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A continued fraction is a form of fraction where the numerator or denominator contains another fraction.

## Examples

• $\sqrt 2 = 1 + \frac{1}{ 2+\frac{1}{ 2+\frac{1}{...} } }$
• $\sqrt 2 = [1;(2)]$

## Calculating from decimal number

With a decimal number, you can obtain a continued fraction with the following process.

1. Write the whole number portion to start the continued fraction. ([2])
2. Set the whole number portion to zero, leaving the number less than 0.
3. If 0, stop. Otherwise, take the reciprocal
4. Repeat step 1 for the following numbers in the continued fraction.

For example, with 2.285:

• 2.285 - 2 -> 0.285 ([2])
• 1 / 0.285 -> 3.508772
• 3.508772 - 3 -> 0.508772 ([2; 3])
• 1/0.508772 -> 1.965517
• 1.965517 - 1 -> 0.965517 ([2; 3, 1])
• 1/0.965517 -> 1.035714
• 1.035714 - 1 -> 0.035714 ([2; 3, 1, 1])
• 1/0.35714 -> 28.000224
• 28.000224 - 28 -> 0.000224 ([2; 3, 1, 1, 28])

The process can be stopped here, as the number begins to approach 0, or otherwise generate rounding errors.