Every real number has a unique continued fraction expansion [a₀; a₁, a₂, …]. The convergents pₙ/qₙ are the best rational approximations — no fraction with a smaller denominator gets closer. See how √2, φ (golden ratio), and π are approximated, and how they appear in the Stern–Brocot tree.
| n | aₙ | pₙ/qₙ | error |
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