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Decimals, ratios, percentages, units and scientific notation

Units

  • When doing calculations involving measurements and quantities, remember that these numbers have units attached to them. For example the length of a ruler is \(30\) centimetres (written as \(30~\mbox{cm}\)).
  • Find the perimeter of a rectangle, with length of \(1.2\) metres and width of \(80\) centimetres. Note that the units are not the same. In this case you will need to convert them to either metres or centimetres.
    \begin{eqnarray*}
    P &=& \mbox{Sum of all the sides}\\
    &=& 1.2 \mbox{ m} + 80 \mbox{ cm} + 1.2 \mbox{ m} + 80 \mbox{ cm} \\
    &=& (1.2 +0.8 + 1.2 + 0.8 ) \mbox{ m} \\
    &=& 4 \mbox{ m}
    \end{eqnarray*}
  • What is the area of the same rectangle with length of \(1.2\) metres and width of \(80\) centimetres?
    \begin{eqnarray*}
    A &=& \mbox{length}\times \mbox{width} \\
    &=& 1.2 \mbox{ m} \times 80 \mbox{ cm} \\
    &=& 1.2 \mbox{ m} \times 0.8 \mbox { m} \\
    &=& 0.96 \mbox{ m}^{2}
    \end{eqnarray*}
  • Did you notice the units become \(\mbox{m}\times\mbox{m}\) which is \(\mbox{m}^{2}\) or square metres?
  • Units can also be referred to standard units.