Difference Between pi and 22/7

mathdad

mathdad

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What is the difference (if there is one) between pi and 22/7?
 
22/7 is a rational approximation to pi, just as 3.14 is. That is, both 22/7 and 3.14 are rational numbers (fraction and terminating decimal, respectively) that are close enough to the exact value of pi for elementary work.

Pi is an irrational number, namely 3.1415926535897932384626433832795...

22/7 is a rational number, namely 3.1428571428571428571428571428571...

3.14 is a rational number, namely 3.1400000000000000000000000000000...

We could say that the difference between pi and 22/7 is 0.00126448926734961868021375957764 ;)
 
Dr.Peterson said:
22/7 is a rational approximation to pi, just as 3.14 is. That is, both 22/7 and 3.14 are rational numbers (fraction and terminating decimal, respectively) that are close enough to the exact value of pi for elementary work.

Pi is an irrational number, namely 3.1415926535897932384626433832795...

22/7 is a rational number, namely 3.1428571428571428571428571428571...

3.14 is a rational number, namely 3.1400000000000000000000000000000...

We could say that the difference between pi and 22/7 is 0.00126448926734961868021375957764 ;)
Click to expand...

More interesting notes for my files. There are questions that specifically state to use 22/7 or 3.14 or to leave the answer in terms of pi. Why so?
 
mathdad said:
More interesting notes for my files. There are questions that specifically state to use 22/7 or 3.14 or to leave the answer in terms of pi. Why so?
Click to expand...
When a book says to use 22/7 or 3.14, that is probably either because they don't want the student to use a calculator, and want to keep the manual work simple, or just to make sure everyone's answer agrees, so it's easier to check, and easier for students when they look in the back of the book.

When it says to leave the answer in terms of pi, it may be for more or less the same reasons, or to emphasize that we have an exact answer in that form.

Commonly we keep work in terms of named constants rather than specific numbers (until getting a numerical value at the end) for several reasons: to leave the decision how much precision to use for last; to allow simplification; to see better how the answer depends on various constants; or just to avoid having to copy lots of (rounded) decimal places and risk mistakes at every step.

I suspect that many authors don't even think through why they do this; it's just tradition.
 
Dr.Peterson said:
When a book says to use 22/7 or 3.14, that is probably either because they don't want the student to use a calculator, and want to keep the manual work simple, or just to make sure everyone's answer agrees, so it's easier to check, and easier for students when they look in the back of the book.

When it says to leave the answer in terms of pi, it may be for more or less the same reasons, or to emphasize that we have an exact answer in that form.

Commonly we keep work in terms of named constants rather than specific numbers (until getting a numerical value at the end) for several reasons: to leave the decision how much precision to use for last; to allow simplification; to see better how the answer depends on various constants; or just to avoid having to copy lots of (rounded) decimal places and risk mistakes at every step.

I suspect that many authors don't even think through why they do this; it's just tradition.
Click to expand...

Perhaps it is "just tradition" as you said. I hope my questions are not dull or boring for the site. Honestly, I think you would love to have me in your class because I sincerely love math. I am different than most students. Older people are better students by far.

I find myself buried more in my math books than I do the Bible. I am a Christian. I love God. God is not too happy that right now math is my passion. However, God created math. Therefore, I am hoping that He will understand. BTW, God ALWAYS wants to be first.
 
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