[tex] x=0.\overline{45}=0.454545...\\\\x=0.454545...\ \ \ \ |\cdot100\\\\100x=45.454545...\\\\100x-x=45.454545...-0.454545...\\\\99x=45\ \ \ \ \ |:99\\\\x=\dfrac{45}{99}\\\\x=\dfrac{45:9}{99:9}\\\\x=\dfrac{5}{11}\\\\0.\overline{45}=\dfrac{5}{11} [/tex]
