## In mathematics|lang=en terms the difference between arbitrary and rational

is that

**arbitrary** is (mathematics) any and all possible while

**rational** is (mathematics) a rational number: a number that can be expressed as the quotient of two integers.

## As adjectives the difference between **arbitrary** and **rational**

is that

**arbitrary** is (usually|of a decision) based on individual discretion or judgment; not based on any objective distinction, perhaps even made at random while

**rational** is capable of reasoning.

## As nouns the difference between **arbitrary** and **rational**

is that

**arbitrary** is anything arbitrary, such as an arithmetical value or a fee while

**rational** is (mathematics) a rational number: a number that can be expressed as the quotient of two integers.