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ME 142 Engineering Computation I

Learn about round-off error and truncation error in numerical computation. Understand significant figures, accuracy, precision, and computer representation of numbers.

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ME 142 Engineering Computation I

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  1. ME 142Engineering Computation I Computer Precision & Round-Off Error

  2. Numerical Error • Two major forms of numerical error: • Round-off error • Truncation error • Round-off Error • Is due to the fact that computers can represent only quantities with a finite number of digits • Truncation Error • Is introduced because numerical methods employ approximations to represent exact mathematical operations and quantities

  3. Significant Figures • Significant digits of a number are those that can be used with confidence • Typically, 3 to 4 significant digits is common in the final answer of engineering calculations • Keep all available significant figures on intermediate calculations • Round final answer to 3 or 4 significant digits • Significant Figures in Excel • By default Excel keeps all available significant figures and displays a round answer, per user setting

  4. Accuracy vs. Precision • Two terms commonly used within engineering • Both are important and necessary • Accuracy refers to how closely a computed or measured value agrees with the true value. • Precision refers to how closely individual computed or measured values agree with each other.

  5. Increasing Accuracy Inaccurate & Imprecise Accurate & Imprecise Increasing Precision Inaccurate & Precise Accurate & Precise

  6. Computer Representation of Numbers • How do computers represent numbers? • Binary digits or bits or base 2 • Groupings of bits into bytes and words • How do we represent numbers? • Decimal system or base 10 • Need to understand how to convert between these number systems

  7. Base 10 1 2 4 0 5 5 x 100= 5 0 x 101= 00 4 x 102= 400 2 x 103= 2000 1 x 104= 10000 12405

  8. Base 2 1 1 1 0 1 1 x 20= 1 = 1 0 x 21= 00 = 0 1 x 22= 100 = 4 1 x 23= 1000 = 8 1 x 24= 10000 = 16 11101 29

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