Absolute Error in A-B

The absolute error in the value of A-B can be determined based on the given absolute errors in the quantities A and B. To calculate the absolute error in the difference between A and B, we need to consider the maximum possible error that can occur when subtracting two values.

Definition of Absolute Error
Absolute error represents the difference between the measured or approximate value of a quantity and its true or exact value. It indicates the magnitude of the uncertainty or deviation in the measurement.

Absolute Error in A
The absolute error in quantity A is denoted as 'a'. It represents the maximum possible deviation in the value of A from its true value.

Absolute Error in B
The absolute error in quantity B is denoted as 'b'. It represents the maximum possible deviation in the value of B from its true value.

Calculating Absolute Error in A-B
To find the absolute error in A-B, we need to consider the worst-case scenario where the errors in A and B align to maximize the difference. In this case, the maximum possible error in the difference occurs when the absolute errors in A and B have the same sign and add up.

- When both 'a' and 'b' are positive, the maximum possible error in A-B is given by (a + b).
- When both 'a' and 'b' are negative, the maximum possible error in A-B is given by -(a + b).

Example
Let's consider an example:
If the absolute error in quantity A (a) is 2 units and the absolute error in quantity B (b) is 3 units, we can calculate the absolute error in A-B as follows:

- If A = 10 and B = 5, then A-B = 5.
- In the worst-case scenario where the errors align, the maximum possible error in A-B is (a + b) = 2 + 3 = 5 units.

Therefore, the absolute error in the value of A-B is 5 units.

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