CALCULATE WITH CONFIDENCE

Fractions & Decimals

Continued Fraction Calculator

Expand a rational number into a simple continued fraction or evaluate its terms.

Fractions & Decimals

Enter values

Private calculation in your browser
  1. 1EnterProvide the known values
  2. 2CalculateResults update automatically
  3. 3VerifyReview the details and units
Try an example

Use the notation shown in each label and example. Inputs stay on this device and are never sent to a calculation service.

Result

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Enter valid values to see the result.

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Understand the subject

What is Continued Fraction?

A decimal is another place-value form of a rational number: positions to the right of the point represent tenths, hundredths, and smaller powers of ten.

Use it to rewrite the same quantity in a form suited to estimation, comparison, or calculation.

The relationship

Write the rule before calculating

See the structure

What the calculation is doing

Worked interpretation

Read the result in context

415/93 = [4; 2, 6, 7].

Interpret with care

Important boundary

A displayed finite decimal can be an approximation; repeating expansions need their repeating pattern preserved.

Use the Mathematics collection to move between connected concepts without duplicating the calculation.

Quick guide

How to use this calculator

  1. Enter values using the notation shown beside each field.
  2. Choose a calculation mode when the tool offers more than one interpretation.
  3. Read the primary answer first, then inspect the supporting details.

Calculation method

Apply the stated definition

x = a₀ + 1/(a₁ + 1/(…)).

The calculator validates the mathematical domain before returning a result and does not replace undefined states with zero.

Worked example

Worked example

415/93 = [4; 2, 6, 7].

x = a₀ + 1/(a₁ + 1/(…)).

Supported inputs

Precision and limits

Finite, bounded input

Integers, finite decimals, fractions, and mixed numbers are evaluated with exact rational arithmetic wherever the operation permits.

Notation

Enter fractions as a/b and mixed numbers as w n/d. A denominator can never be zero.