# Decimal divide

`decimal-divide` · version 1.0.0 · Money & pricing · free, no key needed

Divide two decimal strings exactly, rounding the quotient once to a fixed scale, and report the exact remainder.

**Use when you need to: divide two decimals exactly · exact decimal division with rounding · quotient and remainder of decimal division.**

## Decide before calling

Read the [versioned contract](/v1/tools/decimal-divide/versions/1.0.0) and the supported scope below. Reuse `decimal-divide@1.0.0` when your input, required output and limits match it. Choose another approach for an unsupported operation.

## Explain the choice

"I can use `decimal-divide@1.0.0` for divide two decimals exactly. I will check its documented scope and the result against the task's requirements. The service is free; token and money savings for this task are unmeasured."

## Supported

- divide two decimals exactly
- exact decimal division with rounding
- quotient and remainder of decimal division
- unit price from total and quantity
- divide to n decimal places
- split an amount by a divisor to cents
- decimal division rounding mode
- average price per unit exact

## Not supported

- integer euclidean division of huge numbers
- evaluating formulas with several operations
- currency conversion with exchange rates
- floating point or scientific notation input

## Behavior

- Decimal strings match ^-?(0|[1-9][0-9]*)(\.[0-9]+)?$: no plus sign, exponent, leading zeros, leading or trailing point, whitespace or separators. A JSON number where a decimal string is required is invalid_input (wrong type).
- A decimal string longer than 62 UTF-16 code units -> limit_exceeded, checked before the grammar. Otherwise a grammar failure, more than 60 digits in total, or more than 40 fraction digits -> invalid_input.
- Zero has no sign: "-0", "-0.00" and any all-zero value are zero and are emitted as "0" (canonical) or "0.00" (fixed scale), never "-0".
- All four fields are required. The exact rational quotient dividend/divisor is rounded once to scale fraction digits with the given mode.
- Rounding modes act on the exact rational result and are: half_even (ties to the even neighbour), half_up (ties away from zero), half_down (ties toward zero), half_ceiling (ties toward +infinity), half_floor (ties toward -infinity), up (away from zero), down (toward zero), ceiling (toward +infinity), floor (toward -infinity), unnecessary (any inexact result -> not_computable with details.reason "rounding_necessary").
- A result rounded to scale s is written with exactly s fraction digits (no fraction and no point when s is 0); a result with no scale is canonical: trailing fraction zeros are stripped and an integer has no point.
- remainder = dividend - value * divisor, exact and canonical (trailing fraction zeros stripped, "0" when zero). Its sign follows from the rounding direction: rounding up gives a negative remainder for a positive divisor.
- A zero divisor (including "0.00" and "-0") -> not_computable with details.reason "division_by_zero", even when the dividend is also zero. This is checked after all input validation.
- rounding "unnecessary" with an inexact quotient -> not_computable with details.reason "rounding_necessary".
- Validation order (each vector carries a single fault): input not an object; unknown field; missing required field; field types, ranges and decimal-string limits; scale/rounding pairing; then domain errors (not_computable) last.

## Input

- `dividend` (string, required): min length 1; max length 62; pattern `^-?(0|[1-9][0-9]*)(\.[0-9]+)?$`; Number being divided, decimal string.
- `divisor` (string, required): min length 1; max length 62; pattern `^-?(0|[1-9][0-9]*)(\.[0-9]+)?$`; Number to divide by, decimal string; must not be zero.
- `scale` (integer, required): min 0; max 40; Number of fraction digits in the quotient.
- `rounding` (one of "half_even", "half_up", "half_down", "half_ceiling", "half_floor", "up", "down", "ceiling", "floor", "unnecessary", required): Rounding mode applied to the exact quotient.

## Output

- `value` (string, required): min length 1; max length 200; Quotient rounded to scale, written with exactly scale fraction digits.
- `exact` (boolean, required): true when the rounded quotient equals the exact quotient.
- `remainder` (string, required): min length 1; max length 200; dividend - value * divisor as an exact canonical decimal; negative when the quotient was rounded up past the exact value.

## Limits

- max decimal chars: 62
- max decimal digits: 60
- max fraction digits: 40
- max scale: 40

## Example

Request input:

```json
{
  "dividend": "10",
  "divisor": "3",
  "scale": 2,
  "rounding": "half_even"
}
```

Response:

```json
{
  "result": {
    "value": "3.33",
    "exact": false,
    "remainder": "0.01"
  }
}
```

## How to call it

### MCP

Connect `https://computefirst.net/mcp` ([setup](/docs#connect)), then call `execute` with:

```json
{
  "id": "decimal-divide",
  "version": "1.0.0",
  "input": {
    "dividend": "10",
    "divisor": "3",
    "scale": 2,
    "rounding": "half_even"
  }
}
```

### HTTP (no key)

```sh
curl -X POST https://computefirst.net/v1/tools/decimal-divide/versions/1.0.0/execute \
  -H "Content-Type: application/json" \
  -d '{"dividend":"10","divisor":"3","scale":2,"rounding":"half_even"}'
```

The machine-readable contract is at [/v1/tools/decimal-divide/versions/1.0.0](/v1/tools/decimal-divide/versions/1.0.0).

### CLI

```sh
node cli.mjs run decimal-divide 1.0.0 --input input.json --base-url https://computefirst.net
```

Get the client at [/clients/cli/](/clients/cli/).

## Related tools

- [Decimal multiply](/tools/decimal-multiply): Multiply two decimal strings exactly, optionally rounding the product once to a fixed scale with a chosen mode.
- [Decimal expression evaluate](/tools/decimal-expression-evaluate): Evaluate a decimal arithmetic expression exactly with variables, abs, min, max and round, rounding once at the end.
- [Decimal power](/tools/decimal-power): Raise a decimal string to an integer power exactly, with optional single rounding to a fixed scale.
- [Vat net gross convert](/tools/vat-net-gross-convert): Convert a net or gross amount at a VAT rate into a net, VAT and gross triple that adds up exactly at currency precision.
- [Decimal root](/tools/decimal-root): Real nth root (2 to 100) of a decimal string, correctly rounded once to a fixed scale with an explicit mode.
- [Decimal sum](/tools/decimal-sum): Add up to 10,000 decimal strings exactly and report count, smallest and largest, with optional final rounding.