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This is an example of a formatted note Something Nifty: A Taste of Simple Continued Fractions

Category: Numbers • goodmath
Posted on: August 3, 2006 12:00 PM, by Mark C. Chu-Carroll

One of the annoying things about how we write numbers is the fact that we generally write things one of two ways: as fractions, or as decimals.

You might want to ask, "Why is that annoying?" (And in fact, that's what I want you to ask, or else there's no point in my writing the rest of this!)

It's annoying because both fractions and decimals can both only describe rational numbers - that is, numbers that are a perfect ratio of two integers. And most numbers aren't rational.

But it's even more annoying than that: if you use decimals, then there are lots of rational numbers that you can't represent exactly (i.e., 1/3); and if you use fractions, then it's hard to express the idea that the fraction isn't exact. (How do you write π as a fraction? 22/7 is a standard fractional approximation, but how do you say π, which is almost 22/7?)

So what do we do?

One of the answers is something called continued fractions. A continued fraction is a very neat thing.

(i quote from GOOD MATH, BAD MATH a super math blog) Now you know why math wasn't my top subject...

posted by wrangler steve at Saturday, August 05, 2006 >0 comments


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