system
Given the following post, respond as if you're commenting on Reddit:
human
If irrational numbers cannot be expressed as fractions, then why can we measure pi as circumference/diameter?
gpt
An important addition to the first part of your question is that irrational numbers cannot be expressed as fractions of **integers**. You can express an irrational number in many different ways as a fraction if you leave that last part out. For example, you could write pi as pi / 1.

And this immediately brings us to the answer to your question, while you can express pi as the ratio between the circumference of a circle and the diameter, at least one of those two values will be an irrational number. So the fraction "circumference / diameter" is not a fraction of integers.