Question

1) Encontre a fração geratriz de cada uma das dízimas a seguir:


a) 0,020202...


b) 3,353535...


c) 42,88888....


d) 0,444....

Urgente, me ajudem!!!​

Answer 1

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$\tt a)~\sf x=0,020202...\cdot100\\\sf 100x=2,020202...\\-\underline{\begin{cases}\sf100x=2,\diagup\!\!\!\!\!02\diagup\!\!\!\!\!02\diagup\!\!\!\!\!02...\\\sf x=0,\diagup\!\!\!\!\!02\diagup\!\!\!\!\!\!02\diagup\!\!\!\!\!02...\end{cases}}\\\sf 99x=2\\\huge\boxed{\boxed{\boxed{\boxed{\sf x=\dfrac{2}{99}}}}}\checkmark$

$\tt b)~\sf x=3,353535...\cdot100\\\sf 100x=335,353535...\\-\underline{\begin{cases}\sf100x=335,\diagup\!\!\!\!\!35\diagup\!\!\!\!\!35\diagup\!\!\!\!\!35...\\\sf x=3,\diagup\!\!\!\!\!35\diagup\!\!\!\!\!35\diagup\!\!\!\!\!35...\end{cases}}\\\sf99x=332\\\huge\boxed{\boxed{\boxed{\boxed{\sf x=\dfrac{332}{99}}}}}$

$\tt c)~\sf x=42,888...\cdot10\\\sf10x=428,888..\\-\underline{\begin{cases}\sf10x=428,\diagup\!\!\!8\diagup\!\!\!8\diagup\!\!\!8...\\\sf x=42,\diagup\!\!\!8\diagup\!\!\!8\diagup\!\!\!8...\end{cases}}\\\sf9x=386\\\huge\boxed{\boxed{\boxed{\boxed{\sf x=\dfrac{386}{9}}}}}\checkmark$

$\tt d)~\sf x=0,444...\cdot10\\\sf 10x=4,444...\\-\underline{\begin{cases}\sf10x=4,\diagup\!\!\!4\diagup\!\!\!\!4\diagup\!\!\!4...\\\sf x=0,\diagup\!\!\!4\diagup\!\!\!4\diagup\!\!\!4\end{cases}}\\\sf 9x=4\\\huge\boxed{\boxed{\boxed{\boxed{\sf x=\dfrac{4}{9}}}}}\checkmark$