Pre-Algebra: Converting Fractions and Decimals
by Thinkwell
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About this Lesson
- Type: Video Tutorial
- Length: 4:37
- Media: Video/mp4
- Posted: 01/28/2009
- Use: Watch Online & Download
- Download: MP4 (iPod compatible)
- Size: 64 MB
This lesson is part of the series: Pre-Algebra Review
Fractions can be converted into decimals by simply dividing the numerator by the denominator. This can be done easily with a calculator or it can be done by hand using long division. Professor Burger shows how this is done both with numbers that divide evenly, and numbers that don't divide evenly. Sometimes, when numbers don't divide evently, you are left with a result that has a decimal. In this lesson, you will also learn shorthand for writing numbers with repeating decimals.
Taught by Professor Edward Burger, this lesson was selected from a broader, comprehensive course, Pre Algebra. This course and others are available from Thinkwell, Inc. The full course can be found at http://www.thinkwell.com/student/product/prealgebra. The full course covers whole numbers, integers, fractions and decimals, variables, expressions, equations and a variety of other pre algebra topics.
Edward Burger, Professor of Mathematics at Williams College, earned his Ph.D. at the University of Texas at Austin, having graduated summa cum laude with distinction in mathematics from Connecticut College.
He has also taught at UT-Austin and the University of Colorado at Boulder, and he served as a fellow at the University of Waterloo in Canada and at Macquarie University in Australia. Prof. Burger has won many awards, including the 2001 Haimo Award for Distinguished Teaching of Mathematics, the 2004 Chauvenet Prize, and the 2006 Lester R. Ford Award, all from the Mathematical Association of America. In 2006, Reader's Digest named him in the "100 Best of America".
Prof. Burger is the author of over 50 articles, videos, and books, including the trade book, Coincidences, Chaos, and All That Math Jazz: Making Light of Weighty Ideas and of the textbook The Heart of Mathematics: An Invitation to Effective Thinking. He also speaks frequently to professional and public audiences, referees professional journals, and publishes articles in leading math journals, including The Journal of Number Theory and American Mathematical Monthly. His areas of specialty include number theory, Diophantine approximation, p-adic analysis, the geometry of numbers, and the theory of continued fractions.
Prof. Burger's unique sense of humor and his teaching expertise combine to make him the ideal presenter of Thinkwell's entertaining and informative video lectures.
About this Author
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- Thinkwell
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Founded in 1997, Thinkwell has succeeded in creating "next-generation" textbooks that help students learn and teachers teach. Capitalizing on the power of new technology, Thinkwell products prepare students more effectively for their coursework than any printed textbook can. Thinkwell has assembled a group of talented industry professionals who have shaped the company into the leading provider of technology-based textbooks. For more information about Thinkwell, please visit www.thinkwell.com or visit Thinkwell's Video Lesson Store at http://thinkwell.mindbites.com/.
Thinkwell lessons feature a star-studded cast of outstanding university professors: Edward Burger (Pre-Algebra through...
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WRITING A FRACTION AS A DECIMAL
Suppose someone gives some number written as a fraction, and we want to convert it to a decimal. That’s pretty easy to do. We can long divide. We have a numerator and a denominator, so we long divide the numerator by the denominator. We set up this thing. Let’s take a look at an example.
Take 11 over 4. Write it as a decimal. I take 11 divided by 4. What I understand here is that after this 11 there’s a decimal point and an infinite army of 0s—as many as I may need. Let’s see what happens. 4 goes into 11 2 times. By the way—I put the decimal point directly above wherever it appears here. 2 times 4 is 8. When I subtract I have 11 minus 8, which is 3. Now I bring down one of my 0 soldiers, and I take 4 and ask how many times does 4 go into 30? 7 times. 7 times 4 is 28. When I subtract I get 2. I bring down another soldier. I see 4 goes into 20 5 times. 5 times 4 is 20, and I see now a remainder of 0. When I hit 0 I know I can stop. I stop, and I see that 11 over 4 is equal to the decimal 2.75. Neat. Long division allows us to figure out the decimal expansion for fractions.
Let’s take a look at 5 over 6. If I divide, I see 5 divided by 6. Again, I put a decimal point here, and I have an infinite army of 0s if I need them. I bring the decimal point straight up, like a periscope coming up. I say 6 goes into 5, 0 times. 0 times 6 is 0. I subtract, and I see 5. I bring down one of my 0s. I see 6 goes into 50, 8 times. 8 times 6 is 48. When I subtract I see 2. Good. I bring down another 0. 6 goes into 20, 3 times. 3 times 6 is 18. When I subtract I see 2. This is interesting because before I saw a 2. I brought down the 0 and made it 20. I bring down a 0, and what do I see? I see a 20 again. I have a repeat. What does that mean? It means I already know the answer. The answer’s going to be 3. 3 times 6 is 18; when I subtract I see a 2 again. This is going to repeat forever. These 3s are going to repeat forever. I don’t have to continue dividing. I am constantly going to get a remainder of 2. This equals 0.8333 repeating forever. There’s a way of expressing this. I want to show it to you. We could write this as 0.83 and to indicate that there’s an infinite long tail of just 3s, we put a bar on top of the 3. This means that this doesn’t end here but continues repeating 3 forever. You can see that for some fractions, when you convert to a decimal, you might have an infinitely long decimal expansion that repeats (or we say is periodic). Alternatively, some decimal expansions for fractions will terminate at some example where it ended in .75. Either is possible, and you have to be ready for both.
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