Approximation, Error, and Tolerance

Approximation, Error, and Tolerance

What is it?

Numerical methods produce approximations; absolute error is

In simple words

• 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.

Important terms

Approximation, error, and tolerance: Numerical methods produce approximations; absolute error is

What you should learn

• 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.

Full school-level explanation

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

How it works

• 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.

Remember

• Approximation, error, and tolerance
• rule
• worked example
• worked example

How the ideas connect

Worked example: true-approx| and tolerance is an accepted bound.|If true=1.4142 and approx=1.41, absolute error=.0042.

Deeper understanding

Go beyond memorising Approximation, Error, and Tolerance. Connect the definition to reasons, relationships, exceptions, and exam wording.

How the ideas connect

Worked example: true-approx| and tolerance is an accepted bound.|If true=1.4142 and approx=1.41, absolute error=.0042.

Common mistakes

Exam focus

Core Idea

Rule / Formula

Method

Worked Example

Exam focus

Quick revision

• Approximation, error, and tolerance
• rule
• worked example
• 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

Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all domain or interval conditions.

For long answers on Approximation, Error, and Tolerance: define clearly → explain the main parts → give one example → state one exam caution.