Rounding Behavior Suppose that we have this statement: This is what happens for combinations of strict and  ERROR_FOR_DIVISION_BY_ZERO  modes. 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: The following example shows how rounding differs for exact and approximate values: 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: 2458 •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. •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.) 12.25.4 Rounding Behavior INSERT INTO t SET i = 1/0; mysql>  SELECT ROUND(2.5), ROUND(25E-1); 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>  SHOW WARNINGS; sql_mode  Value Result ’’  (Default) No warning, no error;  i  is set to  NULL . strict No warning, no error;  i  is set to  NULL . ERROR_FOR_DIVISION_BY_ZERO Warning, no error;  i  is set to  NULL . strict, ERROR_FOR_DIVISION_BY_ZERO Error condition; no row is inserted. +------------+--------------+ | ROUND(2.5) | ROUND(25E-1) | +------------+--------------+ | 3 | 2 | +------------+--------------+ +-------+------+----------------------------------------+ | 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>  SELECT d FROM t; +------+ | d |