Question

Transformar em fração 2,213213213 dízima periódica

Answer 1

$\large\boxed{\begin{array}{l}\rm x=2,213213\dotsc\cdot(1000)\\\rm 1000x=2213,213\dotsc\\-\underline{\begin{cases}\rm 1000x=2213,213213\dotsc\\\rm x=2,213213\dotsc\end{cases}}\\\rm 999x=2211\\\rm x=\dfrac{2211\div3}{999\div3}\\\\\rm x=\dfrac{737}{333}\end{array}}$