# Pi, Schools, and 22/7

A common misconception that $\pi$ is exactly 22/7: origin and remedy

Many of you may have noticed that a large fraction of students are under the impression that the value of $\pi$ is 22/7. Exact. These students have no idea that the rational number 22/7 is just an approximation to the irrational number $\pi$.

I think the reason lies in the way schools treat $\pi$: There might be a couple of mentions that 22/7 is an approximation, but it remains under-emphasized. On the other hand, see the “numerical problems”. Notice the multiples of 7 in diameters or radii in almost all the problems, hinting the students to use 22/7 as $\pi$ and get non-fractional answers! With such practice problems for many years, 22/7 is firmly imprinted on students’ minds as the value of $\pi$.

I think we can do better: Make the students use various approximations. Let them choose their approximation options from many possibilities: 22/7, 355/113, 3.14…, and so on. Also make them aware of the fraction of error with each approximation; possibly ask them to calculate that. When talking about the value of $\pi$ or results of calculations using $\pi$, make them always say “approximately”. (We have such rituals in other places: for example we make them write an additive constant C when they calculate indefinite integrals! We even cut points for missing that!)

The point is that it is not a problem if students do not know the exact value of $\pi$, because nobody does! But they should know that the values that they use are approximations.

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### 3 comments

1. Even I felt the same, while teaching maths to 11 class students, I was amazed to know that they really didn’t know that 22/7 was just an approximation to pi and there exist many more approximations to it. We were introduced to it in our 9th class in CBSE board and in fact we were asked to find out all possible approximations commonly used, as an assignment.

2. In school, we were also taught that the value of pi IS 22/7 and 3.14.. is an approximation of 22/7. This wrong idea was embedded so deep in my mind, that I always substituted 22/7 in every problem. In college, one of my professors noted this and took time to explain how wrong I was, and why all these approximations are equally wrong.

1. Yes, in the sense that any of them is not equal to pi, all of them are equally wrong. But since pi is irrational, all we could have is approximations. And as approximations, all are not equally good; some are better than others: for example 355/113 is much better than 22/7. The choice depends upon the accuracy required by the given problem.