**Percentage Error**

While measuring any physical quantity, it is impossible in principle to find its true value. The difference between the measured and the true values of a physical quantity is called the error of measurement. To determine if a value is accurate compare it to the accepted value. As these values can be anything a concept called percent error has been developed.

**What is Percentage
Error?**

Errors in measurement may also be expressed in terms of percentage. This is similar to relative error except that the error here is converted to a percent value. The percentage error is found by multiplying the relative error by 100%.

It is the absolute value of the difference of the measured value and the actual value divided by the actual value and multiplied by 100.

\(Percentage\,\,Error\,\,=\,\,\frac{Approximate\,Value\,\,-\,\,Exact\,\,Value}{Exact\,\,Value}\times 100\).

**How to find the
Percentage Error?**

**Problem:**

A scale measures wrongly a value as 10cm due to some marginal errors. Calculate the percentage error if the actual measurement of the value is 15cm?

**Solution:**

Given,

Exact value = 15cm,

Approximate value = 10cm,

Percentage Error =?

\(Percentage\,\,Error\,\,=\,\,\frac{Approximate\,Value\,\,-\,\,Exact\,\,Value}{Exact\,\,Value}\times 100=\frac{10-15}{15}\times 100\).

\(Percentage\,\,Error\,\,=\frac{10-15}{15}\times 100=-33.33%\).

\(\therefore \,\,Percentage\,\,Error\,\,=-33.33%\).