Continued Fraction Calculator
This calculator helps you convert a real number into its continued fraction representation, a useful tool for students, mathematicians, and educators dealing with number systems.
Calculator
Results
Data Source and Methodology
Tutti i calcoli si basano rigorosamente sulle formule e sui dati forniti da Wolfram Alpha.
The Formula Explained
The continued fraction of a number is represented as:
$$ a_0 + \cfrac{1}{a_1 + \cfrac{1}{a_2 + \cfrac{1}{a_3 + \cdots}}} $$
Glossary of Terms
- Continued Fraction: A representation of a number as the sum of its integer part and the reciprocal of another number.
How It Works: A Step-by-Step Example
For instance, the continued fraction of 3.245 might be calculated as:
- Take the integer part, 3.
- Subtract from the number, leaving 0.245.
- Take reciprocal, get 4.0816.
- Continue until desired precision is reached.
Frequently Asked Questions (FAQ)
What is a continued fraction?
A continued fraction is a way to represent numbers through an iterative process of representing them as the sum of their integer part and the reciprocal of another number.
How do you calculate a continued fraction?
By iteratively taking the integer part of a number and the reciprocal of the remainder until a desired precision is reached.
Why use continued fractions?
Continued fractions can provide very accurate approximations of irrational numbers and are used in various fields of mathematics and engineering.
Can all numbers be represented as a continued fraction?
Yes, all real numbers can be expressed as a continued fraction.
Where can I learn more about continued fractions?
You can explore more on continued fractions in mathematical textbooks or trusted online resources like Wolfram Alpha.