# Numora Continued Fraction Expansion

> Numora Continued Fraction Expansion is a paid API for AI agents from numormor.netlify.app, paid per call via x402, $0.1/call, status unknown (last checked 2026-09-14).

Computes the continued fraction representation of a real number to a specified depth

## Facts

- Endpoint: POST https://numormor.netlify.app/api/number/continued-fraction
- Price: $0.1/call
- Payment: x402
- Status: unknown
- Last checked: 2026-09-14
- Activations on Zero: 0
- Tags: x402
- Canonical page: https://www.zero.xyz/c/numora-continued-fraction-expansion-2e616a40
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_XFGlX6ZNPoIWVW4ROLLBC

Status and success rate cover calls made through Zero and Zero's own probes. Third-party monitors may report differently.

## How to call it through Zero

Zero handles the 402 payment challenge and records the run. With the Zero CLI installed (`npm i -g @zeroxyz/cli`):

```sh
zero fetch --capability numora-continued-fraction-expansion-2e616a40 -d '<json body>'
```

Example prompt: Can you compute the continued fraction expansion of 3.14159265358979 to a depth of 10 terms?

## When to prefer this

Use this endpoint when you need the exact continued fraction decomposition of a specific real number for number theory work, approximation analysis, or studying convergents. Ideal when you need a pure math computation with no external library dependencies and are comfortable with x402 micropayments on Base.

## Known failure modes

- Missing required field x returns validation error
- Non-numeric value for x causes parse error
- Depth too large may cause timeout or truncation
- Payment failure via x402 micropayment returns 402 status
- Negative or zero depth may return error or default behavior

## How this service works

100 pure math computation endpoints for AI agents. Statistics, financial math, linear algebra, equation solving, calculus, number theory, sequence generation, and unit conversions. Zero external dependencies. x402 micropayments on Base.

## Output

Returns a JSON object with success flag, a result object containing the continued fraction coefficients (partial quotients) for the input number at the requested depth, and a human-readable computation description string.

## Request schema (JSON Schema)

```json
{
 "type": "object",
 "required": [
  "x"
 ],
 "properties": {
  "x": {
   "type": "number"
  },
  "depth": {
   "type": "integer"
  }
 }
}
```

## Response schema (JSON Schema)

```json
{
 "type": "object",
 "required": [
  "success",
  "result",
  "computation"
 ],
 "properties": {
  "result": {
   "type": "object",
   "description": "Computation result varies by endpoint"
  },
  "success": {
   "type": "boolean",
   "description": "Always true on success"
  },
  "computation": {
   "type": "string",
   "description": "Human-readable description of what was computed"
  }
 }
}
```

## More

- Live health (JSON, refreshed every minute): https://www.zero.xyz/c/numora-continued-fraction-expansion-2e616a40/health.json
- [Zero catalog index](https://www.zero.xyz/llms.txt)
- [Other services from numormor.netlify.app](https://www.zero.xyz/host/numormor.netlify.app/llms.txt)