MATH221 · Annotated SlidesChapter 1 — Round-off Errors, Computer Arithmetic and Convergence
Chapter 1 · Annotated slides

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.

Slide text Study notes Highlight: key words Tips, tricks & traps Seen again elsewhere How it can come up
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    1. k-digit chopping drops extra digits; rounding rounds the k-th digit.
    2. Absolute error |p − p*|; relative error |p − p*| / |p|.
    Exam trapRelative error divides by the TRUE value p, not the approximation.
    🎯 How this can come up · 1 question
    MCQ

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

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