# rationalize

rationalize([Type=Int,] x; tol=eps(x))

Approximate floating point number `x` as a Rational number with components of the given integer type. The result will differ from `x` by no more than `tol`.

## Examples

In the Julia programming language, the `rationalize()` function is used to approximate a floating-point number `x` as a rational number with components of the given integer type. The resulting rational number will have a difference from `x` of no more than the specified tolerance `tol`.

``````julia> rationalize(1.5)
3//2

julia> rationalize(0.3333, tol=1e-4)
3333//10000

julia> rationalize(0.987654321, tol=1e-8)
987654321//1000000000``````

Common examples of its use:

1. Rationalize a floating-point number:

``````julia> rationalize(2.75)
11//4``````

This example approximates the floating-point number `2.75` as a rational number.

2. Specify the type of the resulting rational number:

``````julia> rationalize(Float64, 0.5)
1//2``````

The `rationalize` function can optionally take a type parameter to specify the type of the resulting rational number. Here, we specify `Float64` as the type.

3. Control the tolerance for approximation:
``````julia> rationalize(0.333333333, tol=1e-6)
1//3``````

By default, the tolerance `tol` is set to `eps(x)`, which is the machine epsilon for the type of `x`. You can also provide a custom tolerance to control the precision of the rational approximation.

Common mistake example:

``````julia> rationalize(1.23, tol=0)
ERROR: DomainError: Cannot rationalize number within zero tolerance``````

In this example, a tolerance of zero is provided, which results in a `DomainError`. Make sure to provide a non-zero tolerance value to avoid this error.