diff --git a/src/backend/utils/adt/numeric.c b/src/backend/utils/adt/numeric.c
index eb78f0b9c2..d74001c311 100644
--- a/src/backend/utils/adt/numeric.c
+++ b/src/backend/utils/adt/numeric.c
@@ -233,6 +233,7 @@ struct NumericData
  */
 
 #define NUMERIC_DSCALE_MASK			0x3FFF
+#define NUMERIC_DSCALE_MAX			NUMERIC_DSCALE_MASK
 
 #define NUMERIC_SIGN(n) \
 	(NUMERIC_IS_SHORT(n) ? \
@@ -2955,7 +2956,11 @@ numeric_mul_opt_error(Numeric num1, Numeric num2, bool *have_error)
 	 * Unlike add_var() and sub_var(), mul_var() will round its result. In the
 	 * case of numeric_mul(), which is invoked for the * operator on numerics,
 	 * we request exact representation for the product (rscale = sum(dscale of
-	 * arg1, dscale of arg2)).
+	 * arg1, dscale of arg2)).  If the exact result has more digits after the
+	 * decimal point than can be stored in a numeric, we round it.  Rounding
+	 * after computing the exact result ensures that the final result is
+	 * correctly rounded (rounding in mul_var() using a truncated product
+	 * would not guarantee this).
 	 */
 	init_var_from_num(num1, &arg1);
 	init_var_from_num(num2, &arg2);
@@ -2963,6 +2968,9 @@ numeric_mul_opt_error(Numeric num1, Numeric num2, bool *have_error)
 	init_var(&result);
 	mul_var(&arg1, &arg2, &result, arg1.dscale + arg2.dscale);
 
+	if (result.dscale > NUMERIC_DSCALE_MAX)
+		round_var(&result, NUMERIC_DSCALE_MAX);
+
 	res = make_result_opt_error(&result, have_error);
 
 	free_var(&result);
diff --git a/src/test/regress/expected/numeric.out b/src/test/regress/expected/numeric.out
index 30a5642b95..e0bc6d9116 100644
--- a/src/test/regress/expected/numeric.out
+++ b/src/test/regress/expected/numeric.out
@@ -2145,6 +2145,12 @@ select 4769999999999999999999999999999999999999999999999999999999999999999999999
  47699999999999999999999999999999999999999999999999999999999999999999999999999999999999985230000000000000000000000000000000000000000000000000000000000000000000000000000000000001
 (1 row)
 
+select trim_scale((0.1 - 2e-16383) * (0.1 - 3e-16383));
+ trim_scale 
+------------
+       0.01
+(1 row)
+
 --
 -- Test some corner cases for division
 --
diff --git a/src/test/regress/sql/numeric.sql b/src/test/regress/sql/numeric.sql
index db812c813a..2e7507639a 100644
--- a/src/test/regress/sql/numeric.sql
+++ b/src/test/regress/sql/numeric.sql
@@ -1044,6 +1044,8 @@ select 4770999999999999999999999999999999999999999999999999999999999999999999999
 
 select 4769999999999999999999999999999999999999999999999999999999999999999999999999999999999999 * 9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999;
 
+select trim_scale((0.1 - 2e-16383) * (0.1 - 3e-16383));
+
 --
 -- Test some corner cases for division
 --