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=\frac{322}{99} \end{gathered}$$n\text{ =}3.252525\ldots=\frac{322}{99}$