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Roundoff and truncation errors
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New head garb has been ordered http://nm.mathforcollege.com

INTRODUCTION, APPROXIMATION AND ERRORS http://nm.mathforcollege.com

This rapper’s name is Tauheed Epps 2 Chainz Tity Boi Kendrick Lamar http://nm.mathforcollege.com

01.01 INTRODUCTION http://nm.mathforcollege.com

To find velocity from location vs time data of the body, the mathematical procedure used is Differentiation Integration http://nm.mathforcollege.com

The form of the exact solution to is http://nm.mathforcollege.com

Given the f (x) vs x curve, and the magnitude of the areas as shown, the value of y x a 5 7 2 b c -2 2 12 Cannot be determined http://nm.mathforcollege.com

A steel cylindrical shaft at room temperature is immersed in a dry-ice/alcohol bath. A layman estimates the reduction in diameter by using Less More Same while using the value of the thermal expansion coefficient at -108oF. Seeing the graph below, the magnitude of contraction you as a USF educated engineer would calculate would be ______________than the layman’s estimate. http://nm.mathforcollege.com

END http://nm.mathforcollege.com

01.02 MEASURING ERRORS http://nm.mathforcollege.com

The number of significant digits in 2350 is 4 5 3 or 4 http://nm.mathforcollege.com

The absolute relative approximate error in an iterative process at the end of the tenth iteration is 0.007%. The least number of significant digits correct in the answer is 2 3 4 5 http://nm.mathforcollege.com

Three significant digits are expected to be correct after an iterative process. The pre-specified tolerance in this case needs to be less than or equal to 0.5% 0.05% 0.005% 0.0005% http://nm.mathforcollege.com

01.03 SOURCES OF ERROR http://nm.mathforcollege.com

Round-off error Truncation error The error caused by representing numbers such as 1/3 approximately is called Round-off error Truncation error http://nm.mathforcollege.com

The number 6.749832 with 3 significant digits with rounding is 6.75 6.749 6.750 http://nm.mathforcollege.com

Truncation Error Round off Error The error caused by using only a few terms of the Maclaurin series to calculate ex results mostly in Truncation Error Round off Error http://nm.mathforcollege.com

The number 6.749832 with 3 significant digits with chopping is 6.75 6.749 6.750 http://nm.mathforcollege.com

END http://nm.mathforcollege.com

01.04 BINARY REPRESENTATION http://nm.mathforcollege.com

(8)10=(?)2 1110 1011 0100 1000 http://nm.mathforcollege.com

(01011)2 =(?)10 7 11 15 22 http://nm.mathforcollege.com

01.05 FLOATING POINT REPRESENTATION http://nm.mathforcollege.com

Relative absolute true error Using fixed point representation in a computer puts a upper bound on the ________________ in representing a number. Absolute true error Relative absolute true error http://nm.mathforcollege.com

Relative absolute true error Using floating point representation in a computer puts a upper bound on the ________________ in representing a number. Absolute true error Relative absolute true error http://nm.mathforcollege.com

2-bits used for exponent The absolute relative true error in a floating point representation using chopping for a number is less than Machine epsilon 2-bits used for exponent http://nm.mathforcollege.com

add 7 subtract 7 add 15 subtract 15 Five bits are used for the biased exponent. To convert a biased exponent to an unbiased exponent, you would add 7 subtract 7 add 15 subtract 15 http://nm.mathforcollege.com

END http://nm.mathforcollege.com