Question

6)Qual a fração geratriz que representa cada dizima:
a) 0,5555...
b) 1,222...
c)0,5151...
d)2,125125...​

Answer 1

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$\boxed{\begin{array}{l}\rm a)~\sf x=0,555...\cdot10\\\sf 10x=5,555...\\-\underline{\begin{cases}\sf10x=5,\diagup\!\!\!5~\diagup\!\!\!5~\diagup\!\!\!5...\\\sf x=0,\diagup\!\!\!5~\diagup\!\!\!5~\diagup\!\!\!5....\end{cases}}\\\sf9x=5\\\sf x=\dfrac{5}{9}\end{array}}$

$\large\boxed{\begin{array}{l}\rm b)~\sf x=1,222...\cdot10\\\sf 10x=12,222...\\-\underline{\begin{cases}\sf10x=12,\diagup\!\!\!2~\diagup\!\!\!2~\diagup\!\!\!2....\\\sf x=1,\diagup\!\!2~\diagup\!\!\!2~\diagup\!\!\!2....\end{cases}}\\\sf9x=11\\\sf x=\dfrac{11}{9}\end{array}}$

$\boxed{\begin{array}{l}\rm c)~\sf x=0,5151...\cdot100\\\sf 100x=51,515151...\\-\underline{\begin{cases}\sf 100x=51,515151...\\\sf x=0,5151515...\end{cases}}\\\sf99x=51\\\sf x=\dfrac{51\div3}{99\div3}\\\sf x=\dfrac{17}{33}\end{array}}$

$\boxed{\begin{array}{l}\rm d)~\sf x=2,125125...\cdot1000\\\sf 1000x=2125,125125...\\-\underline{\begin{cases}\sf1000x=2125,\diagdown\!\!\!\!\!\!\!125~\diagdown\!\!\!\!\!\!125...\\\sf x=2,\diagdown\!\!\!\!\!\!125~\diagdown\!\!\!\!\!\!125...\end{cases}}\\\sf 999x=2123\\\sf x=\dfrac{2123}{999}\end{array}}$