The unit of percentage error is

The correct option is "Percentage error is unit less".

To understand why percentage error has no units, let us look at its mathematical definition. Percentage error is calculated by finding the ratio of the absolute error to the actual or true value of the physical quantity, and then multiplying that ratio by 100.

The formula for percentage error is given by:

$\text{Percentage Error}=\left(\frac{\text{Absolute Error}}{\text{True Value}}\right)\times 100\text{\%}$

Let us analyze the units of the terms involved in this formula:
1. Absolute Error: This is the difference between the measured value and the true value. Since it is a difference between two measurements of the same physical quantity, it has the exact same unit as the physical quantity itself (for example, meters for length, or kilograms for mass).
2. True Value: This is the actual value of the physical quantity, so it also has the same unit as the physical quantity.

When we calculate the ratio of the absolute error to the true value, the unit in the numerator cancels out with the unit in the denominator. For example, if we are measuring length in meters (m):

$\text{Unit of Ratio}=\frac{\text{meter (m)}}{\text{meter (m)}}=\text{Unitless}$

Since this ratio is unitless, multiplying it by 100 to convert it into a percentage does not introduce any physical units. Therefore, percentage error is a dimensionless and unitless quantity.