# Decimal

A **Decimal** in Internet Object represents fixed-precision decimal values designed for applications that require exact numeric calculations, especially financial computations where floating-point precision issues could lead to significant errors. Decimal is a scalar primitive that stores exact numeric values with a defined precision and scale.

Unlike standard floating-point numbers (which may suffer from approximation issues), Decimal values maintain exact precision throughout arithmetic operations, ensuring accurate and predictable results.

## Syntax

A Decimal value is expressed as a number with the `m` suffix:

```ebnf
decimal = decimalValue | scientificDecimal

decimalValue = ["-" | "+"] digit+ ["." digit+] "m"
scientificDecimal = decimalValue ("e" | "E") ["-" | "+"] digit+

digit = "0" | "1" | "2" | "3" | "4" | "5" | "6" | "7" | "8" | "9"
```

## Structural Characters

| Symbol  | Name           | Unicode  | Description                    |
| ------- | -------------- | -------- | ------------------------------ |
| `m`     | Decimal Suffix | `U+006D` | Identifies value as Decimal    |
| `0-9`   | Digits         | Multiple | Standard decimal digits        |
| `.`     | Decimal Point  | `U+002E` | Separates integer and fraction |
| `-`     | Minus Sign     | `U+002D` | Indicates negative numbers     |
| `e`/`E` | Exponent       | Multiple | Scientific notation exponent   |

## Valid Forms

### Basic Decimal Values

```ruby
123.45m              # Fractional decimal
123m                 # Integer decimal
0.001m               # Leading zeros
-789.01m             # Negative decimal
```

### Scientific Notation

```ruby
1.23e2m              # Equivalent to 123m
1.23e-2m             # Equivalent to 0.0123m
5e3m                 # Equivalent to 5000m
```

## Optional Behaviors

### Fixed-Precision Arithmetic

Decimal values maintain their precision throughout operations:

```ruby
0.1m + 0.2m          # 0.3m (exact representation)
# Compare with floating-point: 0.1 + 0.2 ≈ 0.30000000000000004
```

### Precision and Scale

Each Decimal value is defined by:

* **Precision**: Total number of significant digits
* **Scale**: Number of digits after the decimal point

```ruby
123.45m              # Precision: 5, Scale: 2
0.000123m            # Precision: 6, Scale: 6
```

### Empty Representation

Zero as a decimal:

```ruby
0m                   # Zero decimal
0.0m                 # Zero with scale
```

## Invalid Forms

```ruby
123.45               # ❌ Missing 'm' suffix (should be 123.45m)
123.45mm             # ❌ Multiple suffixes not allowed (should be 123.45m)
m123.45              # ❌ Suffix must be at the end (should be 123.45m)
.45m                 # ❌ Must have leading digit (should be 0.45m)
123.m                # ❌ Must have trailing digit if decimal point used (should be 123.0m or 123m)
```

## Preservation of Structure

Internet Object preserves:

* Exact decimal precision and scale
* The chosen representation form (standard vs scientific notation)
* Syntactic fidelity (as written, except that an explicit plus sign is not preserved)

However, it does **not** interpret:

* Rounding behavior for operations
* Domain-specific precision requirements
* Currency or unit semantics

Such semantics are the responsibility of the **schema layer**, **validators**, or **application logic**.

## See Also

* [Number Types Overview](/the-structure/values/number.md) - Launcher for all number types and formats
* [Number](/the-structure/values/number/number.md) - For standard floating-point numbers
* [BigInt](/the-structure/values/number/bigint.md) - For arbitrary-precision integers
* [Values](/the-structure/values.md)


---

# Agent Instructions: Querying This Documentation

If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question.

Perform an HTTP GET request on the current page URL with the `ask` query parameter:

```
GET https://docs.internetobject.org/the-structure/values/number/decimal.md?ask=<question>
```

The question should be specific, self-contained, and written in natural language.
The response will contain a direct answer to the question and relevant excerpts and sources from the documentation.

Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.