![]() The quotient is the integer part of the fraction, while the remainder is the decimal part. They are created when one number is divided by another number, resulting in a quotient and a remainder. Another way is by their properties, such as being positive or negative, and whether or not they are prime numbers.įractions are the most common type of rational number. One way is by how they are represented, which include fractions, decimals, and percentages. Rational numbers can be classified in different ways. Some irrational numbers, such as ? (pi), can also be expressed as rational numbers by using an infinite decimal expansion. For example:Īll decimal numbers can also be expressed as rational numbers. All whole numbers and integers are rational numbers, as they can be expressed as fractions with a denominator of 1. Rational numbers are any number that can be expressed as a fraction p/q, where p and q are integers and q is not equal to 0. Irrational numbers include ?2 (square root of 2, an algebraic number), ? (pi, a transcendental number), and Euler’s constant e. A real number that is not rational is called irrational. ![]() These statements hold true not just for base 10, but also for any other integer base b ? 2. Moreover, any repeating or terminating decimal represents a rational number. The decimal expansion of a rational number always either terminates after finitely many digits or begins to repeat the same finite sequence of digits over and over. The set of all rational numbers, often referred to as “the rationals”, is usually denoted by a boldface Q (or blackboard bold ?). ![]() In mathematics, a rational number is any number that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q. Rational Numbers Definitions and Examples
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