\(x=0.4\overline{90}=0.4909090\ldots\)
\(10x=4.\overline{90}=4.909090\ldots\)
\(10x-4=0.\overline{90}=0.909090\ldots\)
\(100(10x-4)=90.\overline{90}=90.909090\ldots\)
\(100(10x-4)-(10x-4)=90.\overline{90}-0.\overline{90}=90\)
\(1000x-400-10x+4=90\)
\(990x=486\)
\(x=\dfrac{486}{990}=\dfrac{27}{55}\)
