Question

What steps are needed to convert the non-terminating decimal into a fraction?-2.27272727272727272727272727272727

Answer 1

It is given that the number is x=-2.2727272727...

This is a recurring decimal so multiply by 100 to get:

`100x=-227.27272727\ldots`

Subtract the two equations to get:

`\begin{gathered} 100x-x=-227.272727\ldots+2.27272727\ldots \\ 99x=-225 \\ x=-(225)/(99) \end{gathered}`

Hence the fractional value is given by:

`-2.27272727\ldots=(-225)/(99)`