# Numora Continued Fraction Expansion

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

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

## Facts

- Endpoint: POST https://numormo.vercel.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-8521294c
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_9fsv9SL6sNdQ1yR4VHlqn

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-8521294c -d '<json body>'
```

Example prompt: Can you compute the continued fraction expansion of 3.14159265 to a depth of 8 terms?

## When to prefer this

Use this endpoint when you need a pure server-side continued fraction decomposition with no external library dependencies, especially in agent workflows that require micropayment-gated math computation. Prefer this over client-side JavaScript solutions when you need verifiable, reproducible results in a backend pipeline, or when you need a standardized API response format for downstream agents.

## Known failure modes

- Missing required field x returns an error
- Non-numeric x value causes a validation failure
- Extremely large depth values may cause timeout or memory issues
- Non-finite inputs (NaN, Infinity) may return an error
- Payment failure via x402 prevents the call from executing

## 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=true, a result object containing the continued fraction coefficients (partial quotients) array and related data, and a human-readable computation string describing what was computed.

## 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-8521294c/health.json
- [Zero catalog index](https://www.zero.xyz/llms.txt)
- [Other services from numormo.vercel.app](https://www.zero.xyz/host/numormo.vercel.app/llms.txt)