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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}

\]