Error = │true value - experimental value│. Both approaches give you same result, but this is the common definition of error.

Absolute error=Modulus of difference of True value and observed value. i agree with

Meseret Amde'answer

You have to be a bit careful with these definitions. As an observed value is a measurement. If you read the first work on measurement (I would say it is the 13 books of Euclid, which also includes the Pythagorean Theorem), measurements are not often just Scalar Values, but rather processes, or Vectors or Tensors. In Quantum Mechanics, this is even more difficult, as it is not clear what a measurement is, exactly. With Unitary Entities in Quantum Mechanics, the "Measurement" causes the Entity to take an Eigenvalue, which it can maintain for a long time. A second measurement, say from a different angle, can cause the Eigenvalue to change (which is unlike a Tensor, which assumes that there are Covariant entities, that have a "True Value", but that projection is different for different observers (Say Time Dilation)). There is the claim, that in Hilbert Space these Eigenvalues from different angles are Tensors. Let's look at a simple Hilbert Space, one which we are familiar with because we live in the age of logic, the age of the Computer. Take the truth table for "OR", T OR T = T, T OR F = T, F OR T = T, and F OR F = F. Now let us say the nexus occurs now, and we are given the value T. What argument led to that conclusion? This happens a million times a second on your Cell Phone, so it is not abstract, it is the way Time works on your Cell Phone. You can see that you can't tell what the argument was, but only statistics about it. Let one second pass on your cell phone, and a Million OR's occurred, so that is why when it crashes you have to go to a data store and start the deduction again. Now back to Physics, the space of the truth table is a Hilbert Space with 3 vectors, if you measure "T". Each of these gives the same "Present" Condition, but each gives three different futures, which is the nature of Hilbert Space. You can see how the futures are different if you have studied Law and go into a Court Room. Say, the Lawyer argues that anyone of 10 conditions could have explained the Liquor Store Robbery, but his client was not the condition, but let us say that you have a witness that can't show up but knows that his client was the culprit. So the Lawyer says the present measurement was "My client is at this present moment in time, because he is innocent". The future is different, even though there could be a 9 other reasons why the client could be here ( he could be here, now because he is guilty). So the simple analysis of measurement you present, would not have even been considered a good theory 3000 years ago. They were more advanced even at the time of Euclid, or the formulation of Law. So the way you are defining it in each case is definitely wrong in General, and only applies to a specific case about a Scalar, that is a particularly simple Scalar.