diff --git a/lib/quantity.rb b/lib/quantity.rb
index 2b416da..3fbfabf 100644
--- a/lib/quantity.rb
+++ b/lib/quantity.rb
@@ -73,12 +73,12 @@ def initialize(value, unit = nil )
         @reference_value = value[:reference_value] || (value[:value] * @unit.value)
         @value = @unit.value_for(@reference_value) #dimension.reference.convert_proc(@unit).call(@reference_value)
         #@value = @unit.convert_proc(@unit).call(@reference_value)
-      when Numeric
+      when Numeric, String
         @unit = Unit.for(unit)
         if @unit.nil?
           @unit = Unit.from_string_form(unit)
         end
-        @value = value
+        @value = value.is_a?(Numeric) ? value : value.to_f
         @reference_value = value * @unit.value 
     end
   end
@@ -133,10 +133,10 @@ def coerce(other)
   def +(other)
     if (other.is_a?(Numeric))
       Quantity.new(@value + other, @unit)
-    elsif(other.is_a?(Quantity) && @unit.dimension == other.unit.dimension)
+    elsif compatible_with?(other)
       Quantity.new({:unit => @unit,:reference_value => @reference_value + other.reference_value})
     else
-      raise ArgumentError,"Cannot add #{self} to #{other}"
+      raise ArgumentError,"Cannot add #{self} (#{@unit.dimension}) to #{other} (#{other.class}" + (other.is_a?(Quantity) ? "-#{other.unit.dimension})" : ')')
     end
   end
 
@@ -147,10 +147,10 @@ def +(other)
   def -(other)
     if (other.is_a?(Numeric))
       Quantity.new(@value - other, @unit)
-    elsif(other.is_a?(Quantity) && @unit.dimension == other.unit.dimension)
+    elsif compatible_with?(other)
       Quantity.new({:unit => @unit,:reference_value => @reference_value - other.reference_value})
     else
-      raise ArgumentError, "Cannot subtract #{other} from #{self}"
+      raise ArgumentError, "Cannot subtract #{other} (#{other.class}) from #{self} (#{@unit.dimension})"
     end
   end
 
@@ -161,7 +161,7 @@ def -(other)
   def <=>(other)
     if (other.is_a?(Numeric))
       @value <=> other
-    elsif(other.is_a?(Quantity) && measures == other.measures)
+    elsif compatible_with?(other)
       @reference_value <=> other.reference_value
     else
       nil
@@ -279,6 +279,11 @@ def to_f
     @value.to_f
   end
 
+  def compatible_with?(other)
+    return false if unit.nil?
+    other.respond_to?(:unit) && unit.compatible_with?(other.unit)
+  end
+
   # Round this value to the nearest integer
   # @return [Quantity]
   def round
diff --git a/lib/quantity/dimension.rb b/lib/quantity/dimension.rb
index 325c20b..d7d64fc 100644
--- a/lib/quantity/dimension.rb
+++ b/lib/quantity/dimension.rb
@@ -178,6 +178,12 @@ def <=>(other)
       end
     end
 
+
+    def compatible_with?(other)
+      self === other || (other.respond_to?(:name) && name == other.name)
+    end
+
+
     # Returns a developer-friendly representation of this value.
     #
     # The string will be of the format `#<Quantity::Dimension::0x12345678(...)>`,
diff --git a/lib/quantity/unit.rb b/lib/quantity/unit.rb
index 0f060c6..7994f3a 100644
--- a/lib/quantity/unit.rb
+++ b/lib/quantity/unit.rb
@@ -294,7 +294,7 @@ def calculate_value
       @dimension.numerators.each do | component |
         component.power.times do 
           # we might have a unit for a compound dimension, such as liters for length^3.
-          value *= @units[Quantity::Dimension.for(component.dimension)].value
+          value *= @units[Quantity::Dimension.for(component.dimension)].value if @units[Quantity::Dimension.for(component.dimension)]
         end
       end
       @dimension.denominators.each do | component |
@@ -305,6 +305,12 @@ def calculate_value
       @value = value
     end
 
+
+    def compatible_with?(other)
+      other.respond_to?(:dimension) && dimension.compatible_with?(other.dimension)
+    end
+
+
     # A vaguely human-readable form for this unit
     # @return [String]
     def string_form