page_title: Approximation error
hierarchical_section_title: Approximation error
caption_attribution_description: English: in blue with the linear approximation at , in red. Created in Mathematica.
context_page_description: The approximation error in some data is the discrepancy between an exact value and some approximation to it. An approximation error can occur because:
  the measurement of the data is not precise due to the instruments. or
  approximations are used instead of the real data.
  In the mathematical field of numerical analysis, the numerical stability of an algorithm indicates how the error is propagated by the algorithm.
context_section_description: The approximation error in some data is the discrepancy between an exact value and some approximation to it. An approximation error can occur because:
  the measurement of the data is not precise due to the instruments. (e.g., the accurate reading of a piece of paper is 4.5 cm but since the ruler does not use decimals, you round it to 5 cm.) or
  approximations are used instead of the real data (e.g., 3.14 instead of π).
  In the mathematical field of numerical analysis, the numerical stability of an algorithm indicates how the error is propagated by the algorithm.
caption: Graph of 
    
      
        
          f
          (
          x
          )
          =
          
            e
            
              x
            
          
        
      
      {\displaystyle f(x)=e^{x}}
    
   (blue) with its linear approximation 
    
      
        
          
            P
            
              1
            
          
          (
          x
          )
          =
          1
          +
          x
        
      
      {\displaystyle P_{1}(x)=1+x}
    
   (red) at a = 0. The approximation error is the gap between the curves, and it increases for x values further from 0.
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