Video Transcript
Is 𝜋 over three a rational or an
irrational number?
We begin by recalling the
definition of a rational number. It’s one that can be written in the
form 𝑎 over 𝑏 where 𝑎 and 𝑏 are integers. They’re whole numbers. Once we have this definition, we
can say that an irrational number is one that’s not rational. In other words, it can’t be written
in this form. We’re looking to identify whether
𝜋 divided by three is rational or irrational.
We actually know that 𝜋 is an
example of an irrational number. It’s one of the ones we’re most
familiar with. So, actually, we need to ask
ourselves what happens if we divide an irrational number by an integer? Well, it’s still irrational. There’s no way to write 𝜋 divided
by three in the form 𝑎 over 𝑏 where 𝑎 and 𝑏 are both integers. Three is an integer, 𝜋 is not. So this is irrational. 𝜋 divided by three is an
irrational number.
