \frac{345}{99}$

c) 1,7555...

$\frac{175 - 17}{90} = \frac{158}{90} = \frac{79}{45}$

d) 0,352121...

$\frac{3521 - 35}{9900} = \frac{3486}{9900} =$

e) 0,35444...

$\frac{354 - 35}{900} = \frac{319}{900}$

f) 2,5424242...

$\frac{2542 - 25}{990} = \frac{2517}{990}$