Why are rational numbers denoted by Q?

Rational numbers are denoted by the letter Q because the word “quotient” represents their defining property: every rational number can be expressed as the quotient of two integers (p/q, with q ≠ 0).

• A rational number is any number that can be written in the form p/q, where p and q are integers and q ≠ 0.
• The symbol Q comes from the word quotient in mathematics. The set of rational numbers includes all fractions, integers (since they can be written as p/1), and terminating or repeating decimals.
• Using Q as the symbol helps distinguish rational numbers from other sets:
   
  • N → Natural numbers
  • Z → Integers (from the German Zahlen, meaning numbers)
  • R → Real numbers

Also Check: Is pi a rational or irrational number?

• Thus, mathematicians adopted Q to represent the set of rational numbers, as they are fundamentally numbers expressed as quotients.

Rational numbers are denoted by Q because they are defined as quotients of integers, and “Q” stands for quotient.