Without Converting to a String, How Many Digits Does a Fixnum Have?

I want find the length of a Fixnum, num, without converting it into a String.

In other words, how many digits are in num without calling the .to_s() method:

num.to_s.length

puts Math.log10(1234).to_i + 1 # => 4

You could add it to Fixnum like this:

class Fixnum
  def num_digits
    Math.log10(self).to_i + 1
  end
end

puts 1234.num_digits # => 4