Accuracy & Estimation (DP IB Applications & Interpretation (AI)): Revision Note

Accuracy & Estimation

What are exact values?

• Exact values are forms that represent the full and precise value of a number

  • For example,is an exact value and 3.14 is an approximation using 3 significant figures

• If a number has an infinite number of non-zero digits after the decimal point then you can use three dots to signal that the decimal representation goes on for example

  • For example, √2 = 1.414...

• Exact values can involve

  • Fractions:   

  • Roots: ,  

  • Logarithms: , 

  • Mathematical constants: , 

• Your GDC might automatically give your answer as an exact answer

• If your GDC does not do this then you may need to evaluate parts of the expression separately and use algebra

  • For example: If  then your GDC will probably not give you the exact value of

  • You would insist evaluate it without a GDC to get the exact value:  

Why use estimation?

• We estimate to find approximate answers to difficult sums

• Or to check our answers are about the right size (order of magnitude)

  • For example, if the question is to find a length the answer cannot be negative

  • or if we are looking for the mean age of some people an answer of 150 must be incorrect

• Estimating an answer before carrying out a calculation will help you know what you are looking for and determine if your answer is likely to be correct or not

• In real life estimation skills are used every day in many activities

How do I choose the correct answer?

• Sometimes a mathematical argument will lead to more than one answer

  • This is common with problems involving quadratics, you will usually have two solutions

  • If you have more than one solution after you have solved a problem, always check to see if they are both valid

• Most of the time you can simply use logic to choose the correct answer

  • If the problem involves length or area and one of the answers is negative, the true solution will be the positive answer

• Occasionally you will need to see if an answer can be valid

  • If one of your answers is for example, will not give a true solution