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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.

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