Rational number

A rational number is a number expressible as a quotient of two integers with a nonzero denominator. Its decimal expansion terminates or eventually repeats.

Integer: An integer is a whole number, its negative, or zero. Rational numbers are formed by taking quotients of integers.
Equivalent fractions: Equivalent fractions have different numerators and denominators but represent the same value. A rational number has infinitely many fraction representations.
Irrational number: An irrational number is a real number that cannot be expressed as a quotient of integers. Its decimal expansion neither terminates nor eventually repeats.
Dense order: An order is dense when between any two distinct elements lies another element. Between any two distinct rational numbers lies another rational number.
Fraction: A fraction represents a quantity as one number divided by another. Each rational number can be represented by a fraction with integer terms.
Lowest terms: A fraction is in lowest terms when its numerator and denominator have no common factor greater than one. This gives a canonical representation for each nonzero rational number.
Real number: A real number is a point on the continuous number line, including rational and irrational numbers. The rational numbers form a dense subset of the real numbers.
Archimedean property: The Archimedean property states that repeated addition of any positive quantity eventually exceeds any fixed quantity. Rational numbers have no infinitely large or infinitesimal elements under their usual order.
Divisibility: Divisibility is the relation in which one integer is an exact multiple of another. Common factors determine whether a fraction can be reduced.
Repeating decimal: A repeating decimal has a digit pattern that recurs indefinitely after some point. Every rational number has a terminating or eventually repeating decimal expansion.

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