## 12.25 Precision Math

[12.25.1 Types of Numeric Values](precision-math-numbers.html)
[12.25.2 DECIMAL Data Type Characteristics](precision-math-decimal-characteristics.html)
[12.25.3 Expression Handling](precision-math-expressions.html)
[12.25.4 Rounding Behavior](precision-math-rounding.html)
[12.25.5 Precision Math Examples](precision-math-examples.html)

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 MySQL provides support for precision math: numeric value handling that results in extremely accurate results and a high degree control over invalid values. Precision math is based on these two features:

* SQL modes that control how strict the server is about accepting or rejecting invalid data.

* The MySQL library for fixed-point arithmetic.

 These features have several implications for numeric operations and provide a high degree of compliance with standard SQL:

* **Precise calculations**: For exact-value numbers, calculations do not introduce floating-point errors. Instead, exact precision is used. For example, MySQL treats a number such as `.0001` as an exact value rather than as an approximation, and summing it 10,000 times produces a result of exactly `1`, not a value that is merely “close” to 1.

* **Well-defined rounding behavior**: For exact-value numbers, the result of [`ROUND()`](mathematical-functions.html#function_round) depends on its argument, not on environmental factors such as how the underlying C library works.

* **Platform independence**: Operations on exact numeric values are the same across different platforms such as Windows and Unix.

* **Control over handling of invalid values**: Overflow and division by zero are detectable and can be treated as errors. For example, you can treat a value that is too large for a column as an error rather than having the value truncated to lie within the range of the column's data type. Similarly, you can treat division by zero as an error rather than as an operation that produces a result of `NULL`. The choice of which approach to take is determined by the setting of the server SQL mode.

 The following discussion covers several aspects of how precision math works, including possible incompatibilities with older applications. At the end, some examples are given that demonstrate how MySQL handles numeric operations precisely. For information about controlling the SQL mode, see [Section 5.1.11, “Server SQL Modes”](sql-mode.html).

