Topic 10: Propagation of Errors

What is Propagation of Errors?

When a result is calculated using two or more measured quantities, the errors in those quantities combine and affect the final result. This combining of errors is called propagation of errors.

Rules of Error Propagation

1. Addition or Subtraction

If Z = A + B or Z = A − B, then

Absolute error in Z = Absolute error in A + Absolute error in B

2. Multiplication or Division

If Z = A × B or Z = A / B, then

Percentage error in Z = Percentage error in A + Percentage error in B

3. Power of a Quantity

If Z = Aⁿ, then

Percentage error in Z = n × Percentage error in A

Why Propagation of Errors is Important

Helps estimate reliability of experimental results
Frequently asked in numerical problems
Essential for accurate scientific measurements

Q1. If Z = A + B, the error in Z depends on:
A) Percentage error of A and B
B) Absolute error of A and B
C) Relative error only
D) Least error only
Answer: B

Q2. If Z = A × B, the percentage error in Z is:
A) Difference of errors
B) Product of errors
C) Sum of percentage errors
D) Average of errors
Answer: C

Q3. If Z = A³ and percentage error in A is 2%, then error in Z is:
A) 2%
B) 3%
C) 6%
D) 8%
Answer: C

Q4. Propagation of errors is used to find:
A) Exact value
B) Approximate value
C) Maximum possible error
D) Minimum value
Answer: C

Q5. Which type of error adds directly?
A) Percentage error
B) Relative error
C) Absolute error
D) Mean error
Answer: C

Propagation of Errors – Quick Revision

Key Rules

Addition/Subtraction → Absolute errors add
Multiplication/Division → Percentage errors add
Powers → Multiply percentage error by power

Important Formulae

Z = A ± B → ΔZ = ΔA + ΔB
Z = A × B → %ΔZ = %ΔA + %ΔB
Z = Aⁿ → %ΔZ = n × %ΔA

CET Exam Tip

Always check whether the question asks for absolute error or percentage error. This is a common mistake area.

← Topic 9: Measurement of Area & Volume Topic 11: Least Count of Measuring Instruments →