class Float
  def number_decimal_places
    self.to_s.length-2
  end
  
  def to_fraction
    higher = 10**self.number_decimal_places
    lower = self*higher

    gcden = greatest_common_divisor(higher, lower)

    return (lower/gcden).round, (higher/gcden).round
  end
  
private

  def greatest_common_divisor(a, b)
     while a%b != 0
       a,b = b.round,(a%b).round
     end 
     return b
  end
end

>>> farey(math.pi,100)
(22, 7)