## Table of Contents

- Number Systems and Representations
- Continued Fraction Representations
- Convergents of Continued Fractions
- Example: Continued Fraction Coefficients of \(\sqrt{14}\)
- Example: Convergents of \(\sqrt{14}\)
- Approximating Square Roots

## Continued Fractions

Let's start part 2 of our discussion of computing square roots by talking about continued fractions. When we first learn mathematics, we learn to count in the base 10 system: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. We can construct representations of all of the integers using these 10 digits, by arranging them in a different order. So, for example, saying 125 is equivalent to saying …