Question

I'm trying to find the logical steps to find the "rational number equivalent " to 3.25 (repeating decimal)

Answer 1

The number n = 3.252525...

The repeating part (25) contains two digitis then we have multiply n by 10^2

`\begin{gathered} n=3.252525\ldots. \\ n\cdot10^2=325.252525\ldots \\ \end{gathered}`

Now we substract:

`\begin{gathered} n\cdot10^2=325.252525\ldots \\ - \\ n=3.2525252525\ldots \\ _(---------------------) \\ 99n=322 \\ n=(322)/(99) \end{gathered}`
`n\text{ =}3.252525\ldots=(322)/(99)`