# » Import: decimal

The decimal import provides functions for operating on numbers represented as decimals.

Binary floating-point numbers provided by the `float`

type are unable to
fully represent numbers like `1.1`

and `2.2`

. The decimal import can
represent these numbers exactly, and so should be used when exactness is
required.

Decimals are created through the `new`

function, which takes any type that
can represent a number. Arguments to the decimal operators can also take
a value of any of these types. The full list is:

- float
- int
- string
- existing decimal value

Decimals are represented internally by a sign, coefficient, and exponent.
The value is calculated with the formula `sign * coefficient * 10^exponent`

.
Exponent is limited to 32 bits, and the coefficient is limited by the total
precision.

The maximum precision a decimal can represent is 100 digits. This includes both before and after the decimal place.

### » decimal.infinity(sign)

Creates an infinite-value decimal. Infinite-value decimals are always larger or smaller, depending on sign, than any non-infinite decimals.

```
decimal.infinity(1) // +Infinity
decimal.infinity(-1) // -Infinity
```

Also available as `decimal.inf`

.

### » decimal.nan

A decimal representing a "not-a-number" value. NaNs are not equal to any other number, even themselves.

```
decimal.new(-1).sqrt() // NaN
decimal.new(0).mul(decimal.inf(1)) // NaN
decimal.nan.is(decimal.nan) // false
```

### » decimal.isinfinite(d)

Evaluates to true if the decimal is infinite.

```
decimal.isinfinite(100) // false
decimal.isinfinite("Infinity") // true
```

Also available as `decimal.isinf`

.

### » decimal.isnan(d)

Evaluates to true if the decimal is not-a-number.

```
decimal.isnan("NaN") // true
```

### » decimal.new(v)

Constructs a decimal from another value.

```
decimal.new("1.1") // Constructs a decimal from a string.
decimal.new(2.2) // Constructs a decimal from a float.
decimal.new(3) // Constructs a decimal from an integer.
decimal.new("1.1234E+400") // Constructs a decimal from a string using E-notation.
```

## » Type: number

### » number.string

A string representation of the decimal.

### » number.sign

A number between `-1`

and `+1`

representing the sign of the decimal.

### » number.coefficient

The coefficient component of the decimal.

### » number.exponent

The exponent component of the decimal.

### » number.float

A floating-point representation of the decimal.

### » number.int

An integer representation of the decimal. This always truncates the decimal to the nearest integer less than or equal to itself.

### » number.is(v)

Test for equality with another value.

### » number.is_not(v)

Test for inequality with another value.

### » number.less_than(v)

Test that the decimal is less than another value.
Can also be called as `number.lt(v)`

### » number.less_than_or_equals(v)

Test that the decimal is less than or equals to another value.
Can also be called as `number.lte(v)`

### » number.greater_than(v)

Test that the decimal is greater than another value.
Can also be called as `number.gt(v)`

### » number.greater_than_or_equals(v)

Test that the decimal is greater than or equals to another value.
Can also be called as `number.gte(v)`

### » number.add(v)

Add another number to the decimal.

### » number.subtract(v)

Subtract another number from the decimal.
Can also be called as `number.sub(v)`

### » number.multiply(v)

Multiply the decimal by a number.
Can also be called as `number.mul(v)`

### » number.divide(v)

Divide the decimal by a number.
Can also be called as `number.div(v)`

### » number.modulo(v)

Find the remainder after dividing the decimal by a number.
Can also be called as `mod`

, `remainder`

, or `rem`

.

### » number.power(v)

Raise the decimal to a power.
Can also be called as `number.pow(v)`

### » number.exp()

The natural exponent of the decimal. This calculates `e^number`

.

### » number.loge()

The natural logarithm of the decimal.
Can also be called as `number.ln()`

### » number.log10()

The base-10 logarithm of the decimal.
Can also be called as `number.log()`

### » number.square_root()

The square root of the decimal.
Can also be called as `number.sqrt()`

### » number.ceiling()

Round the decimal to the smallest integer greater or equal to itself.
Can also be called as `number.ceil()`

### » number.floor()

Round the decimal to the largest integer less than or equal to itself.

### » number.absolute()

The absolute value of the decimal.
Can also be called as `number.abs()`

### » number.negate()

The negated value of the decimal. A positive decimal will become negative,
and a negative decimal will become positive.
Can also be called as `number.neg()`