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# Decimals, ratios, percentages, units and scientific notation

### Ratios

• A ratio is a relationship between two or more numbers that can be sometimes expressed as a fraction.
• As with fractions, ratios also need to be written in simplest form, that is divide by all common multiples, for example, $$4:2$$ has a common multiple of $$2$$, so in simplest form can be written as $$2:1$$.
• When using ratios in context, remember that the units need to be the same, for example $$1 \mbox{ cm} :1 \mbox{ m}$$ should be written as:
\begin{eqnarray*}
1\mbox{ cm} &:& 1 \mbox{ m} \\
1 \mbox{ cm}&:& 100 \mbox{ cm}\\
1 &:& 100\,
\end{eqnarray*}

### Proportions

• A proportion is a special form of an algebra equation.
• It is used to compare two ratios or make equivalent fractions.
• For example, the concentration of some medication is expressed as a proportion, e.g. as $$800$$ milligrams in $$10$$ millilitres. If we need to give a patient $$300$$ milligrams, we need to know what proportion of the $$10$$ millilitres will be the correct dose. Once we have the fraction we need to multiply by the volume.
$\frac{300 \mbox{ mg}}{800 \mbox{ mg}} \times 10 \mbox{ ml} = 3.75 \mbox{ ml}$