Approximations, Errors and Significant Figures Quiz
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Questions and Answers

What does accuracy measure in the context of numerical problem solving?

  • The precision of computed values
  • How close a measured or computed values agrees with the true values (correct)
  • How close individual measured or computed values agree with each other
  • The inaccuracy and imprecision of numerical results
  • Which term represents how close individual measured or computed values agree with each other?

  • Error
  • Inaccuracy
  • Accuracy
  • Precision (correct)
  • In the context of this course, what does error represent?

  • Both inaccuracy and imprecision of numerical results (correct)
  • Imprecision only
  • Accuracy
  • Inaccuracy only
  • What is precision in the context of numerical problem solving?

    <p>How close individual measured or computed values agree with each other</p> Signup and view all the answers

    What does accuracy measure in the context of numerical problem solving?

    <p>How close a measured or computed values agrees with the true values</p> Signup and view all the answers

    Which term represents both inaccuracy and imprecision of numerical results in this course?

    <p>Error</p> Signup and view all the answers

    What is the formula for true error?

    <p>Error = True value - Approximation</p> Signup and view all the answers

    How can the error be normalized to the true value?

    <p>By dividing the error by the true value</p> Signup and view all the answers

    In the example given, what is the true error for the bridge measurement?

    <p>1cm</p> Signup and view all the answers

    What is the true percent relative error for the river measurement?

    <p>10%</p> Signup and view all the answers

    What method can be used to estimate the error if the true values are unknown?

    <p>Comparing results from successive calculations</p> Signup and view all the answers

    What does 𝜀𝑎 represent in the context of numerical methods?

    <p>The absolute error</p> Signup and view all the answers

    In most applications, what condition do we want |𝜀𝑎 |< 𝜀𝑠 to satisfy?

    <p>|𝜀𝑎 |&lt; 𝜀𝑠 means a reliable calculation</p> Signup and view all the answers

    What is used to minimize round-off errors in arithmetic calculations?

    <p>Double precision</p> Signup and view all the answers

    What concept designates reliability of numerical values by reporting certain digits and an estimated digit?

    <p>Significant figures (sig figs)</p> Signup and view all the answers

    Which type of digits are always considered significant according to the concept of significant figures?

    <p>Non-zero digits and terminal zeros following the decimal point</p> Signup and view all the answers

    What do terminal zeros in an integer not be considered according to significant figures?

    <p>Never significant</p> Signup and view all the answers

    What does |𝜀𝑎 |< 𝜀𝑠 indicate about a result?

    <p>The result is highly accurate</p> Signup and view all the answers

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