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Question: What is the percentage error if the absolute error is \(\;0.01\) and the actual value is \(\;30.5\)?...

What is the percentage error if the absolute error is   0.01\;0.01 and the actual value is   30.5\;30.5?

Explanation

Solution

We know that accurate measurements are required in the study of sciences, however often there are errors which are observed in the measurements. There are different types of errors on the basis of origin. However, there are certain simple ways to avoid these as well.

Formula used:
percent  of  Error=∣measured  value−actual  value∣actual  value×100percent\; of\; Error=\dfrac{|measured\; value-actual\; value|}{actual\; value}\times 100%
Eabsolute=∣xmeasured−xaccepted∣E_{absolute}=|x_{measured}-x_ {accepted}|

Complete step-by-step solution:
We know that we cannot always get 100100% accurate readings. There are a few errors in which the deviation from their actual value is observed very often. These errors or mistakes lead to uncertainty in the measurement, small errors may be acceptable most of the time. However in research like medicine even a very small error can lead to a heavy cost.
Here, it is given that absolute error is   0.01\;0.01 and the actual value is   30.5\;30.5. We know that absolute error is given asEabsolute=∣xmeasured−xaccepted∣E_{absolute}=|x_{measured}-x_ {accepted}|, then from the formula we have 0.01=∣xmeasured−xaccepted∣0.01=|x_{measured}-x_ {accepted}|
We also we know that percentage error is given as percent  of  Error=∣measured  value−actual  value∣actual  value×100percent\; of\; Error=\dfrac{|measured\; value-actual\; value|}{actual\; value}\times 100%
Then we have   ⟹  percent  of  Error=0.0130.5×100\implies percent\; of\; Error=\dfrac{0.01}{30.5}\times100%
  ⟹  percent  of  Error=0.0327\implies percent\; of\; Error=0.0327%
∴percent  of  Error=0.033\therefore percent\; of\; Error=0.033%
Thus the percentage error for the given data was found to be 0.033  0.033\;%

Note: The major ways of identifying errors in the measurement are: Margin error, absolute error, relative error and percentage error. Which arise due to systematic error, instrumental error, environmental error, observational error or random error. However, there are certain simple ways to avoid it by repeating the experiment multiple times and obtaining their mean values. Clearly, this is a very easy and simple question. Here, we don’t have to find the measured value; we can just substitute the absolute error instead to solve the question.