Lecture 6 Notes

Lecture 6 Notes

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Unformatted text preview: surements, accuracy of results, •  E.g., .77777 = .77777???? hJp://en.wikipedia.org/wiki/Accuracy_and_precision 1 2/11/14 Machine Precision •  Machine Precision (Error) –  Can only store so many digits using decimal representa3on –  pi is a classic example –  Note •  decimal representa3on is not the problem –  1/3 = .3333333…, π = 3.1415926… •  limited number of digits is the problem –  1/3 ~ .333333 (and in fact .333333 < 1/3) –  Analyze using geometric series •  a+a^2+ a^3 + … = a/(1- a), |a|<1 •  a+a^2+ a^3 + … +a^n = (a- a^(n+1))/(1- a), any a Quiz Time •  What is .999…? •  Is 1/3 = .333…? .333... = 3/10 + 3/100 + 3/1000 + … = 3/10 + 3/10^2 + 3/10^3 + … = 3(1/10 + (1/10)^2 + (1/10)^3+…) = 3(a + a^2 + a^3 + …), a = 1/10 = 3(a/(1- a)) = 3([1/10]/(1- [1/10]) = 3([1/10]/[9/10]) = 3(1/9) = 3/9 = 1/3 •  Yes!...
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This document was uploaded on 03/11/2014 for the course CSCI 004 at Brown.

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