# Number engineering format

`number-engineering-format` · version 1.0.0 · Numbers & math · free, no key needed

Format an exact decimal in scientific or engineering notation with explicit precision and rounding.

**Use when you need to: format an exact decimal in engineering notation · format a number in scientific notation · round a decimal to significant digits for engineering display.**

## Decide before calling

Read the [versioned contract](/v1/tools/number-engineering-format/versions/1.0.0) and the supported scope below. Reuse `number-engineering-format@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 `number-engineering-format@1.0.0` for format an exact decimal in engineering notation. 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

- format an exact decimal in engineering notation
- format a number in scientific notation
- round a decimal to significant digits for engineering display
- convert decimal text to normalized exponent notation
- show an SI prefix for an engineering exponent
- format extreme decimal exponents without floating point
- עיצוב מספר בכתיב הנדסי

## Not supported

- locale-aware number formatting or digit grouping
- unit conversion or dimensional analysis
- parsing non-decimal numeric bases

## Behavior

- Decimal input is parsed from text and all significand arithmetic uses strings and BigInt; binary floating point never represents the decimal value.
- Scientific notation has one coefficient digit before the point; engineering notation has one to three and an exponent divisible by three.
- The coefficient contains exactly significant_digits significant digits, including trailing zeros; zero is unsigned with exponent zero.
- half_even breaks exact ties toward an even final retained digit; half_up breaks ties away from zero; directed modes follow their named direction.
- include_si_prefix defaults to false. A prefix is returned only for engineering notation and a nonzero exponent with one NIST SI prefix symbol from -30 through 30.
- Canonical rendered notation is coefficient followed by lowercase e and an exponent with no plus sign or leading zeros.

## Input

- `value` (string, required): min length 1; max length 1024; pattern `^[+-]?(?:(?:[0-9]+)(?:\.[0-9]+)?|\.[0-9]+)(?:[eE][+-]?[0-9]+)?$`; Exact decimal text, optionally with a base-ten exponent.
- `notation` (one of "scientific", "engineering", required): Normalized scientific or engineering notation.
- `significant_digits` (integer, required): min 1; max 100; Exact count of significant digits in the coefficient.
- `rounding_mode` (one of "half_even", "half_up", "toward_zero", "away_from_zero", "floor", "ceiling", required): Explicit rule used when discarded digits are nonzero.
- `include_si_prefix` (boolean, optional): Request an SI prefix when the engineering exponent has one unambiguous symbol.

## Output

- `coefficient` (string, required): min length 1; max length 102; pattern `^-?(?:0|[1-9][0-9]{0,2})(?:\.[0-9]+)?$`; Normalized coefficient with exactly the requested significant digits.
- `exponent` (integer, required): min -1000000; max 1000000; Base-ten exponent.
- `rendered` (string, required): min length 3; max length 112; pattern `^-?(?:0|[1-9][0-9]{0,2})(?:\.[0-9]+)?e-?[0-9]+$`; Canonical coefficient followed by e and the base-ten exponent.
- `si_prefix` (one of "q", "r", "y", "z", "a", "f", "p", "n", "µ", "m", "k", "M", "G", "T", "P", "E", "Z", "Y", "R", "Q", optional): Unambiguous SI prefix symbol for a nonzero engineering exponent.

## Limits

- max input bytes: 1024
- max significant digits: 100
- max abs exponent: 1000000

## Example

Request input:

```json
{
  "value": "12345",
  "notation": "engineering",
  "significant_digits": 4,
  "rounding_mode": "half_even",
  "include_si_prefix": true
}
```

Response:

```json
{
  "result": {
    "coefficient": "12.34",
    "exponent": 3,
    "rendered": "12.34e3",
    "si_prefix": "k"
  }
}
```

## How to call it

### MCP

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

```json
{
  "id": "number-engineering-format",
  "version": "1.0.0",
  "input": {
    "value": "12345",
    "notation": "engineering",
    "significant_digits": 4,
    "rounding_mode": "half_even",
    "include_si_prefix": true
  }
}
```

### HTTP (no key)

```sh
curl -X POST https://computefirst.net/v1/tools/number-engineering-format/versions/1.0.0/execute \
  -H "Content-Type: application/json" \
  -d '{"value":"12345","notation":"engineering","significant_digits":4,"rounding_mode":"half_even","include_si_prefix":true}'
```

The machine-readable contract is at [/v1/tools/number-engineering-format/versions/1.0.0](/v1/tools/number-engineering-format/versions/1.0.0).

### CLI

```sh
node cli.mjs run number-engineering-format 1.0.0 --input input.json --base-url https://computefirst.net
```

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

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