Continued fraction explorer
Open Continued fraction explorer on Happytails.ai. This view has the same page content and links, with explicit tool capabilities. Read the processing notes before using a tool.
Tool capabilities
{
"id": "continued-fraction-explorer",
"category": "calculators",
"built": true,
"requirements": "Enter a decimal, scientific notation or integer fraction. Each part may contain up to 120 digits; decimal exponents must be from โ120 to 120. Choose 1 to 256 convergents. Decimal input is an exact finite rational, not a symbolic irrational constant. Decimal previews truncate after 12 places; exact fractions and signed errors are preserved. A term-limit stop is explicitly distinguished from a terminated expansion.",
"implementation": {
"fields": [
{
"key": "terms",
"label": "Maximum convergents",
"value": 32,
"type": "number",
"min": 1,
"max": 256,
"step": 1
}
],
"live": true,
"background": true,
"presentation": "metrics",
"inputMaxLength": 300,
"inputErrorCode": "SEQ_VALUE",
"note": "Enter one exact decimal, scientific notation or integer fraction, such as 355/113. Inspect coefficients, convergents and exact errors. Finite decimal input does not identify an irrational constant.",
"experience": {
"automatic": true,
"single": true,
"inputMaxLength": 300,
"inputMode": "text",
"label": "Number or fraction",
"placeholder": "355/113",
"help": "Enter a decimal, scientific notation or integer fraction, such as 355/113. Results update as you type. Up to 300 characters.",
"helpParts": [
"Enter a decimal, scientific notation or integer fraction, such as 355/113.",
"Results update as you type.",
"Up to 300 characters."
],
"action": null
},
"mode": "automatic",
"interactive": false
},
"execution": "Browser interface",
"api": null,
"browser_agent": {
"supported": true,
"name": "run_current_tool",
"discovery": "WebMCP on the human page in a supporting browser",
"verification": "See audit/API-AUDIT.md; availability is not verification"
}
}Page guide
See the exact convergents of a fraction or decimal, and compare the error at each step.
How to use Continued fraction explorer
- Enter the exact number you want to approximate.
- Set the maximum number of convergents.
- Compare the coefficients, rational approximations and exact errors; download the full table.
Useful next steps
How to use it
See the exact convergents of a fraction or decimal, and compare the error at each step.
Limits and assumptions
Enter a decimal, scientific notation or integer fraction. Each part may contain up to 120 digits; decimal exponents must be from โ120 to 120. Choose 1 to 256 convergents. Decimal input is an exact finite rational, not a symbolic irrational constant. Decimal previews truncate after 12 places; exact fractions and signed errors are preserved. A term-limit stop is explicitly distinguished from a terminated expansion.
Keep the exact values
Download JSON for the calculation, CSV for the complete table and the method note. Processing stays on your device.