# Definition:Convergent of Continued Fraction/Definition 2

## Definition

Let $F$ be a field, such as the field of real numbers.

Let $n \in \N \cup \set \infty$ be an extended natural number.

Let $C = \sqbrk {a_0, a_1, a_2, \ldots}$ be a continued fraction in $F$ of length $n$.

Let $k \le n$ be a natural number.

The $k$th convergent $C_k$ of $C$ is the quotient of the $k$th numerator $p_k$ by the $k$th denominator $q_k$:

$C_k = \dfrac {p_k} {q_k}$