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Decimals, ratios, percentages, units and scientific notation


  • 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: 
    1\mbox{ cm} &:& 1 \mbox{ m} \\
    1 \mbox{ cm}&:& 100 \mbox{ cm}\\
    1 &:& 100\,


  • 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}

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