Question

6°)encontre a fração geratriz das dízimas periódicas simples a seguir:
a)-3,5555...
b)12,2222...​

Answer 1

Resposta:

As frações geratrizes são calculadas abaixo.

Explicação passo-a-passo:

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$a)\;x=-3{,}555...\\\\\\x=-3-0{,}555...\\\\\\x=-3-\dfrac{5}{9}\\\\\\x=-3\;.\;\dfrac{9}{9}-\dfrac{5}{9}\\\\\\x=-\dfrac{27}{9}-\dfrac{5}{9}\\\\\\\boxed{x=-\dfrac{32}{9}}$

$b)\;x=12{,}222...\\\\\\x=12+0{,}222...\\\\\\x=12+\dfrac{2}{9}\\\\\\x=12\;.\;\dfrac{9}{9}+\dfrac{2}{9}\\\\\\x=\dfrac{108}{9}+\dfrac{2}{9}\\\\\\\boxed{x=\dfrac{110}{9}}$