Question

2. Transforme as dízimas periódicas em frações.
a) 0,6666… = _________________________________________________
b) 1,8888…= _________________________________________________
c) 2,4333…= __________________________________________________

Answer 1

$\boxed{\begin{array}{l}\tt a)~\sf x=0,666...\cdot10\\\sf 10x=6,666...\\-\underline{\begin{cases}\sf 10x=6,666....\\\sf x=0,666....\end{cases}}\\\sf 9x=6\\\sf x=\dfrac{6\div3}{9\div3}\\\sf x=\dfrac{2}{3}\end{array}}$

$\boxed{\begin{array}{l}\tt b)~\sf y=1,888...\cdot10\\\sf 10y=18,888...\\-\underline{\begin{cases}\sf 10y=18,888....\\\sf y=1,888...\end{cases}}\\\sf 9y=17\\\sf y=\dfrac{17}{9}\end{array}}$

$\large\boxed{\begin{array}{l}\tt c)~\sf z=2,4333...\cdot100\\\sf 100z=243,333...\cdot10\\\sf 1000z=2433,333....\\-\underline{\begin{cases}\sf 1000z=2433,333...\\\sf 100z=243,333...\end{cases}}\\\sf 900z=2190\\\sf z=\dfrac{2190\div30}{900\div30}\\\\\sf z=\dfrac{73}{30}\end{array}}$