Is π rational or irrational

Step by step

The question

Question: is π rational or irrational?

Rational means: it can be written as a fraction, with whole numbers on top and at the bottom.

Then its decimal stops, or repeats for ever.

Irrational means: no fraction works.

Its decimal never stops and never repeats.

1 Look at the decimal

π is the distance round a circle divided by the distance across.

Its decimal goes 3.14159265, and so on.

It never stops and never repeats.

Careful!

22/7 is only close to π.

It is not equal.

So π is irrational.

No fraction is exactly π.

2 Check

Let's check: 22 divided by 7 is 3.142857.

π is 3.141592.

They are different from the third digit.

So the answer is right!

Let's look back.

First: look at the decimal.

Last: check.