Errors and Significant Figures
Absolute, relative and percentage error, and error propagation in calculations. (Physics › Physical World, Units and Measurements, NEET UG syllabus.)
What is Errors and Significant Figures?
Absolute error is |amean - ai| in the measured unit; relative error is Δ a / amean, and percentage error expresses it as a percentage
Key formula / rule: Sum or difference
Key points
- Compute absolute, relative and percentage error and propagate them through calculations
Common exam trap
Adding relative errors for a sum instead of absolute errors
Definitions
- Name
Absolute and relative error
- Definition
Absolute error is |amean - ai| in the measured unit; relative error is Δ a / amean, and percentage error expresses it as a percentage
- Name
Significant figures
- Definition
Reliable digits plus the first uncertain digit; trailing zeros after a decimal point count, leading zeros do not
- Name
Exam insight
- Definition
For products and quotients percentage errors add, and a power multiplies its percentage error by that power
- Name
Worked example
- Definition
A length known to 2 percent entering as L2 contributes 4 percent error to the result
Learning objectives
Compute absolute, relative and percentage error and propagate them through calculations
Formulae
- Name
Sum or difference
- Expression
Δ Z = Δ A + Δ B
- Name
Product, quotient or power
- Expression
Δ Z / Z = m (Δ A / A) + n (Δ B / B) for Z = Am Bn
Common mistakes
Adding relative errors for a sum instead of absolute errors
Reporting more significant figures than the least precise measurement allows
Keywords
error
absolute error
relative error
percentage error
significant figures
measurement
precision
unit
Practice preview
When two quantities A and B are added, the maximum error in the sum (A + B) is:…
medium
Relative error is defined as:…
easy
If the length of a rod is measured as 100 cm with an absolute error of 0.5 cm, what is the relative error?…
medium