diff --git a/CHANGELOG.md b/CHANGELOG.md
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -1,3 +1,7 @@
+1.0.1.3 (2016-09)
+-----------------
+* Fixed an issue with applying metric prefixes to units with non-rational conversion factors.
+
 1.0.1.2 (2016-05)
 -----------------
 * Support for GHC 8.0.1-rc4, avoiding GHC Trac issue 12026.
diff --git a/dimensional.cabal b/dimensional.cabal
--- a/dimensional.cabal
+++ b/dimensional.cabal
@@ -1,5 +1,5 @@
 name:                dimensional
-version:             1.0.1.2
+version:             1.0.1.3
 license:             BSD3
 license-file:        LICENSE
 copyright:           Bjorn Buckwalter 2006-2015
diff --git a/src/Numeric/Units/Dimensional.hs b/src/Numeric/Units/Dimensional.hs
--- a/src/Numeric/Units/Dimensional.hs
+++ b/src/Numeric/Units/Dimensional.hs
@@ -665,8 +665,11 @@
 -- Supplying negative defining quantities is allowed and handled gracefully, but is discouraged
 -- on the grounds that it may be unexpected by other readers.
 mkUnitR :: Floating a => UnitName m -> ExactPi -> Unit m1 d a -> Unit m d a
-mkUnitR n s' (Unit _ s x) | isExactZero s = error "Supplying zero as a conversion factor is not valid."
-                          | otherwise     = Unit n (s' Prelude.* s) (approximateValue s' Prelude.* x)
+mkUnitR n s (Unit _ e _) | isExactZero s = error "Supplying zero as a conversion factor is not valid."
+                         | otherwise     = Unit n e' x'
+  where
+    e' = s Prelude.* e
+    x' = approximateValue e'
 
 -- | Forms a new atomic 'Unit' by specifying its 'UnitName' and its definition as a multiple of another 'Unit'.
 --
@@ -675,11 +678,12 @@
 --
 -- For more information see 'mkUnitR'.
 mkUnitQ :: Fractional a => UnitName m -> Rational -> Unit m1 d a -> Unit m d a
-mkUnitQ n s' (Unit _ s _) | s' == 0                       = error "Supplying zero as a conversion factor is not valid."
-                          | Just q <- toExactRational s'' = Unit n s'' (fromRational q)
-                          | otherwise                     = error "The resulting conversion factor is not an exact rational." 
+mkUnitQ n s (Unit _ e x) | s == 0    = error "Supplying zero as a conversion factor is not valid."
+                         | Just x'' <- toExactRational e' = Unit n e' (fromRational x'')
+                         | otherwise = Unit n e' x'
   where
-    s'' = fromRational s' Prelude.* s                               
+    e' = fromRational s Prelude.* e
+    x' = fromRational s Prelude.* x
 
 -- | Forms a new atomic 'Unit' by specifying its 'UnitName' and its definition as a multiple of another 'Unit'.
 --
@@ -688,8 +692,9 @@
 --
 -- For more information see 'mkUnitR'.
 mkUnitZ :: Num a => UnitName m -> Integer -> Unit m1 d a -> Unit m d a
-mkUnitZ n s' (Unit _ s _) | s' == 0                      = error "Supplying zero as a conversion factor is not valid."
-                          | Just z <- toExactInteger s'' = Unit n s'' (fromInteger z)
-                          | otherwise                    = error "The resulting conversion factor is not an exact integer."
+mkUnitZ n s (Unit _ e x) | s == 0    = error "Supplying zero as a conversion factor is not valid."
+                         | Just x'' <- toExactInteger e' = Unit n e' (fromInteger x'')
+                         | otherwise = Unit n e' x'
   where
-    s'' = fromInteger s' Prelude.* s
+    e' = fromInteger s Prelude.* e
+    x' = fromInteger s Prelude.* x