# Decimals, ratios, percentages, units and scientific notation

### Percentages

- Percentages is another kind of fraction meaning "per hundred", represented by the symbol \(\%\). The implied denominator is always \(100\). Thus, \(51\%\) means \(\displaystyle \frac{51}{100}\).
- Percentages greater than \(100\) or less than zero are treated in the same way. For example: \(311\% = \displaystyle \frac{311}{100}\) and \(-27\% =\displaystyle -\frac{27}{100}\).
- You can convert to a percentage from fractions and decimals. For example, \(\displaystyle \frac{1}{8} = 0.125 \). To express as a percentage, multiply by \(100\%\), giving \(0.125\times 100\% = 12.5\%\).
- You can also find a percentage of a number or quantity, by multiplying the percent by the amount. For example how do you find: \(27.5\%\) of \(300\) mg?

\begin{eqnarray*}

27.5\% \times 300 &=& \frac{27.5}{100} \times 300 \\

&=& 0.275 \times 300 \\

&=& 82.5

\end{eqnarray*}

Therefore, \(27.5\%\) of \(300\) mg is \(82.5\) mg.

#### To do

- Percentages worksheet (sigma Mathematics and Statistics Support Coventry University)
- Converting percents to decimals activity
- Converting decimals to percents activity
- Finding percents activity (Khan Academy)

#### More info

- Percentages Quick Tip (Study Support, USQ Library)
- The meaning of percent video
- Percentages information sheet