# Questioning Pi: 3.14159265359 vs 22/7

• Mr.maniac
In summary, a conversation took place where a student's teacher claimed that 22/7 is the exact value of pi and 3.141 is an approximation. The student's classmates and other people on the forum disagreed and explained that both 22/7 and 3.141 are approximations of pi, with the actual value being 3.14159265358979323846264338327950288419716939937510. The conversation also discussed the importance of not blindly believing everything a teacher says and the possibility of the teacher creating an account on the forum to further discuss their beliefs.

#### Mr.maniac

here's my question:which is right:3.14159265359 blah blah blah
-supported by http://www.quora.com/Why-is-PI-22-7 [Broken]
also says that 22/7 is an approximation or

22/7 which is 3.14285714286(I don't know extended or not.)
-supported by my maths teacher
-supported by my fat ol' friend

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Mr.maniac said:
3.14159265359 blah blah blah
-supported by http://www.quora.com/Why-is-PI-22-7 [Broken]
also says that 22/7 is an approximation
-supported by mathematics, which is the only thing that really counts.

Mr.maniac said:
22/7 which is 3.14285714286(I don't know extended or not.)
Which is not a very good approximation, as you can see compared to the value you wrote above.

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Mr.maniac
PI isn't here but like these, 22 / 7 is just an approximation.
Source: http://xkcd.com/1047/

DrewD
If your teacher thinks that pi is exactly equal to 22/7, then I'm worried for your class.

Google is correct. Pi is approximately equal to 22/7, but not exactly equal.

Mr.maniac
Here's https://www.math.hmc.edu/funfacts/ffiles/10004.5.shtml - 355 / 113. It's good to 6 decimal places but like 22 / 7, it isn't exactly equal to PI.

Mr.maniac
She says that 22/7 is the correct value of pi and 3.141 blah blah is just an approximation.

Mr.maniac said:
She says that 22/7 is the correct value of pi and 3.141 blah blah is just an approximation.
Wow. I'm with Mentallic on this. Sorry for your class if that's what she is teaching.

Mr.maniac
Then shall I conclude that my maths teacher is wrong along eith my fatso friend.

Alsi it wasn't taught a simple algaebric expression was given to break down which was
3.14r
As I like pi strarted all about pi and my friend calculated 22/7 and then a debate then asking the teacher (asking for a fez).

Mr.maniac said:
Then shall I conclude that my maths teacher is wrong along eith my fatso friend.
The problem is that she is teaching this to people. It would be great if you could get her to create an account and post her logic here. There would be plenty of people who would be happy to explain it to her. :)

Here's an interesting take on this:

##\pi = \frac{22}{7} - \int_{0}^{1} \frac{x^4(1-x)^4}{1+x^2} dx##

Since your teacher is not here to defend him- or her-self, did he or she say that "pi is equal to 22/7" or "It is better to use 22/7 for pi than 3.14"?

Let me quote my teacher :

"22/7 is the exact value of pi and 3.141 is an approximation"
(I'm I getting her wrong")

Mr.maniac said:
Let me quote my teacher :

"22/7 is the exact value of pi and 3.141 is an approximation"
(I'm I getting her wrong")

She is right about the second part, but the first is also an approximation.

Mr.maniac, I don't know you so please don't be offended by what I say/ask: Is that actually an exact quote or is that what you think you remember from the middle of an argument. I only ask this because I teach, and while I have definitely misspoken, I am more often misquoted.

Is it possible that this is on a standardized test that explicitly told you to use the value 3.14 or 22/7 for ##\pi## in your calculations? If this is the case, you may have misunderstood her telling you to use that value. If there wasn't some strange context (eg. she preceded it by saying, "the next statement I make is false" ), she was wrong.

Also, in these sorts of debates (math debates) wikipedia is usually pretty reliable.

Mr.maniac said:
Let me quote my teacher :

"22/7 is the exact value of pi and 3.141 is an approximation"
22/7 ##\approx## 3.142857. Both 22/7 and 3.141 are approximations to the actual value of ##\pi##. According to wikipedia, the first 50 digits of ##\pi## are 3.14159265358979323846264338327950288419716939937510 (http://en.wikipedia.org/wiki/Pi). Clearly 3.141 is a better approximation than 22/7.
Mr.maniac said:
(I'm I getting her wrong")
?
Are you trying to say "Am I getting her wrong?"

(Yes it's am I getting her wrong)
And DrewD they are the exact words of my teacher.

And she is saying 3.141 blah blah is wrong

Please see Mark44's post #16 above.
22/7 AND 3.1416 are both approximations. He has listed the correct value of Pi to 50 digits.

If your teacher is saying anything otherwise, she is wrong.

Mr.maniac said:
(Yes it's am I getting her wrong)
And DrewD they are the exact words of my teacher.

Well that's unfortunate. I would nicely do what she wants in class but carefully check to be sure it is correct. If it is incorrect, ask her and if she doesn't realize the mistake, keep track of it and let an administrator know. Well, that's not actually what I would have done, but it is the most likely way to actually accomplish something.

Your teacher is teaching you a very good lesson here. Don't believe everything your teacher says.

jasonRF, TheDemx27, Mr.maniac and 1 other person
Khashishi said:
Your teacher is teaching you a very good lesson here. Don't believe everything your teacher says.

Very much so. In year 7, I had a teacher that claimed that the orbits of the planets were perfect circles. When another student questioned him he said "That's just how they draw it".
Mr.maniac, do you think it's possible if you can get your teacher to create an account here? Or as Drew said, talk to an administrator. The problem is that this teacher will continue to teach in the future, and it means all future students will be taught incorrectly.

Khashishi said:
Your teacher is teaching you a very good lesson here. Don't believe everything your teacher says.
Well said Khashishi

pwsnafu said:
Very much so. In year 7, I had a teacher that claimed that the orbits of the planets were perfect circles. When another student questioned him he said "That's just how they draw it".
Mr.maniac, do you think it's possible if you can get your teacher to create an account here? Or as Drew said, talk to an administrator. The problem is that this teacher will continue to teach in the future, and it means all future students will be taught incorrectly.
Well not possible to make her make a account here but will try to convince her.
(By the way how to close a thread cause will close this one after she is convinced)

Mr.maniac said:
Well not possible to make her make a account here but will try to convince her.
(By the way how to close a thread cause will close this one after she is convinced)
You cannot close threads, only moderators can do that. If you really feel the need to close a thread you can hit the "report" button and ask for it to be closed, but whether or not it IS closed is up to the moderators.

Mr.maniac

Mr.maniac said:
Well not possible to make her make a account here but will try to convince her.

Wikipedia lists a number of proofs that pi is irrational (i.e. pi isn't a fraction including 22/7). Niven's proof is probably the most convincing because it only uses high school level calculus.

Edit: a simpler non-rigorous argument: if pi was equal to 22/7, then we wouldn't have world records for calculating the digits of pi (22/7 has a repeating decimal).

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## 1. What is the difference between 3.14159265359 and 22/7?

The number 3.14159265359, known as pi, is an irrational number that represents the ratio of a circle's circumference to its diameter. It is typically rounded to 3.14 for practical calculations. On the other hand, 22/7 is a rational number that is often used as an approximation for pi. It is equal to 3.14285714286, which is slightly closer to the true value of pi than 3.14.

## 2. Why is pi important in mathematics and science?

Pi is a fundamental constant in mathematics and science. It appears in various mathematical equations and is essential for calculating the circumference, area, and volume of circles and spheres. It is also used in many scientific fields, such as physics, engineering, and statistics.

## 3. How do we know that pi is an irrational number?

We can prove that pi is an irrational number using mathematical proofs. One of the most famous proofs is by the Greek mathematician Euclid, who showed that the ratio of a circle's circumference to its diameter cannot be expressed as a fraction of two integers, making it an irrational number.

## 4. Are there any practical applications for knowing the digits of pi?

While knowing the digits of pi may seem like a fun challenge, it does have practical applications. For example, NASA uses the digits of pi to calculate the trajectories of spacecraft, and the banking industry uses it for data encryption. It can also be used to test the accuracy of computer algorithms and to study patterns in random numbers.

## 5. Is there an end to the digits of pi?

No, there is no end to the digits of pi. It is an infinite, non-repeating decimal, meaning that the digits after the decimal point go on forever without following a pattern. As of 2021, pi has been calculated to over 31 trillion digits, and there is still no end in sight.