Note: for this particular topic in mathematics, we encourage you to write percentages as decimals rather than fractions. Also, you will be making extensive use of your calculator this lesson and next. Be sure to bring it and use this opportunity to get good at using it. Ask your tutor for help in using this tool as it is powerful and will be a good friend to you for at least the next 3 years!

\begin{examplebox}
    \subsection{Examples}
    \begin{questions}
        \question[1] Convert the following from percentages to fractions
        \begin{multicols}{2}
        \begin{parts}
            \part $42\%=$\fillin[$0.42$][0.3\textwidth]
            \part $12\frac{1}{4}\%=$\fillin[$\frac{49}{400}$][0.3\textwidth]
        \end{parts}
        \end{multicols}
        \question[1] Convert the following from fractions to percentages
        \begin{multicols}{2}
        \begin{parts}
            \part $\frac{3}{5}=$\fillin[$60\%$][0.3\textwidth]
            \part $\frac{7}{20}=$\fillin[$35\%$][0.3\textwidth]
        \end{parts}
        \end{multicols}
        \question[1] The Brilliant Light Bulb Company estimates that \(3.5 \%\) of its light bulbs are defective. If a shop owner buys 1250 light bulbs to light the shop, how many would he expect to be defective?
        \begin{solutionordottedlines}[1in]
            Number of defective bulbs \(=1250 \times 3.5 \%\)
            \[
            \begin{aligned}
            & =1250 \times 0.035 \\
            & \approx 44 \quad(\text { Round } 43.75 \text { to } 44 .)
            \end{aligned}
            \]
        \end{solutionordottedlines}
        \question[1] A typical computer weighs about \(25 \mathrm{~kg}\). When it is broken down as waste, it yields about \(3 \mathrm{~g}\) of arsenic. What percentage of the total is this?
        \begin{solutionordottedlines}[1in]
            Using grams, the computer weighs \(25000 \mathrm{~g}\) and the arsenic weighs \(3 \mathrm{~g}\).

            Hence percentage of arsenic \(=\frac{3}{25000} \times 100 \%\)

            \[
            =\frac{3}{250} \%
            \]

            \[
            =0.012 \%
            \]
        \end{solutionordottedlines}
    \end{questions}
\end{examplebox}

\begin{exercisebox}
    \subsection{Exercises}
    \begin{questions}
        \question[2] Express each percentage as a decimal:
        \begin{multicols}{2}
        \begin{parts}
            \part $72\%=$\fillin[0.72]
            \part $7.6\%=$\fillin[0.076]
            \part $77\frac{3}{4}\%=$\fillin[0.7775]
            \part $0.1\%=$\fillin[0.001]
        \end{parts}
        \end{multicols}
        \question[3] Express each percentage as a fraction:
        \begin{multicols}{3}
        \begin{onehalfspacing}
        \begin{parts}
            \part $35\%$\fillin[\(\frac{7}{20}\)]
            \part $33\frac{1}{3}\%=$\fillin[\(\frac{1}{3}\)]
            \part $210\%=$\fillin[\(\frac{21}{10}\) or \(2\frac{1}{10}\)]
            \part $125\%=$\fillin[\(\frac{5}{4}\) or \(1\frac{1}{4}\)]
            \part $7.25\%=$\fillin[\(\frac{29}{400}\)]
            \part $112\frac{1}{2}\%=$\fillin[\(\frac{9}{8}\) or \(1\frac{1}{8}\)]
        \end{parts}
        \end{onehalfspacing}
        \end{multicols}
        \question[3] Express each fraction or decimal as a percentage:
        \begin{multicols}{2}
        \begin{onehalfspacing}
        \begin{parts}
            \part \(\frac{3}{5}=\)\fillin[60\%]
            \part \(\frac{7}{20}=\)\fillin[35\%]
            \part $0.43=$\fillin[43\%]
            \part $1.2=$\fillin[120\%]
            \part $0.225=$\fillin[22.5\%]
            \part $2.03=$\fillin[203\%]
        \end{parts}
        \end{onehalfspacing}
        \end{multicols}
        \question[3] Evaluate these amounts, correct to 2 decimal places where necessary.
        \begin{multicols}{2}
        \begin{onehalfspacing}
        \begin{parts}
            \part \(15 \%\) of 40 = \fillin[6]
            \part \(57 \%\) of 1000 =\fillin[570]
            \part \(120 \%\) of 538 =\fillin[645.60]
            \part \(15.8 \%\) of 972 = \fillin[153.57]
            \part \(2.8 \%\) of 318 =\fillin[8.90]
            \part \(0.1 \%\) of 6000 = \fillin[6]
        \end{parts}
        \end{onehalfspacing}
        \end{multicols}
        \question[3] Find what percentage the first quantity is of the second quantity, correct to 1 decimal place.
        \begin{parts}
            \part \(70 \mathrm{~m}, 50 \mathrm{~m}\)=\fillin[140.0\%]
            \part 15 weeks, 60 weeks=\fillin[25.0\%]
            \part 60 weeks, 15 weeks=\fillin[400.0\%]
        \end{parts}
        \question[3] Find what percentage the first quantity is of the second quantity, correct to 2 decimal places where necessary. You will need to express both quantities in the same unit first.
        \begin{multicols}{2}
        \begin{parts}
        \begin{onehalfspacing}
            \part 68 cents, \(\$ 5.00\)=\fillin[13.60\%]
            \part \(7 \mathrm{~g}, 3 \mathrm{~kg}\)=\fillin[0.23\%]
            \part 15 days, 3 years=\fillin[\(\approx\) 1.37\%]
            \part \(4 \mathrm{~km}, 250 \mathrm{~m}\)=\fillin[1600.00\%]
            \part 1 year, 1 day=\fillin[\(\approx\) 0.27\%]
            \part \(56 \mathrm{~cm}, 2.4 \mathrm{~km}\)=\fillin[0.02\%]
        \end{onehalfspacing}
        \end{parts}
        \end{multicols}
        \question[2] There are 740 students at a primary school, \(5 \%\) of whom have red hair. Calculate the number of students in the school who have red hair.
        \begin{solutionordottedlines}[1in]
        37 students
        \end{solutionordottedlines}
        \question[2] A soccer match lasted 92 minutes (including injury time). If team A was in possession for \(55 \%\) of the match, for how many minutes and seconds was team A in possession?
        \begin{solutionordottedlines}[1in]
        50 minutes and 36 seconds
        \end{solutionordottedlines}
    \end{questions}
\end{exercisebox}