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Percentage Error (DP IB Applications & Interpretation (AI)): Revision Note

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Percentage Error

What is percentage error?

  • Percentage error is how far away from the actual value an estimated or rounded answer is

    • Percentage error can be calculated using the formula epsilon equals open vertical bar fraction numerator v subscript A minus v subscript E over denominator v subscript E end fraction close vertical bar cross times 100 percent sign

      • where v subscript E is the exact value and v subscript A is the approximate value of v

      • The | | is the absolute value meaning if you get a negative value within these straight brackets, you should take the positive value

    • This formula is in the formula booklet so you do not need to remember it

  • The further away the estimated answer is from the true answer the greater the percentage error

  • If the exact value is given as a surd or a multiple of π make sure you enter it into the formula exactly as you see it

  • Percentage error should always be a positive number

Examiner Tips and Tricks

  • In the exam percentage error will usually be a part of a bigger question on another topic, make sure you know how to find the formula for it in the formula book so that you are prepared to answer these questions

Worked Example

Let P equals x cos open parentheses 2 y close parentheses, where  y equals 15 degree and x equals 4.

a) Calculate the exact value of P.

 

ai-sl-1-1-3-percentage-error-a

b) Calculate the percentage error if an estimate for P was 3.5.

 

ai-sl-1-1-3-percentage-errorb

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    Amber

    Author: Amber

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    Amber gained a first class degree in Mathematics & Meteorology from the University of Reading before training to become a teacher. She is passionate about teaching, having spent 8 years teaching GCSE and A Level Mathematics both in the UK and internationally. Amber loves creating bright and informative resources to help students reach their potential.