What this calculator does
Continued fraction expansion works out expands a fraction p/q into continued-fraction terms and lists its convergents. Enter your own figures above and the answer updates as you type: nothing is fixed in the code, so the result reflects exactly the numbers you supply.
The formula this calculator evaluates is printed under the tool and explained below, so you can check the working by hand or reuse it in a spreadsheet.
The formula
Formulaa₀=⌊p/q⌋, then repeat on the reciprocal of the remainder; convergents hₙ=aₙhₙ₋₁+hₙ₋₂, kₙ=aₙkₙ₋₁+kₙ₋₂
The inputs explained
| Field | What to enter |
|---|---|
| Numerator p | A number. Starts at 415. |
| Denominator q | A number. Starts at 93. |
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How the answer changes with numerator p
Every other input is held at the calculator’s starting values while numerator p varies. Select any row to load that scenario into the calculator.