Decimal To Fraction Converter
Parse a finite decimal as an integer over a power of ten and reduce it with integer greatest common divisors.
Open toolContinued Fraction Calculator
Expand an exact rational or finite decimal into continued-fraction coefficients and convergents. Provide Exact rational or decimal, Maximum continued-fraction terms to compute results directly in your browser. Decimals are converted to exact base-10 rational values. Euclidean steps use floor division, including negative inputs. Zero denominator is rejected; output states whether expansion completed or stopped at the supplied term limit. Exact BigInt arithmetic is used for integer steps.
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Enter the inputs, then select Calculate.
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How the Continued Fraction Calculator Works & Core Formula
The Continued Fraction Calculator evaluates Exact rational or decimal, Maximum continued-fraction terms in client-side JavaScript using the deterministic rule below and updates the output panel immediately without uploading data to a server.
Expand an exact rational or finite decimal into continued-fraction coefficients and convergents.
Decimals are converted to exact base-10 rational values. Euclidean steps use floor division, including negative inputs. Zero denominator is rejected; output states whether expansion completed or stopped at the supplied term limit. Exact BigInt arithmetic is used for integer steps.
Continued Fraction Calculator Quick Reference & Input Guide
Review the input parameters, allowed value ranges, and worked reference cases for the Continued Fraction Calculator below before running your calculation.
| Parameter / Scenario | Default / Sample Value | Rule or Allowed Range | Output / Usage Note |
|---|---|---|---|
| Input: Exact rational or decimal | 355/113 | Signed integers, ordinary decimals without exponent, or numerator/denominator; at most 100 digits per component. | Required workspace parameter |
| Input: Maximum continued-fraction terms | 20 | Range: 1 to 1000 | Required workspace parameter |
| Worked Case 1: Baseline run (Exact rational or decimal = 355/113) | Preloaded / test values | Expand an exact rational or finite decimal into continued-fraction coefficients and convergents | Exact rational or decimal = 355/113; Maximum continued-fraction terms = 20. Output: Continued-fraction coefficients: 3, 7, 16; Convergents: 3/1, 22/7, 355/113; Status: Exact expansion complete. |
| Worked Case 2: Comparison scenario (continued fraction calculator with steps) | Preloaded / test values | Expand an exact rational or finite decimal into continued-fraction coefficients and convergents | Exact rational or decimal = -1.25; Maximum continued-fraction terms = 10. Output: Continued-fraction coefficients: -2, 1, 3; Convergents: -2/1, -1/1, -5/4; Status: Exact expansion complete. |
Step-by-Step Guide to Using the Continued Fraction Calculator
Follow these three steps to configure Exact rational or decimal, Maximum continued-fraction terms, verify unit and boundary rules, and export your Continued Fraction Calculator output.
Enter the inputs
Start with exact rational or decimal. Signed integers, ordinary decimals without exponent, or numerator/denominator; at most 100 digits per component.
Input and settings
Check units and mode
Decimals are converted to exact base-10 rational values. Euclidean steps use floor division, including negative inputs. Zero denominator is rejected; output states whether expansion completed or stopped at the supplied term limit. Exact BigInt arithmetic is used for integer steps.
Tool result
Calculate and save
Select Calculate, check the labelled result, then use Copy result or Download result.txt.
Review the details
Practical Worked Examples for Continued Fraction Calculator
These concrete scenarios illustrate how the Continued Fraction Calculator processes baseline inputs, comparison checks, and boundary constraints.
Baseline run (Exact rational or decimal = 355/113)
Exact rational or decimal = 355/113; Maximum continued-fraction terms = 20. Output: Continued-fraction coefficients: 3, 7, 16; Convergents: 3/1, 22/7, 355/113; Status: Exact expansion complete.
Comparison scenario (continued fraction calculator with steps)
Exact rational or decimal = -1.25; Maximum continued-fraction terms = 10. Output: Continued-fraction coefficients: -2, 1, 3; Convergents: -2/1, -1/1, -5/4; Status: Exact expansion complete.
Boundary & unit check (Continued Fraction Calculator)
When solving for 'continued fraction calculator', verify that Exact rational or decimal, Maximum continued-fraction terms use consistent units and stay within the documented scope: Decimals are converted to exact base-10 rational values. Euclidean steps use floor division, including negative inputs. Zero denominator is rejected; output states whether expansion completed or stopped at the supplied term limit. Exact BigInt arithmetic is used for integer steps.
How to Read and Verify the Continued Fraction Calculator Output
The output panel reports the exact result derived from Exact rational or decimal, Maximum continued-fraction terms alongside any unit or formatting notes.
Every calculation follows the rule: Expand an exact rational or finite decimal into continued-fraction coefficients and convergents. Because JavaScript uses IEEE 754 double-precision floating-point arithmetic, numeric outputs display up to 12 significant digits where applicable.
Always cross-check the displayed result against the scope note (Decimals are converted to exact base-10 rational values. Euclidean steps use floor division, including negative inputs. Zero denominator is rejected; output states whether expansion completed or stopped at the supplied term limit. Exact BigInt arithmetic is used for integer steps) before applying the value to production specifications, financial models, or lab records.
Scope Limits, Accuracy Assumptions & Related Everyday Math Tools
Review these boundary constraints and validation rules before relying on the Continued Fraction Calculator output.
Operational scope: Decimals are converted to exact base-10 rational values. Euclidean steps use floor division, including negative inputs. Zero denominator is rejected; output states whether expansion completed or stopped at the supplied term limit. Exact BigInt arithmetic is used for integer steps. Inputs that violate minimum/maximum bounds or required format rules are rejected with a clear diagnostic prompt.
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Open toolFrequently Asked Questions About Continued Fraction Calculator
Answers about using Continued Fraction Calculator and understanding its results.
What formula or rule does the Continued Fraction Calculator use?
The Continued Fraction Calculator applies the rule: Expand an exact rational or finite decimal into continued-fraction coefficients and convergents. Enter Exact rational or decimal, Maximum continued-fraction terms into the workspace and the tool computes the exact output in your browser.
What input parameters and units are required for Continued Fraction Calculator?
Yes. Provide Exact rational or decimal, Maximum continued-fraction terms using the documented units and format shown in the quick reference table above. Preloaded default values let you test the workflow immediately.
What are the accuracy limits and boundary assumptions for Continued Fraction Calculator?
Decimals are converted to exact base-10 rational values. Euclidean steps use floor division, including negative inputs. Zero denominator is rejected; output states whether expansion completed or stopped at the supplied term limit. Exact BigInt arithmetic is used for integer steps. Confirm that your inputs fall within the allowed ranges before exporting the result.
Is the Continued Fraction Calculator free and does it keep my inputs private?
Yes. All calculations for the Continued Fraction Calculator execute 100% locally in your browser's JavaScript runtime. No inputs or results are uploaded to any external server.
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