# Scientific Notation Converter

> Writes a number in normalised scientific notation m × 10^e with 1 ≤ |m| < 10, in E-notation, and in engineering notation (exponent a multiple of 3).

- Calculator id: `scientific-notation` · Category: Math (`math`) · Tool name: `convert_to_scientific_notation`
- Canonical page: https://tttkmbb.com/math/scientific-notation · This document: https://tttkmbb.com/math/scientific-notation.md · JSON definition: https://tttkmbb.com/math/scientific-notation.json

## Purpose

Writes a number in normalised scientific notation m × 10^e with 1 ≤ |m| < 10, in E-notation, and in engineering notation (exponent a multiple of 3).

**Use when:** You need a very large or very small number in scientific or engineering form, or its order of magnitude.

**Do not use when:** You want to round a number to a given precision (use rounding) or compute a power (use exponent).

## Input

| Parameter | Type | Unit | Required | Description |
| --- | --- | --- | --- | --- |
| `value` | number |  | required | Any number, e.g. 123400 or 0.000123. (min -1e+300, max 1e+300) |

## Output

| Field | Type | Unit | Description |
| --- | --- | --- | --- |
| `mantissa` | number |  | Significand with 1 ≤ \|m\| < 10 (0 for zero). |
| `exponent` | integer |  | Power of 10 such that value = m × 10^e; also the order of magnitude. |
| `scientific_notation` | string |  | e.g. '1.234 × 10^5'. |
| `e_notation` | string |  | Calculator/programming form, e.g. '1.234e5'. |
| `engineering_notation` | string |  | Exponent a multiple of 3 and mantissa between 1 and 999.999…, e.g. '123.4 × 10^3'. |
| `engineering_mantissa` | number |  | Mantissa of the engineering form. |
| `engineering_exponent` | integer |  | Exponent of the engineering form (…, −6, −3, 0, 3, 6, …). |

## Formula

`e = ⌊log10|value|⌋, m = value / 10^e; engineering: e₃ = 3·⌊e/3⌋, m₃ = value / 10^e₃`

The digits come from the shortest decimal representation that round-trips the input, so 0.000123 is reported as 1.23 × 10^-4 without floating-point noise.

## Data Sources

- Wikipedia – Scientific notation — https://en.wikipedia.org/wiki/Scientific_notation (reference, retrieved 2026-09-23)
- Wikipedia – Engineering notation — https://en.wikipedia.org/wiki/Engineering_notation (reference, retrieved 2026-09-23)
- Wolfram MathWorld – Scientific Notation — https://mathworld.wolfram.com/ScientificNotation.html (reference, retrieved 2026-09-23)

Data freshness: `static`. Deterministic formula with fixed constants; results never go stale. Inputs supplied by the caller determine the output.

## API

- `GET https://tttkmbb.com/api/v1/calculate/scientific-notation?value=…`
- `POST https://tttkmbb.com/api/v1/calculate/scientific-notation` with JSON body `{"inputs": {…}}`
- Response: unified envelope (`success`, `request`, `result.values`, `result.units`, `sources`, `freshness`, `timestamp`, `next_actions`, `links`); see https://tttkmbb.com/docs/response-format.md
- Schema: https://tttkmbb.com/api/v1/calculators/scientific-notation · OpenAPI operationId `convert_to_scientific_notation` in https://tttkmbb.com/openapi.json
- Authentication: none. Rate limit: fair use, see https://tttkmbb.com/docs/rate-limits.md.

## MCP

- Server: `https://tttkmbb.com/mcp` (Streamable HTTP, JSON-RPC 2.0, no auth)
- Tool:  `run_calculator` with `{"calculator_id": "scientific-notation", "inputs": {…}}`

## Example

- 123400: inputs `{"value":123400}` → `{"mantissa":1.234,"exponent":5,"scientific_notation":"1.234 × 10^5","e_notation":"1.234e5","engineering_notation":"123.4 × 10^3","engineering_mantissa":123.4,"engineering_exponent":3}`
- 0.000123: inputs `{"value":0.000123}` → `{"mantissa":1.23,"exponent":-4,"scientific_notation":"1.23 × 10^-4","e_notation":"1.23e-4","engineering_notation":"123 × 10^-6","engineering_mantissa":123,"engineering_exponent":-6}`

```
GET https://tttkmbb.com/api/v1/calculate/scientific-notation?value=123400
```

## Limitations

You want to round a number to a given precision (use rounding) or compute a power (use exponent). The digits come from the shortest decimal representation that round-trips the input, so 0.000123 is reported as 1.23 × 10^-4 without floating-point noise. All values are computed from the formula above; no measurement or live data is involved.

## FAQ

**What is the difference between scientific and engineering notation?**

Scientific notation keeps one digit before the decimal point; engineering notation uses exponents that are multiples of 3 so the number maps onto SI prefixes (10^3 = kilo, 10^-6 = micro).

**How many digits are kept?**

All significant digits of the input (up to 12 in the text forms); to shorten the mantissa, round the value first with the rounding calculator.

## Related

- [Rounding Calculator](https://tttkmbb.com/math/rounding.md) — Round to a number of significant figures before formatting.
- [Exponent Calculator](https://tttkmbb.com/math/exponent.md) — Evaluate powers of 10 and other bases.
- [Logarithm Calculator](https://tttkmbb.com/math/logarithm.md) — log10 gives the exponent directly.