Roman numeral kata in Elixir
Your code looks very nice indeed, I only have some minor observations you code use to improve this code:

Naming
Use the imperative form of the verb (convert instead of converts)

Implementation Hiding
Use defp for methods which are not intended for external use. You might consider also renaming them to start with underscore _ to further differentiate them as internal.

Multiple assignment in method signature
To make you code more succinct, you can use multiple assignment - meaning that instead of:

def converts(number, roman_value, [[decimal, roman] | numerals]) when number &gt;= decimal do
  converts(number - decimal, roman_value ++ roman, [[decimal, roman] | numerals])
end


you can write:

def converts(number, roman_value, [[decimal, roman] | _] = numerals) 
  when number &gt;= decimal do
  converts(number - decimal, roman_value ++ roman, numerals)
end


to the same effect. This form assigns the first item in the list to [decimal, roman], as well as assigning the whole list (including the first element) to numerals, so you don't have to re-build it inside the method body.



Implementing the above suggestions, your code will look like this:

defmodule RomanNumeral do

  @decimal_roman_numerals [[5, 'V'], [4, 'IV'], [1, 'I']]

  def convert(number) do
    _convert(number, [], @decimal_roman_numerals)
  end

  defp _convert(number, roman_value, _) when number &lt; 1 do
    roman_value
  end

  defp _convert(number, roman_value, [[decimal, roman] | _] = numerals) 
    when number &gt;= decimal do
    _convert(number - decimal, roman_value ++ roman, numerals)
  end

  defp _convert(number, roman_value, [_ | numerals]) do
    _convert(number, roman_value, numerals)
  end
end