This is the final section and it relies on an understanding of the previous section. Conceptually, it is almost obvious what a \emph{significant} figure is - it is a figure which is important.

Let us consider $1.618$. This number has 4 significant figures. We could equally write $1.618000000\ldots$, but these zeros do not add any accuracy or information to our number. As such they are considered insignificant.

Similarly, there are \fillin[5] significant figures in $5.9736$ and 8 significant figures in \fillin[9.1093826].

\begin{examplebox}
    \subsection*{Worked Example:}
        \(0.00034061=3.4061 \times 10^{-4}\)

        \[
        \begin{aligned}
        & \approx 3 \times 10^{-4} \quad(\text { correct to } 1 \text { significant figure }) \\
        & \approx 3.4 \times 10^{-4} \quad(\text { correct to } 2 \text { significant figures }) \\
        & \approx 3.41 \times 10^{-4} \quad(\text { correct to } 3 \text { significant figures }) \\
        & \approx 3.406 \times 10^{-4} \quad(\text { correct to } 4 \text { significant figures })
        \end{aligned}
        \]
    \subsection{Examples:}
    \begin{questions}
        \Question[2] Write in scientific notation and then round correct to 3 significant figures.
        \begin{multicols}{2}\begin{parts}
            \part $235.674 = \fillin[$2.36\times 10^2$]$
            \part $0.00724546 = \fillin[$7.25\times 10^{-3}$]$
        \end{parts}\end{multicols}
        \Question[2] Write in scientific notation and then round correct to 2 significant figures.
        \begin{multicols}{2}\begin{parts}
            \part $276000000 \approx \fillin[$2.8\times 10^8$]$
            \part $0.000000654 \approx \fillin[$6.5\times 10^{-7}$]$
        \end{parts}\end{multicols}
    \end{questions}
\end{examplebox}

 \begin{exercisebox}                                                                                            
     \subsection{Exercises:}                                                                                    
     \begin{questions}                                                                                          
         \Question[6] Write in scientific notation, correct to 3 significant figures.                           
         \begin{multicols}{2}\begin{parts}                                                                      
             \part 2.7043                                                                                       
             \begin{solutionordottedlines}[2cm]                                                                 
                 $2.70 \times 10^0$                                                                             
             \end{solutionordottedlines}                                                                        
             \part 634.96                                                                                       
             \begin{solutionordottedlines}[2cm]                                                                 
                 $6.35 \times 10^2$                                                                             
             \end{solutionordottedlines}                                                                        
             \part 8764.37                                                                                      
             \begin{solutionordottedlines}[2cm]                                                                 
                 $8.76 \times 10^3$                                                                             
             \end{solutionordottedlines}                                                                        
             \part 256412                                                                                       
             \begin{solutionordottedlines}[2cm]                                                                 
                 $2.56 \times 10^5$                                                                             
             \end{solutionordottedlines}                                                                        
             \part 0.003612                                                                                     
             \begin{solutionordottedlines}[2cm]                                                                 
                 $3.61 \times 10^{-3}$                                                                          
             \end{solutionordottedlines}                                                                        
             \part 0.024186                                                                                     
             \begin{solutionordottedlines}[2cm]                                                                 
                 $2.42 \times 10^{-2}$                                                                          
             \end{solutionordottedlines}                                                                        
         \end{parts}\end{multicols}                                                                             
         \Question[16]$\,$                                                                                      
             \begin{center}                                                                                     
             \begin{tabular}{|l|l|l|l|l|}                                                                       
             \hline                                                                                             
              & 4 sig. figs & 3 sig. figs & 2 sig. figs & 1 sig. fig. \\                                        
             \hline                                                                                             
             274.62 & $2.746 \times 10^2$ & $2.75 \times 10^2$ & $2.7 \times 10^2$ & $3 \times 10^2$ \\         
             \hline                                                                                             
             0.041236 & $4.124 \times 10^{-2}$ & $4.12 \times 10^{-2}$ & $4.1 \times 10^{-2}$ & $4 \times       
 10^{-2}$ \\                                                                                                    
             \hline                                                                                             
             1704.28 & $1.704 \times 10^3$ & $1.70 \times 10^3$ & $1.7 \times 10^3$ & $2 \times 10^3$ \\        
             \hline                                                                                             
             \(1.9925 \times 10^{27}\) & $1.993 \times 10^{27}$ & $1.99 \times 10^{27}$ & $2.0 \times 10^{27}$  
 $2 \times 10^{27}$ \\                                                                                          
             \hline                                                                                             
             \end{tabular}                                                                                      
             \end{center}                                                                                       
     \end{questions}                                                                                            
 \end{exercisebox}                                                                                              


