MathematicsChapter 10: Numerical Methods
Approximation, Error, and Tolerance
Numerical methods produce approximations; absolute error is
Learning objectives
- State the rule for approximation, error, and tolerance.
- Solve a approximation, error, and tolerance problem step by step.
- Check the result, restrictions, notation, and units.
Definition
Numerical methods produce approximations; absolute error is
Mathematical form
true=1.4142 and approx
error=.0042.
Where / symbols
- Approximation, error, and tolerance
- Numerical methods produce approximations; absolute error is
CONCEPT AND RULE
Numerical methods produce approximations; absolute error is
METHOD
For approximation, error, and tolerance, identify the given information and required result. Select the matching definition or formula, state its conditions, substitute carefully, simplify one line at a time, and check.
WORKED EXAMPLE
true-approx| and tolerance is an accepted bound.|If true=1.4142 and approx=1.41, absolute error=.0042.
COMMON MISTAKE
Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all domain or interval conditions.
How to solve approximation, error, and tolerance
- Identify the mathematical objects, givens, restrictions, and required result.
- Choose and write the relevant definition, theorem, or formula.
- Substitute with brackets and carry out one justified step per line.
- Simplify, state the final answer clearly, and verify it in the original setting.
Worked example
- Worked example:
- true-approx| and tolerance is an accepted bound.|If true=1.4142 and approx=1.41, absolute error=.0042.
In simple words
Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all domain or interval conditions.
Key points
- Approximation, error, and tolerance
- rule
- worked example
Exam preparation
Exam Focus
Quick revision
Revision Zone
Review the key facts, formulas and checks before you move on.Approximation, Error, and Tolerance
Sticky Notes · Formula and Worked Revision
Core Idea
- Numerical methods produce approximations; absolute error is
Rule / Formula
- Numerical methods produce approximations; absolute error is
Method
- Identify givens and restrictions.
- Write the rule.
- Substitute and simplify.
- Check the result.
Worked Example
- true-approx| and tolerance is an accepted bound.|If true=1.4142 and approx=1.41, absolute error=.0042.
Common Error
- Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all domain or interval conditions.
FBISE Exam Tip
- Show the formula, substitutions, algebra, restrictions, and final answer; method marks need visible reasoning.
60-second revision
- Numerical methods produce approximations; absolute error is
- Worked pattern: true-approx| and tolerance is an accepted bound.|If true=1.4142 and approx=1.41, absolute error=.0042.
- Final check: domain, sign, notation, units, and reasonableness.
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