Question

Find the rational number equivalent to 0.490 with 90 repeating?

Answer 1

`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=(486)/(990)=(27)/(55)`