Understanding SQL Numeric Floating-Point Data Types

You can use floating-point columns to store both whole numbers and numbers with a fractional part—numbers with nonzero digits to the right of the decimal point. Unlike the INTEGER data types (INTEGER, SMALLINT, TINYINT), which have precision set by the implementation, you control the precision of the columns you define as NUMERIC or DECIMAL. (The precision of the other floating-point data types—REAL, DOUBLE PRECISION, and FLOAT—is machine-dependent.)

The SQL floating-point data types are:

• NUMERIC (precision, scale)

• DECIMAL (precision, scale) or DEC (precision, scale)

• REAL

• DOUBLE PRECISION

• FLOAT (precision)

NUMERIC Data Type

When identifying a column as type NUMERIC, you should specify both the precision and the scale the DBMS is to use in storing values in the column. A number's precision is the total number of digits in a number. The scale is the maximum number of digits in the fractional part of the number. Thus, to allow for numeric data in the range -9999.999 to 9999.9999 you could use the following SQL statement:

 CREATE TABLE numeric_table
  (numeric_column NUMERIC(8,4))

Both the precision and the scale of a NUMERIC column must be positive, and the scale (digits to the right of the decimal) cannot be larger than the precision (the maximum number of digits in the number). In the current example, the column NUMERIC_COLUMN has a precision of 8 and a scale of 4, meaning it can hold a number with, at most, eight digits, with four of them to the left and four of them to the right of the decimal point. Thus, if you attempt to insert the value 12345.6 into the column, the DBMS will return an arithmetic overflow error because your value has more than four digits to the left of the decimal. Similarly, if you insert the value 123.12345 into the column, the DBMS will round the value to 123.1235 because the scale is, at most, four digits (to the right of the decimal point).

Note

If you don't specify the precision and scale when you identify a column of type NUMERIC, you will get the DBMS default for precision and scale. For example, if you are using MS-SQL Server and enter the following SQL statement CREATE TABLE numeric_table (numeric_column NUMERIC) MS-SQL Server will give you a precision of 18 and a scale of 0. Thus, you can enter whole numbers 18 digits—the DBMS ignores any digits you enter to the right of the decimal point since the default scale is 0. Other DBMS products may give you a scale that is half of the precision. Thus, if the default precision is 18, the scale would be 9. When using the NUMERIC type, don't leave the precision and scale up to the DBMS—specify both. Otherwise, you may find that applications using your tables on one DBMS work fine but fail when running on another DBMS because the default precision and scale are different between the two products.

DECIMAL and DEC Data Types

The DECIMAL data type is similar to NUMERIC in that you specify both the precision and the scale of the numbers the DBMS is to store in columns of type DECIMAL. When a column is of type decimal, however, it may hold values with a greater precision and scale than you specify if the DBMS and the computer on which it is running allow for a greater precision. Thus, if you use the SOL statement

CREATE TABLE decimal_table
 (decimal_column DECIMAL (6,2))

you can always put values up to 9999.99 into the column DECIMAL_COLUMN. However, if the implementation uses a greater precision, the DBMS will not reject values with values greater than 9999.99.

Note

An implementation is a DBMS product running on a specific hardware platform.

REAL Data Type

Unlike the NUMERIC, DECIMAL, and DEC data types, which define columns with precise values, REAL, DOUBLE PRECISION, and FLOAT are approximate data types. When you define a column of TYPE NUMERIC(5,2), the computer will store the exact value of the number. You can specify the precision and scale for the precise floating point types (NUMERIC, DECIMAL, DEC), but there is a limit to the largest value you can store "exactly." Using MS-SQL Server running on an NT platform, for example, you can store a NUMERIC value with up to 38 digits. Therefore, if you need to store very large or very small numbers, you will need to use the REAL, DOUBLE, or FLOAT approximate data types.

The precision of the REAL data type depends on the platform on which you're running. A 64-bit machine (such as one based on the Alpha processor) will give you more precision than a 32-bit machine (such as one based on the Intel processor). When you define a column to be of type REAL using MS-SQL Server running under Windows NT on an INTEL platform, for example, the column can hold values with up seven digits of precision in the range 3.4E-38 to 3.4E+38.

In case, you're a bit "rusty" on the scientific notation you learned in high school, let's digress for a quick review. As you know (or knew), you can represent any number as a mantissa and an exponent. For example, if you have the number 32,768, you can express it as 3.2768E+4, which is the mantissa (3.2768, in this example) multiplied by 10 raised to the power or exponent (4, in this example). Thus, writing 3.2768E+4 is the same as writing 3.2768 * 10**4, which equals 32,768. Similarly, you could write 0.000156 as 1.56E-4.

A column of type REAL in an MS-SQL Server database running on an Intel platform can hold up to eight digits in the mantissa and have a value in the range 3.4E-38 to 3.4E+38.

Note

Check your system manual to find out the exact precision and value range of REAL numbers for your implementation.

DOUBLE PRECISION Data Type

When you define a column as being a DOUBLE PRECISION type, you are telling the DBMS that you want to store values with double the precision of a REAL data type. Like the REAL data type, the actual precision of a DOUBLE PRECISION column depends on the implementation (the combination of DBMS and platform on which it is running). The SQL-92 specification does not specify exactly what DOUBLE PRECISION means. It requires only that the precision of a DOUBLE PRECISION number be greater than the precision of a REAL (or single precision) number.

In some systems, the DOUBLE PRECISION data type will let you store numbers with twice the number of digits of precision defined for the REAL data type and twice the exponent. Other systems will let you store less than double the number of REAL digits in the mantissa, but let you store much larger (or smaller) numbers by letting you more than double the exponent allowed for the REAL data type.

The DOUBLE PRECISION data type for MS-SQL Server running under Windows NT on an INTEL platform gives you 16 digits of precision (17 digits total) for the mantissa and much more than twice the exponent of a REAL number. While an MS-SQL Server column of type REAL can hold values with up to 8 digits (7 digits of precision) and be in the range 3.4E-38 to 3.4E+38, a DOUBLE PRECISION column on the same system can hold 17-digit mantissas (16 digits of precision) and be in the range of 1.7E-308 to 1.7E+308.

Check your system manual to find out the exact precision and value range of DOUBLE PRECISION numbers for your implementation. Don't assume that DOUBLE PRECISION means twice the precision and twice the exponent.

FLOAT Data Type

Whether the FLOAT data type has the precision and range of a REAL number or a DOUBLE PRECISION number depends on the precision you specify when defining a column to be of type FLOAT.

When you define a column of type FLOAT, you specify the precision you want. If the hardware on which you are running the DBMS will support the precision using single-precision (REAL) registers, then you will get the default precision for REAL numbers. If, on the other hand, the hardware supports only the precision you specified for the FLOAT data type using DOUBLE PRECISION registers, the DBMS will store values of type FLOAT using the default precision for the DOUBLE PRECISION data type.

In reality, you will have to check your system manual or experiment with storing numbers in columns of type FLOAT to see the actual precision you will get based on the precision you specify for the FLOAT data type. For example, when running MS-SQL Server under Windows NT on an INTEL computer, the SQL statement

CREATE TABLE float_table
 (float_column FLOAT (15))

will result in only seven digits of precision (eight digits total). Thus, MS-SQL Server will insert 123456789012 as 1.2345679E+11 in the FLOAT_COLUMN, even though you specified a precision as 15. In fact, any precision less than 25 will result in only a single-precision (REAL) 7 digits of precision. If you specify a FLOAT precision of 26–53 (or omit the precision), the DBMS will store values using the DOUBLE PRECISION 16 digits of precision (17 digits total).