Lecture 6 Notes

# 333333 is now almost correct eg hw 11 surface area

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Unformatted text preview: Quiz Time A) Almost one B) 9/10 C) 1 D) I dunno •  What is .999…? .999… = 9(1/10 + 1/100 + 1/1000 + …) = 9([1/10]/(1- [1/10]) = 9 (1/9) = 1 A) Almost one B) 9/10 C) 1 D) I dunno Non- unique Representa3on Uncertainty •  Yes, it’s true, 1.0 = .999… (but 1.0 ~= .99999999) What is .777???... •  .777 <= .777???... <= .777999… •  .777 <= .777???... <= .778 1 = .999… => right bound is <= (and not <)! (If this is unclear, you should prove it) 2 2/11/14 Computa3onal Errors •  Round- oﬀ errors –  Machine precision errors propagate (obviously) –  But errors also creep in •  1 and 3 are perfectly represented •  1/3 = .333333 is now almost correct •  E.g., HW 1.1 Surface Area –  These small errors accumulate •  insigniﬁcant when doing a few opera3ons •  problem grows with 3me...
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