Question

Determine a fração geratriz das dizimas periódicas simples a seguir. Sempre que possível, simplifique as frações.

Answer 1

Resposta:

a) $\frac{2}{3}$, b) $\frac{67}{333}$, c) $\frac{5}{1111}$, d) $\frac{49}{9}$

Explicação passo-a-passo:

a)

$x=0,666...$

$10x = 6,666...$

Subtraímos as duas equações:

$10x-x=6,666...-0,666...$

$9x=6$

$x=\dfrac{6}{9}$

$x=\dfrac{2}{3}$

b)

$x = 0,201201201...$

$1000x=201,201201201...$

$1000x-x=201,201201201...-0,201201201...$

$999x=201$

$x=\dfrac{201}{999}$

$x=\dfrac{67}{333}$

c)

$x=0,004500450045...$

$10000x=45,004500450045...$

$10000x-x=45,004500450045...-0,004500450045$

$9999x=45$

$x=\dfrac{45}{9999}$

$x=\dfrac{5}{1111}$

d)

$x=5,444...$

$10x=54,444...$

$10x-x=54,444...-5,444...$

$9x=49$

$x=\dfrac{49}{9}$