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If someone says that they know 10 digits of pi, does that mean that they know ten digits starting with the 3 in 3.14 or with the 1 in 3.14?

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    $\begingroup$ Depends on the speaker; you pretty much have to ask. I careful speaker would say something like I know pi to 64 decimal places (or however many was the case). $\endgroup$ Aug 26, 2015 at 1:22
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    $\begingroup$ Fortunately, I don't have this problem of ambiguity. I know the digits of $\pi$ in decimal form up until the first zero. It is a convenient place to stop. $\endgroup$
    – JMoravitz
    Aug 26, 2015 at 1:27
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    $\begingroup$ @JMoravitz The next one is a $2$. Now that I've told you this, would you say that you know 2 many? $\endgroup$ Aug 26, 2015 at 1:33
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    $\begingroup$ @JMoravitz I've always thought the most convenient stopping-point would be after "3.14." $\endgroup$ Aug 26, 2015 at 4:56
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    $\begingroup$ I know all ten digits that occur in the decimal expansion of $\pi$. I'm pretty sure there aren't any others. $\endgroup$ Aug 26, 2015 at 11:29

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People generally specify digits after the decimal place to say how many digits of pi they know.

Fun fact: if you know pi to 39 digits, you have the accuracy to approximate any circle around the observable universe to the width of a proton: going farther is not practical.

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    $\begingroup$ As if we're memorizing pi in order to find areas of circles :P $\endgroup$ Aug 26, 2015 at 1:34
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    $\begingroup$ One cannot actually measure any circle around the observable universe. Besides general relativity gets very important as such scales, and it gets hard if not impossible to even define what a circle is, what its circumference and diameter are, and even then the formula from Euclidean plane geometry is no longer valid. $\endgroup$ Aug 26, 2015 at 7:50
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    $\begingroup$ Another fun fact: If you express the largest distance we can observe (46 million light years) in terms of the planck length (the smallest length that actually makes sense physically), you get that it is about $2.7\cdot 10^{58}$ planck lengths. Thus with $\pi$ to about 60 digits, you should be able to calculate the circumference of every circle in the universe to the accuracy permitted by physics (of course the objection by @MarcvanLeeuwen about GR still applies; even more so, since at that precision, every local object will change the geometry). $\endgroup$
    – celtschk
    Aug 26, 2015 at 8:26
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    $\begingroup$ Another fun fact: You can express pi with perfect accuracy. You just have to do it in base pi. The value is then simply 10. :D $\endgroup$ Aug 26, 2015 at 8:46
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    $\begingroup$ Obligatory $\endgroup$
    – Mike G
    Aug 26, 2015 at 13:20

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