# why is 22/7 used for pi?

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• Seth
Lv 4
7 years ago

Because it is a best rational approximation to pi, which is an irrational number. Note that I said "a" best, not "the" best - there is no such thing!

See the Wikipedia article I cited for continued fraction expansions, which provide all of the best rational approximations (also called Diophantine approximations) to irrational numbers for all denominators of that size or less. Scroll down a bit to see the continued fraction expansions for pi.

For pi, the best rational approximations are 3/1, 22/7, 333/106, 355/113, etc.

Each one of these is closer than any other fraction with a smaller denominator. So it is in that sense that they are the "best" approximations.

One thing to note is that there is a large gap in denominators from 22/7 to 333/106. That means that 22/7 is closer to pi than ANY other fraction with a denominator under 106! That makes 22/7 a particularly good approximation to pi for such a small denominator.

And this fraction isn't just something made up for students. It has been known and used since antiquity to approximate pi in rational calculations, well before calculators and decimal approximations became common.

• 7 years ago

Anthony---

22/7 is the smallest irrational improper fraction that approximates pi closely and allows students to present solutions to perimeters and areas in terms of improper fractions..

For example, let's say a circle has diameter 10 cm then C = pi*d = 22*10/7 = 220/7 cm.

Source(s): math tutor for several years.
• Flukey
Lv 5
7 years ago

Because that is what pi is mathematically. It is how it is calculated, though it is not possible to write out in full. That is why we write it that way, or more inaccurately for convenience as 3.14 in the decimal format.

• Anonymous
7 years ago

I cannot consider it infinitesimally close to 3.1415926535... but it is I believe the closest possible fraction? Please remind me if I'm mistaken. It is approximately 3.142857 repeating...

Source(s): Me.