This section provides some examples that show precision math query results in MySQL. These examples demonstrate the principles described in Section 12.24.3, “Expression Handling” , and Section 12.24.4, “Rounding Behavior” . Example 1 . Numbers are used with their exact value as given when possible:

mysql> SELECT (.1 + .2) = .3;
+----------------+
| (.1 + .2) = .3 |
+----------------+
|              1 |
+----------------+

For floating-point values, results are inexact:

mysql> SELECT (.1E0 + .2E0) = .3E0;
+----------------------+
| (.1E0 + .2E0) = .3E0 |
+----------------------+
|                    0 |
+----------------------+

Another way to see the difference in exact and approximate value handling is to add a small number to a sum many times. Consider the following stored procedure, which adds .0001 to a variable 1,000 times.

CREATE PROCEDURE p ()
BEGIN
  DECLARE i INT DEFAULT 0;
  DECLARE d DECIMAL(10,4) DEFAULT 0;
  DECLARE f FLOAT DEFAULT 0;
  WHILE i < 10000 DO
    SET d = d + .0001;
    SET f = f + .0001E0;
    SET i = i + 1;
  END WHILE;
  SELECT d, f;
      The sum for both d and f
      logically should be 1, but that is true only for the decimal
      calculation. The floating-point calculation introduces small
      errors:
    
+--------+------------------+
| d      | f                |
+--------+------------------+
| 1.0000 | 0.99999999999991 |
+--------+------------------+

      Example 2. Multiplication is
      performed with the scale required by standard SQL. That is, for
      two numbers X1 and
      X2 that have scale
      S1 and S2,
      the scale of the result is S1
      + S2:
    
mysql> SELECT .01 * .01;
+-----------+
| .01 * .01 |
+-----------+
| 0.0001    |
+-----------+

      Example 3. Rounding behavior for
      exact-value numbers is well-defined:
      Rounding behavior (for example, with the
      ROUND() function) is independent of
      the implementation of the underlying C library, which means that
      results are consistent from platform to platform.
          Rounding for exact-value columns
          (DECIMAL and integer) and
          exact-valued numbers uses the “round half away from
          zero” rule. A value with a fractional part of .5 or
          greater is rounded away from zero to the nearest integer, as
          shown here:
        
mysql> SELECT ROUND(2.5), ROUND(-2.5);
+------------+-------------+
| ROUND(2.5) | ROUND(-2.5) |
+------------+-------------+
| 3          | -3          |
+------------+-------------+

          Rounding for floating-point values uses the C library, which
          on many systems 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:
        
mysql> SELECT ROUND(2.5E0), ROUND(-2.5E0);
+--------------+---------------+
| ROUND(2.5E0) | ROUND(-2.5E0) |
+--------------+---------------+
|            2 |            -2 |
+--------------+---------------+
      Example 4. In strict mode,
      inserting a value that is out of range for a column causes an
      error, rather than truncation to a legal value.
      When MySQL is not running in strict mode, truncation to a legal
      value occurs:
    
mysql> SET sql_mode='';
Query OK, 0 rows affected (0.00 sec)
mysql> CREATE TABLE t (i TINYINT);
Query OK, 0 rows affected (0.01 sec)
mysql> INSERT INTO t SET i = 128;
Query OK, 1 row affected, 1 warning (0.00 sec)
mysql> SELECT i FROM t;
+------+
| i    |
+------+
|  127 |
+------+
1 row in set (0.00 sec)

      However, an error occurs if strict mode is in effect:
    
mysql> SET sql_mode='STRICT_ALL_TABLES';
Query OK, 0 rows affected (0.00 sec)
mysql> CREATE TABLE t (i TINYINT);
Query OK, 0 rows affected (0.00 sec)
mysql> INSERT INTO t SET i = 128;
ERROR 1264 (22003): Out of range value adjusted for column 'i' at row 1
mysql> SELECT i FROM t;
Empty set (0.00 sec)

      Example 5: In strict mode and
      with ERROR_FOR_DIVISION_BY_ZERO
      set, division by zero causes an error, not a result of
      NULL.
      In nonstrict mode, division by zero has a result of
      NULL:
    
mysql> SET sql_mode='';
Query OK, 0 rows affected (0.01 sec)
mysql> CREATE TABLE t (i TINYINT);
Query OK, 0 rows affected (0.00 sec)
mysql> INSERT INTO t SET i = 1 / 0;
Query OK, 1 row affected (0.00 sec)
mysql> SELECT i FROM t;
+------+
| i    |
+------+
| NULL |
+------+
1 row in set (0.03 sec)

      However, division by zero is an error if the proper SQL modes are
      in effect:
    
mysql> SET sql_mode='STRICT_ALL_TABLES,ERROR_FOR_DIVISION_BY_ZERO';
Query OK, 0 rows affected (0.00 sec)
mysql> CREATE TABLE t (i TINYINT);
Query OK, 0 rows affected (0.00 sec)
mysql> INSERT INTO t SET i = 1 / 0;
ERROR 1365 (22012): Division by 0
mysql> SELECT i FROM t;
Empty set (0.01 sec)

      Example 6. Exact-value literals
      are evaluated as exact values.
      Approximate-value literals are evaluated using floating point, but
      exact-value literals are handled as
      DECIMAL:
    
mysql> CREATE TABLE t SELECT 2.5 AS a, 25E-1 AS b;
Query OK, 1 row affected (0.01 sec)
Records: 1  Duplicates: 0  Warnings: 0
mysql> DESCRIBE t;
+-------+-----------------------+------+-----+---------+-------+
| Field | Type                  | Null | Key | Default | Extra |
+-------+-----------------------+------+-----+---------+-------+
| a     | decimal(2,1) unsigned | NO   |     | 0.0     |       |
| b     | double                | NO   |     | 0       |       |
+-------+-----------------------+------+-----+---------+-------+
2 rows in set (0.01 sec)

      Example 7. If the argument to an
      aggregate function is an exact numeric type, the result is also an
      exact numeric type, with a scale at least that of the argument.
      Consider these statements:
    
mysql> CREATE TABLE t (i INT, d DECIMAL, f FLOAT);
mysql> INSERT INTO t VALUES(1,1,1);
mysql> CREATE TABLE y SELECT AVG(i), AVG(d), AVG(f) FROM t;

      The result is a double only for the floating-point argument. For
      exact type arguments, the result is also an exact type:
    
mysql> DESCRIBE y;
+--------+---------------+------+-----+---------+-------+
| Field  | Type          | Null | Key | Default | Extra |
+--------+---------------+------+-----+---------+-------+
| AVG(i) | decimal(14,4) | YES  |     | NULL    |       |
| AVG(d) | decimal(14,4) | YES  |     | NULL    |       |
| AVG(f) | double        | YES  |     | NULL    |       |
+--------+---------------+------+-----+---------+-------+

      The result is a double only for the floating-point argument. For
      exact type arguments, the result is also an exact type.