302 HW 6 - 3.123456789101112 is irrational because no part...

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M302 HOMEWORK #6 Dr. Schurle Assignment: page 131, #2, 6, 8, 10, 14, 20, 23, 36 Grade the following for 2 points each, then give all or part of the remaining two points depending on how much work they've done on the other problems. #6. Sometimes, because the unending decimal expansion could repeat and so be a rational number, or not repeat and so be an irrational number. For example, the decimal 3.78787878. .. is a rational number because the part “78” repeats, but
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Unformatted text preview: 3.123456789101112. .. is irrational because no part repeats. #8. 12.03456915 works, as do many other numbers. [The decimal must either end or repeat.] #23. S = 0.01010101. .. 100S = 1.01010101. .. [Subtract the top from the bottom to get] 99S = 1, so S=1/99. #36. 2 [or in fact the square root of any prime number.] NOTE: Anything inside [ ] need not be part of the student's solution. It is for explanation purposes only....
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This note was uploaded on 03/19/2008 for the course M 302 taught by Professor Irwin during the Spring '08 term at University of Texas.

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