Question

determine a geratriz da seguinte dicimas periodica 0,333

Answer 1

$x=0,333\ldots\\ \\ 10x=3,333\ldots\\ \\ \\ 3,333\ldots=3+0,333\ldots\\ \\ 10x=3+x\\ \\ 10x-x=3\\ \\ 9x=3\\ \\ x=\dfrac{3}{9}\\ \\ x=\dfrac{3\div 3}{9\div 3}\\ \\ x=\dfrac{1}{3} \Rightarrow \boxed{0,333\ldots=\dfrac{1}{3}}$