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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.