使用精确数学时，尽可能使用给定的精确数值。例如，在比较中使用的数字会按给定的值精确使用，不会改变数值。在严格 SQL 模式下，对于具有精确数据类型（DECIMAL 或整数）的列进行 INSERT 操作时，如果数字在列的范围内，则会以其精确值插入。检索时，值应与插入时相同。（如果未启用严格 SQL 模式，则允许对 INSERT 进行截断。）With precision math, exact-value numbers are used as given whenever possible. For example, numbers in comparisons are used exactly as given without a change in value. In strict SQL mode, for INSERT into a column with an exact data type (DECIMAL or integer), a number is inserted with its exact value if it is within the column range. When retrieved, the value should be the same as what was inserted. (If strict SQL mode is not enabled, truncation for INSERT is permissible.)

数值表达式的处理取决于表达式包含的值类型：Handling of a numeric expression depends on what kind of values the expression contains:

如果数值表达式包含任何字符串，它们会被转换为双精度浮点值，并且该表达式是近似的。If a numeric expression contains any strings, they are converted to double-precision floating-point values and the expression is approximate.

插入到数字列受 SQL 模式的影响，该模式由 sql_mode 系统变量控制。（参见 第 7.1.11 节，“服务器 SQL 模式”。）以下讨论提到严格模式（由 STRICT_ALL_TABLES 或 STRICT_TRANS_TABLES 模式值选择）以及 ERROR_FOR_DIVISION_BY_ZERO。要启用所有限制，您可以简单使用 TRADITIONAL 模式，其中包括严格模式值和 ERROR_FOR_DIVISION_BY_ZERO：Inserts into numeric columns are affected by the SQL mode, which is controlled by the sql_mode system variable. (See Section 7.1.11, “Server SQL Modes”.) The following discussion mentions strict mode (selected by the STRICT_ALL_TABLES or STRICT_TRANS_TABLES mode values) and ERROR_FOR_DIVISION_BY_ZERO. To turn on all restrictions, you can simply use TRADITIONAL mode, which includes both strict mode values and ERROR_FOR_DIVISION_BY_ZERO:

SET sql_mode='TRADITIONAL';

如果一个数字被插入到精确类型列（DECIMAL 或整数）中，并且该数字在列的范围和精度之内，则会以其精确值插入。If a number is inserted into an exact type column (DECIMAL or integer), it is inserted with its exact value if it is within the column range and precision.

如果数值的小数部分位数过多，则会进行四舍五入，并生成一条通知。四舍五入的方法如 第 14.24.4 节，“四舍五入行为” 中所述。即使在严格模式下，由于小数部分四舍五入而导致的截断也不算错误。If the value has too many digits in the fractional part, rounding occurs and a note is generated. Rounding is done as described in Section 14.24.4, “Rounding Behavior”. Truncation due to rounding of the fractional part is not an error, even in strict mode.

如果值的整数部分位数过多，则值过大（超出范围），处理方式如下：If the value has too many digits in the integer part, it is too large (out of range) and is handled as follows:

下溢不会被检测，因此下溢处理未定义。Underflow is not detected, so underflow handling is undefined.

对于将字符串插入数值列，如果字符串包含非数字内容，则字符串到数字的转换处理如下：For inserts of strings into numeric columns, conversion from string to number is handled as follows if the string has nonnumeric contents:

默认情况下，除以零会产生 NULL 结果且不会有警告。通过适当设置 SQL 模式，可以限制除以零的操作。By default, division by zero produces a result of NULL and no warning. By setting the SQL mode appropriately, division by zero can be restricted.

启用 ERROR_FOR_DIVISION_BY_ZERO SQL 模式时，MySQL 对除以零的处理方式会有所不同：With the ERROR_FOR_DIVISION_BY_ZERO SQL mode enabled, MySQL handles division by zero differently:

换句话说，涉及执行除以零运算的表达式的插入和更新可以被视为错误，但这需要除了严格模式之外，还需要ERROR_FOR_DIVISION_BY_ZERO。In other words, inserts and updates involving expressions that perform division by zero can be treated as errors, but this requires ERROR_FOR_DIVISION_BY_ZERO in addition to strict mode.

假设我们有以下语句：Suppose that we have this statement:

INSERT INTO t SET i = 1/0;

这是严格模式和 ERROR_FOR_DIVISION_BY_ZERO 模式组合时的情况。This is what happens for combinations of strict and ERROR_FOR_DIVISION_BY_ZERO modes.