Definition:Percentage

Definition

A percentage is a convenient way of expressing (usually) a fraction as an easily-grasped number, by multiplying it by $100$ and appending the symbol $\%$ which means per cent.

As conventionally understood, the number being rendered as a percentage is between $0$ and $1$, thus determining the range of a percentage to be $0 \%$ to $100 \%$.

However in many contexts that range is frequently extended (in particular, in the field of rhetoric):

I want every member of this team to give one hundred and ten percent.

Examples

Example: $5 \%$

$5$ per cent is the same as $\dfrac 5 {100}$, or $\dfrac 1 {20}$.

Example: $20 \%$

$20$ per cent is the same as $0.2$ or $\dfrac 1 5$.

Example: $25 \%$

$25$ per cent is the same as $\dfrac 1 4$.

Example: $50 \%$

$\dfrac 1 2$ can be expressed in percentage form as:

$\dfrac 1 2 \times 100 = 50 \%$

Example: $120 \%$

$1.2$ can be expressed in percentage form as:

$1.2 \times 100 = 120 \%$

Example: $b - a$ as a Percentage

A change in a quantity from $a$ to $b$ can be expressed as a percentage as:

$\dfrac {100 \paren {b - a} } a \%$

Also see

• Results about percentages can be found here.

Sources

• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): percentage
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): percent
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): percent
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): percentage
• 2021: Richard Earl and James Nicholson: The Concise Oxford Dictionary of Mathematics (6th ed.) ... (previous) ... (next): percentage