---
title: "Define error and its types"
subject: "Numerical Method"
chapter: 1
key: "semester_4/numerical_method:define-error-types"
source: https://www.bctengineer.com/q/semester_4/numerical_method/define-error-types
site: BCT Engineering
---

# Define error and its types

Numerical Method · Chapter 1: Introduction, Approximation and errors of computation

- Asked in: 2071 Magh, 4 marks; 2070 Bhadra, 6 marks (asked 2 times)
- Video: [3. Types of Error in Numerical Analysis | Error Analysis Numerical Methods](https://www.youtube.com/watch?v=vIUpqtbAreg) — Start Practicing
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/numerical_method/define-error-types
- Whole chapter: https://www.bctengineer.com/md/semester_4/numerical_method/chapter-1

## Question

Define error. Explain different types of errors in numerical computation.

## Short answer

Error is the departure of an approximate value from the true value. Types include inherent error (from input data), round-off error (from finite digit representation), truncation error (from cutting infinite processes), modelling error (from simplifications), and blunder (human mistakes).

## Answer

**Error** is the difference between the true (exact) value of a quantity and its approximate value obtained by calculation or measurement: Error = X − X′. In numerical computation, errors cannot be avoided, so we study their type and size.

#### Types of errors
1. **Inherent (input) error:** error already present in the data given to the problem, due to faulty measurement or an approximate model of the physical situation. Example: taking π = 3.14 or a length read as 5.2 cm.
2. **Round-off error:** caused by the computer or calculator keeping only a limited number of digits. A number such as 1/3 = 0.333... is cut or rounded to, say, 4 digits. Example: rounding 37.46235 to 37.46.
3. **Truncation error:** caused by replacing an infinite process by a finite one, such as cutting a series after a few terms. Example: sin x ≈ x − x³/3! drops the terms x⁵/5! and higher. It also occurs when a derivative is replaced by a finite difference.
4. **Modelling error:** from simplifying assumptions in the mathematical model (e.g. neglecting air resistance).
5. **Blunder (human) error:** mistakes such as wrong reading, wrong formula or program bug (e.g. 4.317 written as 4.371). It is avoidable.

#### Ways of expressing error
- Absolute error = |X − X′|
- Relative error = |X − X′| / |X|
- Percentage error = relative error × 100 %

#### Other related terms
- **Gross error:** another name for a blunder.
- **Propagated error:** error in the inputs carried into the result of later calculations.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. Error in numerical computation is:
   A. Difference between true value and approximate value
   B. The sum of true and approximate values
   C. Only a mistake by the user
   D. The ratio X'/X
   Answer: A. Error = X - X'. (Key point: Definition)

2. Rounding 37.46235 to 37.46 is an example of:
   A. Truncation error
   B. Round-off error
   C. Blunder
   D. Modelling error
   Answer: B. Round-off arises from keeping only a limited number of digits. (Key point: Round-off)

3. Using sin x ~ x - x^3/3! drops later terms. This is:
   A. Round-off error
   B. Inherent error
   C. Truncation error
   D. Blunder
   Answer: C. Replacing an infinite series by a finite one causes truncation error. (Key point: Truncation)

4. Writing 4.317 as 4.371 is:
   A. Round-off error
   B. Truncation error
   C. Inherent error that cannot be avoided
   D. A blunder (human error), avoidable
   Answer: D. Wrong readings or formulas are blunders, also called gross errors. (Key point: Blunder)

## Related in Numerical Method

- [Round off and compute errors](https://www.bctengineer.com/question.md?key=semester_4%2Fnumerical_method%3Around-off-significant-figures) — Numerical Method, chapter 1
- [Absolute versus relative error](https://www.bctengineer.com/question.md?key=semester_4%2Fnumerical_method%3Aabsolute-relative-error-difference) — Numerical Method, chapter 1, asked 2×

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