\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)

Percentages

Definition

Definition Percentage
A percentage is a ratio out of \(100\).
\(\pourcent\) is read ``percent'', meaning ``out of a hundred.''
Example
As \(\textcolor{colorprop}{23}\) parts out of \(\textcolor{colordef}{100}\) are colored, this is \(\textcolor{colorprop}{23}\textcolor{colordef}{\pourcent} = \dfrac{\textcolor{colorprop}{23}}{\textcolor{colordef}{100}}\).

Percentage as a Number


By definition, the percentage \(\textcolor{colorprop}{5}\textcolor{colordef}{\pourcent}\) is equal to the fraction \(\dfrac{\textcolor{colorprop}{5}}{\textcolor{colordef}{100}}\). Also, the fraction \(\dfrac{\textcolor{colorprop}{5}}{\textcolor{colordef}{100}}\) is equal to the decimal number \(0.05\), since \(5\div 100=0.05\). It is important to be able to convert between these different representations of a percentage.

Method Converting a Percentage to a Fraction
To convert the percentage \(\textcolor{colorprop}{5}\textcolor{colordef}{\pourcent}\) into a fraction, use the definition:$$\textcolor{colorprop}{5}\textcolor{colordef}{\pourcent} = \dfrac{\textcolor{colorprop}{5}}{\textcolor{colordef}{100}}$$
Method Converting a Fraction to a Percentage
To convert the fraction \(\dfrac{\textcolor{colorprop}{3}}{\textcolor{colordef}{4}}\) into a percentage:
  • Method 1 (Equivalent Fractions)
  • Method 2 (Formula)$$\begin{aligned}\dfrac{\textcolor{colorprop}{3}}{\textcolor{colordef}{4}} &= \left( \dfrac{\textcolor{colorprop}{3}}{\textcolor{colordef}{4}} \times \textcolor{colordef}{100} \right)\textcolor{colordef}{\pourcent} \\&= \textcolor{colorprop}{75}\textcolor{colordef}{\pourcent} \quad \text{(compute } 3 \div 4 \times 100 = 75)\end{aligned}$$
Method Converting a Percentage to a Decimal
To convert the percentage \(\textcolor{colorprop}{5}\textcolor{colordef}{\pourcent}\) into a decimal:$$\begin{aligned}\textcolor{colorprop}{5}\textcolor{colordef}{\pourcent} &= \dfrac{\textcolor{colorprop}{5}}{\textcolor{colordef}{100}} \\&= \textcolor{colorprop}{5} \div \textcolor{colordef}{100} \\&= 0.05\end{aligned}$$
Method Converting a Decimal to a Percentage
To convert the decimal \(0.05\) into a percentage:$$\begin{aligned}0.05 &= 0.05 \times \textcolor{colordef}{100}\textcolor{colordef}{\pourcent} \\&= \textcolor{colorprop}{5}\textcolor{colordef}{\pourcent}\end{aligned}$$