Question

encontre a fração geratriz das seguintes dízimas periódicas:
a) 2,666...
b) 0,121212...
c) 5,323232...
d) 0,3111...​

Answer 1

Resposta:

Explicação passo-a-passo:

a) $\frac{8}{3}$

Cálculo

$26,666... = 10x\\2,666...=x\\\\26,666...-2,666...=10x-x\\\\9x=24\\\\x=\frac{24}{9} =\frac{8}{3}$

b) $\frac{4}{33}$

Cálculo

$12,1212...=100x\\0,1212...=x\\\\12,1212...-0,1212...=100x-x\\\\12=99x\\\\x=\frac{12}{99} =\frac{4}{33}$

c) $\frac{527}{99}$

Cálculo

$532,3232...=100x\\5,3232...=x\\\\532,3232...-5,3232...=100x-x\\\\527=99x\\\\x=\frac{527}{99}$

d) $\frac{14}{45}$

Cálculo

$3,111...=10x\\31,111...=100x\\\\31,111...-3,111...=100x-10x\\\\28=90x\\\\x=\frac{28}{90} =\frac{14}{45}$