ITPEC FE Morning October 2022 Question 2

Subtracting two nearly equal floating-point numbers leaves few significant digits — that is loss of significance, also called cancellation.

A floating-point number keeps a fixed number of significant digits. When two close values are subtracted, their matching leading digits cancel, and only the few trailing digits, which may carry rounding error, remain significant. For example, with 7 digits, 1.234567 − 1.234560 = 0.000007: the result has a single significant digit.

Answer (b)

Why not others:

• •(a) — a result beyond the largest representable value is overflow
• •(c) — discarding the part below the least significant digit by rounding off, up or down is rounding error
• •(d) — the small addend's digits vanishing when it is added to a much larger number is information loss (absorption), which happens on addition of very different magnitudes, not subtraction of close ones

Key rule: Name floating-point errors by their cause: too large is overflow, cut-off digits is rounding error, a small value swallowed by a large one is information loss, and close values subtracted is loss of significance.

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