# Definition:Partial Quotient

## Contents

## Definition

Let $k$ be a field.

Let $(a_n)_{n\geq0}$ be a continued fraction in $k$, either finite or infinite.

Let $n \geq 0$ be a natural number.

The **$n$th partial quotient** is the $n$th term $a_n$.

## Also known as

A **partial quotient** is also known as a **partial denominator**, particularly in the case of a general continued fraction.

## Also see

- Definition:Complete Quotient
- Definition:Sequence of Partial Quotients
- Definition:Sequence of Complete Quotients

## Sources

- Weisstein, Eric W. "Partial Denominator." From
*MathWorld*--A Wolfram Web Resource. http://mathworld.wolfram.com/PartialDenominator.html