Question

What is 3.8 repeating as a fraction in simplest form

Answer 1

$\bf 3.8888888\overline{8}\\\\ -------------------------------\\\\ x=3.8888888\overline{8}\qquad thus\qquad \begin{array}{llcll} 10x&=&38.888888\overline{8}\\ &&\downarrow \\ &&35+3.8888888\overline{8}\\ &&\downarrow \\ &&35+x \end{array} \\\\\\ 10x=35+x\implies 9x=35\implies x=\cfrac{35}{9}$

the idea being, you multiply the "x" by some power of 10 that moves the repeating part to the left of the decimal point and the split it like above.