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It's possible to work out the digits in the decimal expansion of pi via many methods. The simplest to explain is to measure a large circle with a tape measure, but there are many better, more mathematical algorithms, and computer programs developed specifically for calculating pi.

The current world record is 1,241,100,000,000 decimal digits. That's more than a trillion: http://www.super-computing.org/pi_current.html

See here for more: https://secure.wikimedia.org/wikipedia/en/wiki/Computing_%CF%80

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Q: How do you know what number comes next in pi if you want to write it to more decimal places than anyone ever has before?
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