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CSC_349_HANDOUT#2

# CSC_349_HANDOUT#2 - COMPUTER SCIENCE 349A Handout Number 2...

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1 COMPUTER SCIENCE 349A Handout Number 2 Measures of error (pages 54-57 of the 5 th edition of the textbook; pages 56-59 of the 6 th edition) If p denotes the true (exact) value of some quantity, and * p denotes some approximation to p , then * p p E t = is called the absolute error , and p p p p p t * 1 * = = ε (if 0 p ) is called the relative error . Absolute error is not a meaningful measure of error unless you know the magnitude of p , the quantity you are approximating. For example, if 1234000 * and 1234321 = = p p , then 321 = t E seems large, although * p is quite accurate and agrees with p to 4 significant digits; if 001111 . 0 * and 001234 . 0 = = p p , then 000123 . 0 = t E seems small, although * p is not very accurate and agrees with p to only 1 significant digit. Relative error , which is always meaningful, in fact indicates the number of correct significant digits in an approximation * p . Example Consider L 14159265 . 3 = = π p 000029 . 0 5 1415 . 3 00019 . 0 4 141 . 3 00051 . 0 3 14 . 3 013 . 0 2 1 . 3 error relative digits t significan correct of number to * ions approximat p p

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