# Concept derivation guides

299 concept teaching guides, separate from the 36,000 individual question derivations.

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Concept guide



## [Numerical approximation and error: absolute error, relative error and tolerance for 0.33 approximating 1/3](/en/derivations/derivation-mko-numerical-approximation-error-01/?from=%2Fen%2Fderivations%2F%3Fq%3Dmko-numerical-approximation-error)

Using exact rationals: compute the absolute and relative error of the approximation a=33/100 to the reference x=1/3; decide whether a is within the tolerances τ₁=1/250, τ₂=1/400 and τ₃=1/300 (τ₃ is the endpoint case); prove |a−x|≤τ ⇔ x−τ≤a≤x+τ; compare the errors after scaling by 1000; explain why relative error is undefined for a zero reference and why an error value alone does not reveal the source of the error.

Numerical approximation and error

derivation-mko-numerical-approximation-error-01





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