I'm assuming the '10' in the answers are factorising out the decimal places? But how do they know what powers to put it to? (i.e 10^m, 10^(r-1), etc)?
The idea is that in general (i.e. not always), a decimal number that is rational has one part that is terminating, and a part after it that's recurring.
E.g. \(\frac1{12}=0.083333333\dots=0.08\overline{3}\)
The \(0.08\) part is the terminating part
The \(0.00\overline{3}\) is the recurring part
m and r are integers made to distinguish the purpose. Note that this is a proof where you would say let m and n be blah, not 'suppose' m and n be blah.
I believe that the question wants you to take the first r decimal places (or r-1, you can figure that little thing out) to be the terminating part, and the NEXT m-r decimal places to be the recurring part.