"Q" represents rational numbers because all rational numbers are a quotient. This means that each rational number can be expressed by a fraction with a denominator other than zero and a numerator that is a whole number. Whole numbers, fractions and decimals are all rational numbers.
The Italian mathematician, Giuseppe Peano was the first person to use "Q" to refer to the set of rational numbers. He selected "Q" because it was the first letter of the Italian word for quotient, "quoziente." This represented that each member of the rational number set was a quotient. Some other ways to express a quotient include as the answer to a division problem or as a ratio. In typeface or electronic media, the "Q" for the set of rational numbers is commonly displayed in boldface.
Rational numbers are a subset of the set of real numbers, which also includes irrational numbers. When rational numbers are displayed as decimals, they either terminate or form an infinite repeating pattern. When irrational numbers are displayed as decimals, they go on forever without forming a repeating pattern. Rational numbers are countable, but irrational numbers aren't countable. There are more irrational numbers in the set of real numbers than there are rational numbers.