Question

What fraction is equivalent to 3.5 repeating

Answer 1

the idea being, we start off by making the number a variable and then we'd multiply it by a power of "10" in order to move the recurring part to t he left, in this case there is only 1 decimal, so we'd use 10¹ or just 10.

`3.\overline{555}\hspace{5em}x=3.\overline{555}\hspace{5em} \boxed{\begin{array}{llll} 10x&=&35.\overline{555}\\\\ &&32+3.\overline{555}\\\\ &&32+x \end{array}} \\\\\\ 10x=32+x\implies 9x=32\implies x=\cfrac{32}{9}\implies x=3(5)/(9)`