happytails.ai

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 โˆ’120 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
  1. Enter the exact number you want to approximate.
  2. Set the maximum number of convergents.
  3. 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 โˆ’120 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.