# Numbers

A **number** in Lua is a double precision floating point number (or just **double**). For instance:

* 5
* 9.12761656
* -1927

In Lua, numbers can range from -1.7 × 10308 to 1.7 × 10308 (around 15 digits, positive or negative).

### Signed and Unsigned <a href="#signed-and-unsigned" id="signed-and-unsigned"></a>

The sign of the number indicates whether it’s positive or negative. A signed number can be positive or negative, but an unsigned number cannot be negative. In Lua, `-0` is distinct from `0`.

### Notation <a href="#notation" id="notation"></a>

Numbers are notated with the most significant digits first (big-endian). There are multiple ways to notate number literals in Lua:

* [Decimal (base-10)](https://en.wikipedia.org/wiki/Decimal) — Write the digits of the number normally using digits 0–9 with a single optional decimal point, for example `7`, `1.25`, or `-22.5`.
* [Scientific notation](https://en.wikipedia.org/wiki/Scientific_notation) — Write a decimal number followed by `e` or `e+`, then an integer to raise the decimal number to a power of 10. For instance, `12e3` is 12 × 10^3 (12,000).
* [Hexadecimal (base-16)](https://en.wikipedia.org/wiki/Hexadecimal) — Begin the number with `0x` followed by digits 0–9 or A–F (capitalization ignored). For example, `0xF` is 15 and `0x3FC` is 1020.
* [Binary (base-2)](https://en.wikipedia.org/wiki/Binary_number) — Begin the number with `0b` followed by 0s or 1s, for instance `0b1100` (12 in decimal format).

{% hint style="info" %}
To aid in the readability of long numbers, underscores can be included anywhere within a number literal without changing the value, **except** at the beginning (in which case it would become an identifier). For example, `1_234_567` is the same as `1234567`, both of which are equal to 1,234,567.
{% endhint %}

### Operations <a href="#operations" id="operations"></a>

Lua math and relational [operators](https://developers.brickverse.gg/bricklua-coding-with-lua/learn-lua/opeartors) can be used on numbers to manipulate and compare them. Mathematical functions such as `math.sqrt()` and `math.exp()` can be found in the [math](https://developers.brickverse.gg/game-api/api/math) library and, for bitwise operations, the [bit32](https://developers.brickverse.gg/bricklua-coding-with-lua/learn-lua/bit32) library has been back-ported.

### Number Classifications <a href="#number-classifications" id="number-classifications"></a>

In BrickLua, there is no technical difference between the following types of numbers. However, number classifications are used in documentation to indicate which kind of number is involved with an API member.

#### int <a href="#int" id="int"></a>

The `int` number type refers to a number without a fractional portion (integer) like 0, 60, or -42. Properties and functions that expect integers may automatically round or raise errors when provided with non-integers.

When working with integers in Lua, note the following:

* The fractional portion of a number can be trimmed by rounding down with `math.floor()`.
* You can determine if a number is an integer by comparing `math.floor(x) == x`.
* To [round](https://en.wikipedia.org/wiki/Rounding#Rounding_to_the_nearest_integer) a number to the nearest integer (half up), use `math.floor(x + 0.5)`.

#### int64 <a href="#int64" id="int64"></a>

The `int64` number type refers to a signed 64-bit integer, a signed 64-bit integer is expected (-263 to 263 - 1).

#### float <a href="#float" id="float"></a>

The `float` number type refers to a [single-precision (32-bit) floating point number](https://en.wikipedia.org/wiki/Single-precision_floating-point_format). This type isn’t as precise as normal numbers, but the difference typically won’t matter.


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