MySQL 5.7 Reference Manual Including MySQL NDB Cluster 7.5 and NDB Cluster 7.6

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

function and for inserts
into columns with exact-value types
(`DECIMAL`

and integer).

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. (In other words, it is rounded toward zero.)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 a fractional part exactly half way between two integers is rounded to the nearest even integer.

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

mysql>+------------+--------------+ | ROUND(2.5) | ROUND(25E-1) | +------------+--------------+ | 3 | 2 | +------------+--------------+`SELECT ROUND(2.5), ROUND(25E-1);`

For inserts into a `DECIMAL`

or
integer column, the target is an exact data type, so rounding uses
“round half away from zero,” regardless of whether
the value to be inserted is exact or approximate:

mysql>Query OK, 0 rows affected (0.00 sec) mysql>`CREATE TABLE t (d DECIMAL(10,0));`

Query OK, 2 rows affected, 2 warnings (0.00 sec) Records: 2 Duplicates: 0 Warnings: 2 mysql>`INSERT INTO t VALUES(2.5),(2.5E0);`

+-------+------+----------------------------------------+ | Level | Code | Message | +-------+------+----------------------------------------+ | Note | 1265 | Data truncated for column 'd' at row 1 | | Note | 1265 | Data truncated for column 'd' at row 2 | +-------+------+----------------------------------------+ 2 rows in set (0.00 sec) mysql>`SHOW WARNINGS;`

+------+ | d | +------+ | 3 | | 3 | +------+ 2 rows in set (0.00 sec)`SELECT d FROM t;`

The `SHOW WARNINGS`

statement
displays the notes that are generated by truncation due to
rounding of the fractional part. Such truncation is not an error,
even in strict SQL mode (see
Section 12.22.3, “Expression Handling”).