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Continued Fraction Calculator
To find the generalized continued fraction, write the fraction and hit calculate button
Continued Fraction Calculator
Continued fraction calculator is used to calculate the continued fraction representation of simple fractional numbers. It converts the simple fraction into a sequence of numbers and the reciprocal of a simple fraction.
What is a Continued Fraction?
Continued fractions are a unique way of representing real numbers as an infinite sequence of numbers where each number is the sum of an integer and the reciprocal of a simple fraction. A continued fraction is used to approximate the real numbers to their simple form.
Formula
The formula to find the continued fraction is:
r = a_{0 }+ 1/a_{1}+1
Where,
- a_{0 }= first term.
- a_{1} = next term.
How to calculate the Continued Fraction?
Example 1:
Find the Continued fraction when the simple fraction is “7/8”.
Solution:
Step 1: Write the given fraction.
Simple fraction = 7/8, Continued fraction =?
Step 2: Write the formula to find continued fraction
r = a_{0 }+ 1/a_{1}+1
Step 3: Write the given fraction in the above expression.
Simple fraction = 7/8
Simple fraction = 1/(8/7)
Simple fraction = 1/[1 + 1/7] ----------> (i)
Continued fraction formula.
r = a_{0 }+ 1/a_{1}+1 ---------> (ii)
Compared the equation (i) & (ii) then get the answer.
Generalized continued fraction = [0; 1, 7]
More results
Here are some other results of the continued fraction.
Simple Fraction | Generalized Continued Fraction |
15/10 | [1; 2] |
12/4 | [3; ] |
16/7 | [2; 3, 1, 1] |
13/7 | [1; 1, 6] |
12/5 | [2;2,1,1] |
113/3 | [37; 1, 1, 1] |