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Continued Fractions |
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An irrational number is a number that cannot be written as either a repeating or terminating decimal. The most common examples are pi and the square root of 2. A continued fraction allows us to approximate an irrational number to any desired accuracy. In other words, we have a way to approximate an irrational number as a rational number.
A fraction is one number divided by another number—a numerator over a denominator. In a continued fraction, the denominator is a sum, one of whose terms is a fraction. In that fraction, the denominator is a sum, one of whose terms is a fraction, and so on. Click the Activity link to see an example. |
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Internet Activity |
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Activity 10.6
Click this link to view your assignment for this activity.
http://go.hrw.com/resources/go_mt/e1/c10/ECONFRAC.PDF |
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Adobe Acrobat Reader
You will need Adobe Acrobat Reader to open and print the activity. To download the reader, click "Adobe Acrobat Reader" above.
http://www.adobe.com/products/acrobat/readstep.html |
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Exploration |
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University of Maryland
Professor Walter Gilbert’s entertaining pages include an easy introduction to the subject of continued fractions. There are some very nice examples as well. He also has an interactive “calculator” you should try. Be sure to look at “Communicating with Alien Civilizations Using Continued Fractions.”
http://www.inform.umd.edu/TeachTech/Staff/misc/cftxt01.htm |
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MAA Online
In an interesting article, Ivars Peterson shows how approximating years with months leads to continued fractions.
http://www.maa.org/mathland/mathtrek_10_13.html |
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Cut-the-Knot
This site has a mixture of simple and technical materials.
http://cut-the-knot.com/do_you_know/fraction.html |
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