Error Analysis Examples in Math
Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Error Analysis.
This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.
Concept Recap
The systematic study of how errors arise in calculations or models, how large they are, and how they propagate through subsequent steps.
Error analysis asks "how wrong could my answer be?" — not just "what is my answer?" — because every measurement and approximation carries uncertainty.
Read the full concept explanation →How to Use These Examples
- Read the first worked example with the solution open so the structure is clear.
- Try the practice problems before revealing each solution.
- Use the related concepts and background knowledge badges if you feel stuck.
What to Focus On
Core idea: Errors propagate through calculations: a 1% error in x causes about a 2% error in x^2. Knowing error growth rates helps decide where precision matters.
Common stuck point: Rounding at intermediate steps accumulates error — carry extra digits during computation and only round at the final answer.
Sense of Study hint: Redo the problem step by step and compare each line to the correct solution. The first line where they diverge tells you exactly which skill or concept needs attention.
Worked Examples
Example 1
easySolution
- 1 Identify the error: the student incorrectly 'distributed' the square root over addition. \sqrt{x+y} \ne \sqrt{x}+\sqrt{y} in general.
- 2 Counterexample: a=3, b=4. LHS: \sqrt{9+16}=\sqrt{25}=5. RHS: 3+4=7. 5 \ne 7.
- 3 Correct statement: \sqrt{a^2+b^2} \le |a|+|b| (triangle inequality), with equality only when a=0 or b=0.
Answer
Example 2
mediumPractice Problems
Try these problems on your own first, then open the solution to compare your method.