# Is 4 the second or third digit of pi

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?

• 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). – Brian M. Scott Aug 26 '15 at 1:22
• 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. – JMoravitz Aug 26 '15 at 1:27
• @JMoravitz The next one is a $2$. Now that I've told you this, would you say that you know 2 many? – Akiva Weinberger Aug 26 '15 at 1:33
• @JMoravitz I've always thought the most convenient stopping-point would be after "3.14." – Kyle Strand Aug 26 '15 at 4:56
• I know all ten digits that occur in the decimal expansion of $\pi$. I'm pretty sure there aren't any others. – Marc van Leeuwen Aug 26 '15 at 11:29

## 1 Answer

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.

• As if we're memorizing pi in order to find areas of circles :P – Akiva Weinberger Aug 26 '15 at 1:34
• 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what a circle is, what its circumference and diameter are, and even then the formula from Euclidean plane geometry is no longer valid. – Marc van Leeuwen Aug 26 '15 at 7:50
• 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). – celtschk Aug 26 '15 at 8:26
• 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 – Jamie Hanrahan Aug 26 '15 at 8:46
• Obligatory – MikeTheLiar Aug 26 '15 at 13:20