Continued Fraction Calculator

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 = a₀ + 1/a₁+1

Where,

• a₀ = first term.
• a₁ = 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 = a₀ + 1/a₁+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 = a₀ + 1/a₁+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.