This section discusses precision math rounding for the
`ROUND()`

function and for inserts into
`DECIMAL`

columns.

The `ROUND()`

function rounds differently
depending on whether its argument is exact or approximate:

For exact-value numbers, `ROUND()`

uses the
“round half up” rule: A value with a fractional
part of .5 or greater is rounded up to the next integer if
positive or down to the next integer if negative. (In other
words, it is rounded away from zero.) A value with a
fractional part less than .5 is rounded down to the next
integer if positive or up to the next integer if negative.

For approximate-value numbers, the result depends on the C
library. On many systems, this means that
`ROUND()`

uses the “round to nearest
even” rule: A value with any fractional part is rounded
to the nearest even integer.

The following example shows how rounding differs for exact and
approximate values:

mysql> `SELECT ROUND(2.5), ROUND(25E-1);`

+------------+--------------+
| ROUND(2.5) | ROUND(25E-1) |
+------------+--------------+
| 3 | 2 |
+------------+--------------+

For inserts into a `DECIMAL`

column, the target
is an exact data type, so rounding uses "round half up,"
regardless of whether the value to be inserted is exact or
approximate:

mysql> `CREATE TABLE t (d DECIMAL(10,0));`

Query OK, 0 rows affected (0.00 sec)
mysql> `INSERT INTO t VALUES(2.5),(2.5E0);`

Query OK, 2 rows affected, 2 warnings (0.00 sec)
Records: 2 Duplicates: 0 Warnings: 2
mysql> `SELECT d FROM t;`

+------+
| d |
+------+
| 3 |
| 3 |
+------+