Question

Mostre que a dízima 2,1333333... é um número racional.​

Answer 1

$\Large\boxed{\begin{array}{l}\sf basta\,escrever\,a\,d\acute izima\,\\\sf na\,forma\, x=\dfrac{a}{b},com\,a,b\in\mathbb{Z},b\ne0\end{array}}$

$\Large\boxed{\begin{array}{l}\sf x=2,13333\dotsc\cdot10\\\sf 10x=21,333\dotsc\cdot10\\\sf 100x=213,333\dotsc\\-\underline{\begin{cases}\sf 100x=213,333\dotsc\\\sf 10x=21,333\dotsc\end{cases}}\\\sf90x=192\\\sf x=\dfrac{192\div6}{90\div6}\\\\\sf x=\dfrac{32}{15}\\\sf portanto~2,1333\dotsc\in\mathbb{Q}\end{array}}$