Decimal to Continued Fraction Calculator

Enter value and click on calculate. Result will be displayed.

Formula:

Decimal Number :
Result:
Continued Fraction :

What is a Decimal to Continued Fraction Calculator?

A Decimal to Continued Fraction Calculator converts a decimal number (e.g., 3.14159) into its continued fraction representation, which expresses numbers as a sequence of integer terms separated by fractions.

Why use a Decimal to Continued Fraction Calculator?

  • Exact Representation: Continued fractions provide precise expressions for irrational numbers.
  • Simplification: Useful for approximating real numbers with simple fractions.
  • Mathematical Applications: Used in number theory, cryptography, and engineering.

How does a Decimal to Continued Fraction Calculator work?

  1. Separate the integer and fractional parts.
  2. Take the reciprocal of the fractional part.
  3. Repeat the process until a desired accuracy is reached or the fraction terminates.

For example, converting 3.245 gives:

When should you use a Decimal to Continued Fraction Calculator?

  • When approximating irrational numbers with rational fractions.
  • When analyzing periodicity in fractions (e.g., for quadratic irrationals).
  • When solving Diophantine equations in number theory.