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Good Math by Mark C. Chu-Carroll

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11Continued Fractions

The way that we write numbers that aren’t integers is annoying and frustrating.

We’ve got two choices: we can write them as fractions or we can write them as decimals. But both have serious problems. There are some numbers that we can write easily as fractions, like 1/3 or 4/7. That’s great. But there are some numbers that you just can’t write as a fraction, like π.

For numbers like π, there are fractions that are close. 22/7 is a common approximation for π. But fractions are terrible for that: if you need to be a bit more precise than that, you can’t change it a little bit; you need to come up with a totally different fraction. That’s one of the reasons that decimals are great. We can approximate a number like π using ...

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