# Is 22/7 the same as pi?

Mar 27, 2017

$\pi = 3.142$

#### Explanation:

$\pi$ is roughly $3.142$

Writing that as a fraction, we get $\frac{3142}{1000}$ which subsequently gives $\frac{22}{7} \approx 3.142$

Mar 27, 2017

They are not equal, but their values are very close.

$\pi \ne \frac{22}{7} , \text{ } \pi \approx \frac{22}{7}$

#### Explanation:

$\frac{22}{7} \mathmr{and} \pi$ are not equal, but we can say that

$\pi \approx \frac{22}{7} \text{ }$ they are approximately equal.

$\pi$ is an irrational number - it is an infinite, non-recurring decimal.
Its value is $3.141592654 \ldots \ldots \ldots \ldots . .$ There is NO pattern.

$\frac{22}{7}$ is a fraction which is very close to $\pi$.

However, $\frac{22}{7}$ is a rational number which can be written as a recurring decimal . $\frac{22}{7} = 3.142857 \overline{142857.} . .$ There IS a pattern.

If $\pi \mathmr{and} \frac{22}{7}$ were equal, their difference would be $0$

However: $\frac{22}{7} - \pi = 0.00126448925 \ldots$

Therefore they are not equal, but,

$\frac{22}{7} = 3 \frac{1}{7}$ is very close to $\pi$