# What are percentage errors

## Absolute, relative and percentage errors

This post explains the terms using a simple example absolute, relative and percentage errors.

#### Absolute mistake

The difference between an approximate value (or measured value) and the actual value of a quantity is called absolute mistake.

#### Example:

Instead of the exact solution x = 1/3 of the equation 3x = 1, a student gives x = 0.33.

He makes an absolute mistake in doing this

0,33 – 1/3 = 99/300 – 100/300 = -1/300 = -0,00333…

An absolute error is of the same dimension as the size under consideration, i.e. it can be with a unit (such as euros, kilograms or meters).

#### Relative error

The Quotient from absolute error and actual value is called relative error.

We do that example away from above. There is a relative error of

-1/300 : 1/3 = -1/300 * 3/1 = -1/100 = -0,01

The relative error is always a number without unity and with that same sign like the corresponding absolute error.

#### Percentage error

The percentage errors is exactly the relative error - just as Percentage specified.

The relative error of -0.01 im example above therefore corresponds to a percentage error of -1%.

### Also interesting:

Tags: AbsoluteDifferenceUnitQuotientRelative