Absolute and Fractional Error – Rankers Physics
Topic: Unit And Dimensions
Subtopic: Error Analysis

Absolute and Fractional Error

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): The absolute error has the same unit as the quantity itself.
Reason (R): Fractional error has no unit.
In the light of above statements, choose the correct answer from the options given below.
Both (A) and (R) are true and (R) is the correct explanation of (A)
Both (A) and (R) are true but (R) is not the correct explanation of (A)
(A) is true but (R) is false
Both (A) and (R) are false

Solution:

Absolute error \(\Delta x\) has the same unit as the physical quantity. Fractional error is the ratio \(\Delta x / x\) and is dimensionless (no unit). Both statements are true, but the lack of unit in fractional error does not explain why absolute error has a unit.

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