An irrational number cannot be expressed as a ratio in the form p/q where p and q are integers and q > 0. Integers can be.
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A rational number can be expressed as a ratio of two integers, p/q where q > 0. An irrational number cannot be expressed in such a way.
There are numbers which cannot be expressed as ratios of two integers. These are called irrational numbers.
No prime numbers are irrational: All prime numbers are integers, and all integers are rational, since they can be expressed as themselves divided by 1.