simple continued fraction

A simple continued fraction (SCF) is a mathematical expression representing a number as a sum of an integer and a quotient. The denominator of this quotient is itself a sum of an integer and another quotient, continuing this pattern. In an SCF, all the integer parts are positive, and the numerators of the fractional parts are all 1.1

An SCF can be written compactly as [a₀; a₁, a₂, a₃, \u2026], where a₀ is an integer and a₁, a₂, a₃, \u2026 are positive integers.1

If the number of terms in an SCF is finite, it represents a rational number. For example, ⁸⁰²/₂₅₁ can be expressed as [3; 5, 8, 6].1

If the number of terms is infinite and a sequence of terms repeats, the SCF represents an irrational number that is a root of a quadratic equation with rational coefficients. Nonterminating SCFs can also approximate irrational numbers like \u03c0 or e.1