{
  "title": "Continued fraction explorer",
  "human_url": "https://happytails.ai/en/calculators/continued-fraction-explorer/",
  "agent_url": "https://happytails.ai/agents/en/calculators/continued-fraction-explorer/",
  "language": "en",
  "markdown_url": "https://happytails.ai/en/calculators/continued-fraction-explorer.md",
  "content": "Continued fraction explorer\nSee the exact convergents of a fraction or decimal, and compare the error at each step.\nHow can we improve this tool?\nReport a problem or share an idea.\nPlease leave out private information. Your message and the tool name go to our team via PostHog.\nHow to use Continued fraction explorer\nEnter the exact number you want to approximate.\nSet the maximum number of convergents.\nCompare the coefficients, rational approximations and exact errors; download the full table.\nUseful next steps\nFinite difference table explorer\nHow to use it\nSee the exact convergents of a fraction or decimal, and compare the error at each step.\nLimits and assumptions\nEnter a decimal, scientific notation or integer fraction. Each part may contain up to 120 digits; decimal exponents must be from −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.\nKeep the exact values\nDownload JSON for the calculation, CSV for the complete table and the method note. Processing stays on your device.",
  "content_format": "text/plain",
  "visibility": "public",
  "links": [
    {
      "name": "Finite difference table explorer",
      "url": "https://happytails.ai/en/calculators/finite-difference-table-explorer/"
    }
  ],
  "tool": {
    "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 −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.",
        "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"
    }
  },
  "markdown": "# Continued fraction explorer\n\n- Human page: https://happytails.ai/en/calculators/continued-fraction-explorer/\n- Markdown: https://happytails.ai/en/calculators/continued-fraction-explorer.md\n- Structured JSON: https://happytails.ai/agents/en/calculators/continued-fraction-explorer/index.json\n- Visibility: public\n\n## Tool capabilities\n\n| Property | Value |\n| --- | --- |\n| Tool ID | `continued-fraction-explorer` |\n| Category | calculators |\n| Implementation | Registered implementation. Registration alone is not a production-quality guarantee. |\n| Browser execution | Automatic updates after valid input or file selection. |\n| Browser processing | Browser; see tool notes for network behavior. |\n| HTTP API | Not callable through HTTP. |\n| Browser-agent interface | run_current_tool |\n\n### Implementation notes\n\nEnter 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.\n\n### Inputs and settings\n\nText input: Number or fraction.\n\nExample or placeholder shown in the interface (not a validated fixture):\n\n```text\n355/113\n```\n\nEnter a decimal, scientific notation or integer fraction, such as 355/113. Results update as you type. Up to 300 characters.\n\n| Setting | Meaning | Control type | Default | Constraints |\n| --- | --- | --- | --- | --- |\n| `terms` | Maximum convergents | number | 32 | min=1 max=256 step=1 |\n\n### Browser-agent workflow\n\n1. Open the human page in a browser that supports WebMCP.\n2. Discover the interface exposed by that page; use its actual schema.\n3. Select files on the page first when the tool requires files.\n4. Call `run_current_tool` with valid input and settings.\n5. Inspect the returned result or error and the displayed output. Retrieve files from the displayed download links.\n\nCalls do not automatically copy or download results. Browser permissions still apply. Interface availability alone is not proof of successful execution.\n\n### Planning specification\n\nEnter a decimal, scientific notation or integer fraction. Each part may contain up to 120 digits; decimal exponents must be from −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.\n\nThis describes intended requirements. Use the implementation notes, interface schema and observed output to determine current support.\n\n### Complete machine-readable capability record\n\n```json\n{\n  \"id\": \"continued-fraction-explorer\",\n  \"category\": \"calculators\",\n  \"built\": true,\n  \"requirements\": \"Enter a decimal, scientific notation or integer fraction. Each part may contain up to 120 digits; decimal exponents must be from −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.\",\n  \"implementation\": {\n    \"fields\": [\n      {\n        \"key\": \"terms\",\n        \"label\": \"Maximum convergents\",\n        \"value\": 32,\n        \"type\": \"number\",\n        \"min\": 1,\n        \"max\": 256,\n        \"step\": 1\n      }\n    ],\n    \"live\": true,\n    \"background\": true,\n    \"presentation\": \"metrics\",\n    \"inputMaxLength\": 300,\n    \"inputErrorCode\": \"SEQ_VALUE\",\n    \"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.\",\n    \"experience\": {\n      \"automatic\": true,\n      \"single\": true,\n      \"inputMaxLength\": 300,\n      \"inputMode\": \"text\",\n      \"label\": \"Number or fraction\",\n      \"placeholder\": \"355/113\",\n      \"help\": \"Enter a decimal, scientific notation or integer fraction, such as 355/113. Results update as you type. Up to 300 characters.\",\n      \"action\": null\n    },\n    \"mode\": \"automatic\",\n    \"interactive\": false\n  },\n  \"execution\": \"Browser interface\",\n  \"api\": null,\n  \"browser_agent\": {\n    \"supported\": true,\n    \"name\": \"run_current_tool\",\n    \"discovery\": \"WebMCP on the human page in a supporting browser\",\n    \"verification\": \"See audit/API-AUDIT.md; availability is not verification\"\n  }\n}\n```\n\n## Page guide\n\nSee the exact convergents of a fraction or decimal, and compare the error at each step.\n\nHow can we improve this tool?\n\nReport a problem or share an idea.\n\nPlease leave out private information. Your message and the tool name go to our team via PostHog.\n\n### How to use Continued fraction explorer\n\n1. Enter the exact number you want to approximate.\n2. Set the maximum number of convergents.\n3. Compare the coefficients, rational approximations and exact errors; download the full table.\n\n## Useful next steps\n\n- [Finite difference table explorer](https://happytails.ai/en/calculators/finite-difference-table-explorer/) ([Markdown](https://happytails.ai/en/calculators/finite-difference-table-explorer.md))\n\n## How to use it\n\nSee the exact convergents of a fraction or decimal, and compare the error at each step.\n\n### Limits and assumptions\n\nEnter a decimal, scientific notation or integer fraction. Each part may contain up to 120 digits; decimal exponents must be from −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.\n\n### Keep the exact values\n\nDownload JSON for the calculation, CSV for the complete table and the method note. Processing stays on your device.\n"
}