MATH221 · Chapter 1 · Annotated SlidesRound-off Errors, Computer Arithmetic and Convergence
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Round-off Errors, Computer Arithmetic and Convergence

Floating-point representation, chopping vs. rounding, absolute and relative error, significant digits, loss of significance, and rates of convergence.

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Every original slide is shown unchanged. Yellow marks on a slide point to a numbered note: hover or tap a mark to jump to its note, and hover a note to see its marks. Questions tagged Past exam appeared on a real paper; Prediction questions are likely angles, not confirmed. Pick an answer to each question: a wrong pick tells you why it is wrong, so you can try again.

All 8 slides
  1. 1 Slide 1
  2. 2 Convert to Floating-number
  3. 3 Slide 3
  4. 4 Slide 4
  5. 5 Slide 5
  6. 6 Slide 6
  7. 7 Slide 7
  8. 8 Slide 8
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Convert to Floating-number

Slide 2: Convert to Floating-number

Notes

  1. k-digit chopping drops extra digits; rounding rounds the k-th digit.

  2. Absolute error |p − p*|; relative error |p − p*| / |p|.

  3. Trap Relative error divides by the TRUE value p, not the approximation.

Exam angle

PredictionQ1

p = 3.1416, p* = 3.14. The relative error is about:

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Notes

  1. Subtracting nearly equal numbers loses significant digits; rewrite the formula (e.g. rationalize) to avoid it.

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