ITPEC FE Morning October 2022 Question 2
ITPEC FE Morning October 2022 — Question 2 of 80
Loss of Significance — cancellation error when subtracting nearly equal floats.
When two floating-point numbers of similar magnitude are subtracted, the leading significant digits cancel out, leaving a result with far fewer meaningful digits.
Example:
- 1.0000000 − 0.9999999 = 0.0000001
- Input had 7 significant digits → result has only 1
Why not others:
- (a) — describes overflow (exceeding max value and raising an exception)
- (c) — describes rounding error (truncating bits below the least significant digit)
- (d) — describes information loss in addition (adding numbers of very different magnitudes)
Key rule: Loss of significance = subtraction of nearly equal values → catastrophic cancellation of significant digits.
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