Contact The Learning Centre

# 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.