Welcome to the final section. This is your party trick:

Here are 2 worked examples and then a number of exercises for you to mimic the method with:

\begin{examplebox}
    \subsection{Worked Examples}
    \begin{multicols}{2}
        \begin{doublespace}
        \begin{minipage}{0.5\textwidth}
            \subsubsection*{Question 1}
            Write \(0 . \dot{2}\) as a fraction.

            \subsubsection*{Solution 1}
            Let \(\quad S=0 . \dot{2}\)

            So \(\quad S=0.2222 \ldots\)

            Then \(\quad 10 S=2.2222 \ldots \quad\) (Multiply by 10.) \(10 S=2+0.222 \ldots\)

            Therefore \(10 S=S+2\)

            Hence \(\quad 9 S=2\)

            So \(\quad S=\frac{2}{9}\)

            Thus \(\quad 0 . \dot{2}=\frac{2}{9}\)
        \end{minipage}
        \begin{minipage}{0.5\textwidth}
            \subsubsection*{Question 2}
            Write 0.12 as a fraction.

            \subsubsection*{Solution 2}
            Let \(\quad S=0.12\)

            So \(\quad S=0.12121212 \ldots\)

            Then \(\quad 100 S=12121212 \ldots\)

            Therefore \(100 S=12+S\)

            Hence \(\quad 99 S=12\)

            So \(\quad S=\frac{12}{99} = \frac{4}{33}\)

            Thus \(\quad 0 . \dot{1} \dot{2}=\frac{4}{33}\)
            
        \end{minipage}
        \end{doublespace}
    \end{multicols}
\end{examplebox}

 \begin{exercisebox}                                                                                                                  
     \subsection{Exercises}                                                                                                           
     \begin{questions}\begin{onehalfspacing}                                                                                          
         \Question[10]                                                                                                                
         \begin{parts}                                                                                                                
             \begin{multicols}{2}                                                                                                     
             \part \(0 . \dot{5}=\frac{5}{9}\)                                                                                        
             \part \(0 . \dot{7}=\frac{7}{9}\)                                                                                        
             \part \(0 . \dot{9}=\frac{9}{9}=1\)                                                                                      
             \part \(0.1 \dot{4}=\frac{14}{99}\)                                                                                      
             \part \(0.2 \dot{3}=\frac{23}{99}\)                                                                                      
             \part \(0.6 \dot{2}=\frac{62}{99}\)                                                                                      
             \part \(0 . \dot{1} \dot{3}=\frac{13}{99}\)                                                                              
             \part \(0 . \dot{0} 7=\frac{7}{90}\)                                                                                     
             \part \(0 . \dot{9} \dot{1}=\frac{91}{99}\)                                                                              
             \part \(0 . \dot{2} 4 \dot{1}=\frac{239}{990}\)                                                                          
             \end{multicols}                                                                                                          
             \begin{multicols}{4}                                                                                                     
             \part Which of these numbers are irrational?                                                                             
                 \begin{enumerate}                                                                                                    
                     \item[\CheckedBox] \(\sqrt{7}\)                                                                                  
                     \item[\Square] \(\sqrt{25}\)                                                                                     
                     \item[\Square] \(0 . \dot{6}\)                                                                                   
                     \item[\CheckedBox] \(\frac{\pi}{3}\)                                                                             
                 \end{enumerate}                                                                                                      
             \end{multicols}                                                                                                          
         \end{parts}                                                                                                                  
     \end{onehalfspacing}\end{questions}                                                                                              
 \end{exercisebox}                                                                                                                    
