12.19.3. Expression Handling

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. (Without strict mode, truncation for INSERT is permissible.)

Handling of a numeric expression depends on what kind of values the expression contains:

If any approximate values are present, the expression is approximate and is evaluated using floating-point arithmetic.
If no approximate values are present, the expression contains only exact values. If any exact value contains a fractional part (a value following the decimal point), the expression is evaluated using DECIMAL exact arithmetic and has a precision of 65 digits. The term "exact" is subject to the limits of what can be represented in binary. For example, 1.0/3.0 can be approximated in decimal notation as .333..., but not written as an exact number, so (1.0/3.0)*3.0 does not evaluate to exactly 1.0.
Otherwise, the expression contains only integer values. The expression is exact and is evaluated using integer arithmetic and has a precision the same as BIGINT (64 bits).

If a numeric expression contains any strings, they are converted to double-precision floating-point values and the expression is approximate.

Inserts into numeric columns are affected by the SQL mode, which is controlled by the sql_mode system variable. (See Section 5.1.7, "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:

mysql> SET
        sql_mode='TRADITIONAL';

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.

If the value has too many digits in the fractional part, rounding occurs and a warning is generated. Rounding is done as described in Section 12.19.4, "Rounding Behavior".

If the value has too many digits in the integer part, it is too large and is handled as follows:

If strict mode is not enabled, the value is truncated to the nearest legal value and a warning is generated.
If strict mode is enabled, an overflow error occurs.

Underflow is not detected, so underflow handling is undefined.

By default, division by zero produces a result of NULL and no warning. With the ERROR_FOR_DIVISION_BY_ZERO SQL mode enabled, MySQL handles division by zero differently:

If strict mode is not enabled, a warning occurs.
If strict mode is enabled, inserts and updates involving division by zero are prohibited, and an error occurs.

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.

Suppose that we have this statement:

INSERT INTO t SET i = 1/0;

This is what happens for combinations of strict and ERROR_FOR_DIVISION_BY_ZERO modes.

`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.

For inserts of strings into numeric columns, conversion from string to number is handled as follows if the string has nonnumeric contents:

A string that does not begin with a number cannot be used as a number and produces an error in strict mode, or a warning otherwise. This includes the empty string.
A string that begins with a number can be converted, but the trailing nonnumeric portion is truncated. If the truncated portion contains anything other than spaces, this produces an error in strict mode, or a warning otherwise.