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Percent_Carbon comments on Harry Potter and the Methods of Rationality discussion thread, part 14, chapter 82 - Less Wrong Discussion
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The sixth decimal digit of pi after the decimal point is 2.
The value of the millionths place in the decimal expression of pi when rounded to the millionths place is 3.
The reason I know pi out to the sixth decimal digit past the decimal point is because the digits to the fifth fit into an easy rhyme, but the fifth decimal digit after the decimal point is a 9. If it were to round up there would be a little cascade, so it's good to know the next digit.
If Harry knew to round up the millionths place in the decimal expression of pi when rounded to the millionths place, he would know pi out to the ten millionths place, or the seventh decimal digit following the decimal point.
Rounding errors at the millionths place are errors of less than one part in a million.
The original text remains correct.
One doesn't need to remember what the digit past the rounded one is in order to memorize the rounded figure.
Did I say that the text was incorrect? I'm 99.999% sure I didn't, but looking back . . . no, still looks like I didn't. All I said was that I was annoyed, and what I think Harry should have memorized instead.