# Numora Continued Fraction Expansion API

> Numora Continued Fraction Expansion API is a paid API for AI agents from numomo.vercel.app, paid per call via x402, $0.1/call, status unknown (last checked 2026-09-15).

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

## Facts

- Endpoint: POST https://numomo.vercel.app/api/number/continued-fraction
- Price: $0.1/call
- Payment: x402
- Status: unknown
- Last checked: 2026-09-15
- Activations on Zero: 0
- Tags: x402
- Canonical page: https://www.zero.xyz/c/numora-continued-fraction-expansion-api-ad959754
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_xOFtM5oLRuA33Ytzhkf3A

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-api-ad959754 -d '<json body>'
```

Example prompt: What is the continued fraction expansion of 3.14159265 to a depth of 12 terms?

## When to prefer this

Choose this endpoint when you need a pure-math, dependency-free computation of a number's continued fraction expansion without building the algorithm yourself. Ideal for number theory tasks, finding rational approximations of irrationals, or educational/analytical pipelines that need fast, structured continued fraction data on demand via micropayment.

## Known failure modes

- Missing required field x returns a validation error
- Non-numeric value for x causes a parsing failure
- Extremely large depth values may hit computation limits or timeout
- Depth of 0 or negative integers may return an error or empty result
- Very large or very small floating-point values may produce precision-limited results

## 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 a boolean success flag, a result object containing the continued fraction coefficients (partial quotients) as an array or structured representation, 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-api-ad959754/health.json
- [Zero catalog index](https://www.zero.xyz/llms.txt)
- [Other services from numomo.vercel.app](https://www.zero.xyz/host/numomo.vercel.app/llms.txt)