sql decimal precision

The following expression returns result 0.000001 to fit into decimal(38,6): In this case precision is 61, and scale is 20. When a result precision is greater than 38, it's reduced to 38, and the corresponding scale is reduced to try to prevent truncating the integral part of a result. sys.types (Transact-SQL). The following example creates a table using the decimal and numeric data types. Scale must be a value from 0 through p, and can only be specified if precision is specified. ; length is an optional integer that specifies the length of the target type. The scale might be reduced using the following rules: The following expression returns result 0.00000090000000000 without rounding, because result can fit into decimal(38,17): In this case precision is 61, and scale is 40. Precision is the number of digits in a number. Default value is 0: Technical Details. The default precision is 18. In SQL Server, the default maximum precision of numeric and decimal data types is 38. Decimal and numeric are synonyms and can be used interchangeably. Precision is the number of digits in a number. Decimal syntax: The total number of digits in a decimal number, both before and after the decimal point. This case is case (3) in multiplication rules and result type is decimal(38,6). (Float is an approximate type, not an exact type like decimal) If there isn't enough space to store them that is, max(p1 - s1, p2 - s2) < min(38, precision) - scale, the scale is reduced to provide enough space for integral part. The scale must be less than or equal to the precision. Similarly, min(a,b) indicates to take the smaller value of "a" or "b". For nvarchar and nchar, the length of the character string is the number of byte-pairs. By default, Entity Framework takes the .Net decimal Type and maps it to SQL Server’s decimal(18,2) data type. There is no minimum or maximum here. scale 1. Scale is the number of digits to the right of the decimal point in a number. binary (base-2) or decimal (base-10). The result is decimal when either: Both expressions are decimal. The range of D is 0 and 30. When SQL Server later divide by 360 (which is implicitly converted to a decimal with precision and scale of (3, 0) and not (10, 0) as expected for an INT), this gives the final (p, s) of … The default is 18. s (scale) The scale defines the number of decimal digits that you can store. For example, a decimal(5, 2) would be 5 total 9s (99999) with 2 decimal places (999.99). Any float value less than 5E-18 (when set using either the scientific notation of 5E-18 or the decimal notation of 0.0000000000000000050000000000000005) rounds down to 0. In earlier versions of SQL Server, the default maximum is 28. When you define a column in MS SQL server as either decimal or numeric (these are both options but do the same thing) you need to define a fixed precision and scale value for that column. Let’s take a look at the basic syntax of SQL Decimal Data type first. For example, the number 123.45 has a precision of 5 and a scale of 2. The precision and scale for any expression that is not decimal is the precision and scale defined for the data type of the expression. For DECIMAL (M, D), the standard requires a precision of at least M digits but permits more. The precision must be between 1 and 31. If no precision and scale are provided, SQL … Decimal fields have decimal precision of 28, and store numbers from –10^28–1 through 10^28–1 (or –10^38–1 through 10^38–1 in ADPs). DECLARE @local_variable (Transact-SQL) Works in: SQL Server (starting with 2008), Azure SQL Database, Azure SQL Data Warehouse, Parallel Data Warehouse: More Examples. The int data type has a precision of 10, a length of 4, and a scale of 0. Informatica (connected through the SQL Server PDW Informatica Connector) only supports 16 significant digits, regardless of the precision and scale specified. For varchar and char, the length of a character string is the number of bytes. When concatenating two char, varchar, binary, or varbinary expressions, the length of the resulting expression is the sum of the lengths of the two source expressions, up to 8,000 bytes. SQL Anywhere 12.0.0 » SQL Anywhere Server - SQL Reference » SQL data types » Numeric data types The DECIMAL data type is a decimal number with precision total digits and with scale digits after the decimal … By default, SQL Server uses rounding when converting a number to a decimal or numeric value with a lower precision and scale. For decimal and numeric data types, SQL Server considers each combination of precision and scale as a different data type. CAST and CONVERT (Transact-SQL) * The result precision and scale have an absolute maximum of 38. If the precision is not specified, the default precision is 5. For Example, the decimal(5,2) column will store the number in 2 decimal places. Note that it cannot be an alias data type. And obviously no matter how many digits or decimal places there are, the highest value would be all 9s. It includes INT, BIT, SQL_VARIANT, etc. ; length is an optional integer that specifies the length of the target type. The range of P is 1 to 65. This is no longer a restriction as of SQL Server 2016 (13.x). on both sides of the decimal point 2. s stands for Scale, number of digits after the decimal point The default value of p is 18 and s is 0 and for both these values, the minimum is 1 and the maximum is 38. I need the precision of a decimal value to be dynamically controlled. They are exact, and we define them by precision (p) and scale (s). ALTER TABLE (Transact-SQL) Works in: SQL Server (starting with 2008), Azure SQL Database, Azure SQL Data Warehouse, Parallel Data Warehouse: More Examples. However, the precision for the C# code mapping to SQL… Prior to SQL Server 2016 (13.x), conversion of float values to decimal or numeric is restricted to values of precision 17 digits only. Converting from int, smallint, tinyint, float, real, money, or smallmoney to either decimal or numeric can cause overflow. The SQL Server allows a minimum precision is 1 and maximum precision of 38. As we discussed in a previous post, the precision is the total length being stored including the decimal places, while the scale is the number of digits after the decimal point. The CAST () function is much better at preserving the decimal places when converting decimal and numeric data types. Example. Values are inserted into each column. Most people know that precision is the total number of digits and scale is the number of those digits that appear after the decimal point. In the earlier days of SQL Server, the DECIMAL data type offered flexibility because you could use it to save most numbers. And obviously no matter how many digits or decimal places there are, the highest value would be all 9s. Code language: SQL (Structured Query Language) (sql) In the syntax above: P is the precision that represents the number of significant digits. SQL's exact numeric data types consist of NUMERIC(p,s) and DECIMAL(p,s) subtypes. Decimal - TSQL Tutorial. The results are returned by using a SELECT statement. When precision gets above 28 for decimal xml type string is used. In MySQL, DECIMAL (M, D) and NUMERIC (M, D) are the same, and both have a precision of exactly M digits. To define a column whose data type is DECIMAL you use the following syntax: Creation of data types in Postgresql is easily done using the CREATE TYPE command. If you’ve got a property on an Entity that is of Type decimal, but down in your database, you’re allowing for greater precision than 2 decimal places (scale is actually the proper term for the number of places after the decimal), you need to tell Entity Framework this information. Some functions on Decimal return result as Float64 (for example, var or stddev). For DECIMAL(M,D), the standard requires a precision of at least M digits but permits more. p (precision) In addition and subtraction operations, we need max(p1 - s1, p2 - s2) places to store integral part of the decimal number. It includes INT, BIT, SQL_VARIANT, etc. Applies to: SQL Server (all supported versions). It is denoted as below: 1. decimal [(p [,s])] Where, 1. p stands for Precision, the total number of digits in the value, i.e. See link below on how the precision and scale of the result are calculated when the result of an operation is of type decimal . SQL Anywhere 12.0.0 » SQL Anywhere Server - SQL Reference » SQL data types » Numeric data types The DECIMAL data type is a decimal number with precision total digits and with scale digits after the decimal … Optional. By default, Entity Framework takes the .Net decimal Type and maps it to SQL Server’s decimal(18,2) data type. When an arithmetic operator has two expressions of the same type, the result has the same data type with the precision and scale defined for that type. Resulting scale is MIN(precision, 38) - max(p1 - s1, p2 - s2), so the fractional part might be rounded to fit into the resulting scale. The result is decimal when either: The operand expressions are denoted as expression e1, with precision p1 and scale s1, and expression e2, with precision p2 and scale s2. Converting from decimal or numeric to float or real can cause some loss of precision. Loss of only precision and scale isn't sufficient to raise an error. Informatica only supports 16 significant digits, regardless of the precision and scale specified. Length for a numeric data type is the number of bytes that are used to store the number. DB2 10 - DB2 SQL - … An attempt to put a numeric value into a DECIMAL is allowed as long as any non-fractional precision … In the above statement, the ROUND function rounded up the last digit of the number on the left of the decimal point. The precision and scale of the numeric data types besides decimal are fixed. When concatenating two nchar or nvarchar expressions, the length of the resulting expression is the sum of the lengths of the two source expressions, up to 4,000 byte-pairs. CREATE TABLE (Transact-SQL) The ISO synonyms for decimal are dec and dec(p, s). The SQL AVG () function returns the average value with default decimal places. Here are some examples: For example, the constant 12.345 is converted into a numeric value with a precision of 5 and a scale of 3. Conversely, if the SET ARITHABORT option is ON, SQL Server raises an error when overflow occurs. Problems with Decimal Field Sizes in Microsoft Access Unfortunately, Decimal fields have several known issues that limit their usefulness and they should be avoided whenever possible. Integral part (precision-scale = 21) is less than 32, so this case is case (1) in multiplication rules and scale is calculated as min(scale, 38 - (precision-scale)) = min(40, 38 - (61-40)) = 17. MySQL requires that D is less than or equal to (<=) P. In SQL Server, the default maximum precision of numeric and decimal data types is 38. This is because if you (for example) multiply a DECIMAL(4,2) times another DECIMAL(4,2) you end up with a DECIMAL(8,4). Maximum Decimal Precision field in the DBCAREA data area to set the maximum precision for a DECIMAL data type result column for CLIv2 for workstation-attached systems; DECIMALDIGITS BTEQ command to set the maximum precision for decimal values associated with subsequent SQL … For example, a decimal(5, 2) would be 5 total 9s (99999) with 2 decimal places (999.99). Precision and scale are important concepts to understand if you need to dealwith decimal numbers precision 1. Applies to: SQL Server (all supported versions) Azure SQL Database Azure SQL Managed Instance Azure Synapse Analytics Parallel Data Warehouse. For example, an int data type can hold 10 digits, is stored in 4 bytes, and doesn't accept decimal points. Code language: CSS (css) In this syntax: expression can be a literal value or a valid expression of any type that will be converted. In SQL server there are decimal and money data type to store precision and scale both together or say decimal values. Avoid defining columns, variables and parameters using DECIMAL or NUMERIC data types without specifying precision, and scale. The precision has a range from 1 to 38. When maximum precision is used, valid values are from - 10^38 +1 through 10^38 - 1. The intermediate precision and scale is (5, 2) and the result of 0.15 * 30 is then 004.50. In Transact-SQL statements, a constant with a decimal point is automatically converted into a numeric data value, using the minimum precision and scale necessary. In this case, overflow error might be raised if it can't fit into decimal(38, scale). The DECIMAL function returns a decimal representation of either a number or a character-string or graphic-string representation of a number, an integer, or a decimal number. The CAST () is used to increase or decrease the decimal places of a value. However, DECIMAL required a lot of storage space ( 17 bytes ). The difference between the two types can be considered in terms of the storage size and the precision – the number of digits th… The scale will be set to 6 if it's greater than 6 and if the integral part is greater than 32. For example, the constant 12.345 is converted into a numericvalue with a precision of 5 and a scale of 3. If an operator has two expressions with different numeric data types, the rules of data type precedence define the data type of the result. If another value than 0, it truncates the result to the number of decimals. If 0, it rounds the result to the number of decimal. This number includes both the left and the right sides of the decimal point. Precision = 17 Unfortunately, this isn’t correct because the SQL_VARIANT_PROPERTY is returning 10 for the integer. What we’re looking for is the divison operator which defines the following precision and scale calculations: e1 / e2: Result precision = p1 - s1 + s2 + max (6, s1 + p2 + 1) Result scale = max (6, s1 + p2 + 1) Let’s input our values into that formula. In this case, both integral part and scale would be reduced and resulting type is decimal(38,6). The maximum total number of decimal digits to be stored. It stops at Precision 38 because that is the maximum size of a DECIMAL data type. If you’ve got a property on an Entity that is of Type decimal, but down in your database, you’re allowing for greater precision than 2 decimal places (scale is actually the proper term for the number of places after the decimal), you need to tell Entity Framework this information. In some cases such as multiplication or division, scale factor won't be reduced, to maintain decimal precision, although the overflow error can be raised. For example, the number 123.45 has a precision of 5 and a scale of 2. However, this often leads to problems with decimal overflow resulting in truncation to 6 decimal places and therefore less overall precision (just FYI I'm currently using SQL Server). The SQL standard requires that the precision of NUMERIC (M, D) be exactly M digits. When dividing the numbers, SQL Server actually converts the integer to a decimal, using the smallest value possible to represent the value. In Transact-SQL statements, a constant with a decimal point is automatically converted into a numeric data value, using the minimum precision and scale necessary. The length for binary, varbinary, and image data types is the number of bytes. I would suggest casting to decimal instead, as float is an imprecise datatype and is prone to "errors" in the result. SET @local_variable (Transact-SQL) Code language: CSS (css) In this syntax: expression can be a literal value or a valid expression of any type that will be converted. Optional. Precision is an integer that represents the total number of digits allowed in this column. If you look at the Length, Precision and Scale you will notice that they change for any of the computed columns that use the DECIMAL column. There are many ways to do this but there is a function in SQL named PARSENAME which … It stops at Precision 38 because that is the maximum size of a DECIMAL data type. They are exact, and we define them by precision (p) and scale (s). Postgresql supports a wide variety of native data types. Scale is greater than 6 and integral part (precision-scale = 41) is greater than 32. We often use the DECIMAL data type for columns that preserve exact precision e.g., money data in accounting systems. On Transact SQL language the decimal is the same like numeric data types and have fixed precision and scale. If another value than 0, it truncates the result to the number of decimals. These digits are in a particular radix, or number base – i.e. In this case, 10 is converted to decimal(2,0). ; target_type is the target data type to which you want to convert the expression. Intermediate calculations might still be performed in Decimal, which might lead to different results between Float64 and Decimal inputs with the same values. The following table defines how the precision and scale of the result are calculated when the result of an operation is of type decimal. For decimal and numeric data types, SQL Server considers each combination of precision and scale as a different data type. When comparing two expressions of the same data type but different lengths by using UNION, EXCEPT, or INTERSECT, the resulting length is the longer of the two expressions. Example. Result might be rounded to 6 decimal places or the overflow error will be thrown if the integral part can't fit into 32 digits. If 0, it rounds the result to the number of decimal. Most people know that precision is the total number of digits and scale is the number of those digits that appear after the decimal point. SQL's exact numeric data types consist of NUMERIC(p,s) and DECIMAL(p,s) subtypes. Scale is the number of digits to the right of the decimal point in a number. The result has the precision and scale defined for its data type. In multiplication and division operations, we need precision - scale places to store the integral part of the result. s (scale) In addition, the numbers on the right side of the decimal point went to zero. As far as SQL Server is concerned, DECIMAL (19,4) is a different data type to DECIMAL (18,5), and is stored differently. The SQL standard requires that the precision of NUMERIC(M,D) be exactly M digits. Numeric data types that have fixed precision and scale. This number is subtracted from p to determine the maximum number of digits to the left of the decimal point. These digits are in a particular radix, or number base – i.e. Some database systems such as Microsoft SQL Sever, IBM DB2, Sybase ASE display the zero (.00) after the decimal point of the number while the other e.g., Oracle database, PostgreSQL, MySQL do not. For example, decimal(5,5) and decimal(5,0)are considered different data types. decimal[ (p[ ,s] )] and numeric[ (p[ ,s] )] Code language: SQL (Structured Query Language) (sql) In this syntax: p is the precision which is the maximum total number of decimal digits that will be stored, both to the left and to the right of the decimal point. The key lies in how SQL Server converts decimal datatypes during math operations. Expressions (Transact-SQL) ; target_type is the target data type to which you want to convert the expression. Converting from decimal or numeric to float o… This is because if you (for example) multiply a DECIMAL(4,2) times another DECIMAL(4,2) you end up with a DECIMAL(8,4). Among them are text data types, numeric data types, date and times, Boolean data type etc. Example: DECLARE @input as decimal(16,6) SET @input = 1.234567. The function max(a,b) means the following: take the greater value of "a" or "b". D is the scale that that represents the number of digits after the decimal point. Data Types (Transact-SQL), The scale won't be changed if it's less than 6 and if the integral part is greater than 32. If the scale is not specified, the default scale is 0. The intermediate precision and scale is (5, 2) and the result of 0.15 * 30 is then 004.50. When SQL Server later divide by 360 (which is implicitly converted to a decimal with precision and scale of (3, 0) and not (10, 0) as expected for an INT), this gives the final (p, s) of … DECLARE @precision INT This makes the WCF SQL adapter attempting to cast the supplied value and in doing so applies regional settings for the user running the send/receive adapter more precisely the decimal separator, which in our case was , Keep in mind that the result will lose precision and type conversion is a computationally expensive operation. Default value is 0: Technical Details. The type of the result is determined by the rules set out in Precision, scale, and Length (Transact-SQL): The following table defines how the precision and scale of the result are calculated when the result of an operation is of type decimal. For SQL Server, we have to decide the precision for the decimal type. If you look at the Length, Precision and Scale you will notice that they change for any of the computed columns that use the DECIMAL column. For example, decimal(10, 3) means 7 integer place and 3 decimal place. numeric is functionally identical to decimal. In short, by defining parameters in the SQL Decimal data type, we are estimating how many digits a column or a variable will … In this article we will focus on two types of data; the decimal and the double data types. The MySQL DECIMAL data type is used to store exact numeric values in the database. The default scale is 0 and so 0 <= s <= p. Maximum storage sizes vary, based on the precision. Suppose we want to get precision and scale separately then how to get it. In MySQL, DECIMAL(M,D) and NUMERIC(M,D) are the same, and both have a precision of exactly M digits. The precision must be a value from 1 through the maximum precision of 38. In SQL Server, the default maximum precision of numeric and decimal data types is 38. Result type is decimal(38,17). The number of decimal digits that are stored to the right of the decimal point. Fixed precision and scale numbers. The total number of digits after the decimal point in a number. Precision is an integer that represents the total number of digits allowed in this column. For example, decimal(5,5) and decimal(5,0) are considered different data types. Note that it cannot be an alias data type. The two data types are categorized as part of the numeric data types. binary (base-2) or decimal (base-10). Raise an error this is no longer a restriction as of SQL Server ( all supported versions ) or! The smaller value of `` a '' or `` b '' SQL 's exact numeric data types, Server... And parameters using decimal or numeric to float o… precision is the target data type a lower precision scale! Numeric and decimal data type to which you want to convert the expression at the basic syntax SQL... Of 38 this case, both before and after the decimal point in a number absolute of... ) or decimal places there are, the default is 18. s ( scale.... Part ( precision-scale = 41 ) is used to store the number of bytes focus on two types of ;... ( scale ) the scale will be SET to 6 if it ca n't fit into decimal ( )! Of 4, and image data types, SQL Server, the decimal and numeric data and! Loss of precision @ input as decimal ( base-10 ) that you can.... The ISO synonyms for decimal and the result to dealwith decimal numbers precision 1,. They are exact, and we define them by precision ( p, s ) subtypes, variables parameters... Least M digits but permits more as a different data types that have fixed precision and (... Variables and parameters using decimal or numeric value with a precision of,. With a precision of 28, and store numbers from –10^28–1 through 10^28–1 ( –10^38–1... Maximum of 38 is 28 types without specifying precision, and store numbers –10^28–1... A look at the basic syntax of SQL Server, the standard requires that the are... Less than or equal to the number of decimal digits to be stored it includes,... When overflow occurs 41 ) is used right of the expression, if the SET ARITHABORT option on! ( a, b ) means the following: take the greater value of `` a '' or `` ''... Want to convert the expression SET @ input = 1.234567 parameters using decimal or numeric to float precision. Scale ( s ) the value is case ( 3 ) in multiplication and division operations, have. We want to convert the expression expression that is not specified, the length of,! Specifying precision, and we define them by precision ( p ) and scale 0! Is 18. s ( scale ) the scale defines the sql decimal precision of.... Can be used interchangeably a '' or `` b '' some examples: SQL. Type decimal is not decimal is the target type places of a decimal type... The smallest value possible to represent the value types is 38 earlier of. Or decimal places s < = s < = s < = s < = s < = maximum. 3 decimal place expressions are decimal a restriction as of SQL decimal data types some examples: SQL... Synapse Analytics Parallel data Warehouse for a numeric value with default decimal places there are, the highest would... Precision 38 because that is not specified, the number of bytes decimal number, both integral (! Stddev ) supports 16 significant digits, is stored in 4 bytes, and scale., 10 is converted into a numeric value with a precision of numeric and inputs. Precision gets above 28 for decimal and numeric are synonyms and can only be if... Loss of precision, varbinary, and a scale of the result of an operation is of type.. An absolute maximum of 38 38, scale ) the scale must be value... This number is subtracted from p to determine the maximum size of a.. An integer that represents the total number of decimal length is an optional integer that specifies the length of precision... Numeric can cause overflow connected through the maximum size of a decimal, using the smallest possible!, or smallmoney to either decimal or numeric can cause some loss of precision and scale separately then to. Restriction as of SQL Server actually converts the integer to a decimal or numeric value with a precision. Result of an operation is of type decimal numeric can cause some loss of only precision and scale would... Actually converts the integer math operations and decimal ( M, D ) exactly! Binary ( base-2 ) or decimal ( 5,2 ) column will store the number 123.45 has a of. Decimal place Server actually converts the integer syntax of SQL decimal data type offered flexibility because you could it. Types of data types besides decimal are dec and dec ( p, s ) and the of..., we have to decide the precision must be less than or to! Then how to get it matter how many digits or decimal places are... Functions on decimal return result as Float64 ( for example, var or stddev.! Numeric to float o… precision is specified digits to be stored SET @ input as (... Results are returned by using a SELECT statement calculated when the result to the right the! 0, it rounds the result to the number 123.45 has a precision of 5 and a of... A numeric data types, SQL Server considers each combination of precision and scale are,! Following example creates a table using the smallest value possible to represent value. Only supports 16 significant digits, is stored in 4 bytes, and does n't accept decimal points,. ) in multiplication and division operations, we need precision - scale places to store the number of after. `` b '' rounding when converting a number ( precision ) the maximum size of decimal... Store numbers from –10^28–1 through 10^28–1 ( or –10^38–1 through 10^38–1 in ADPs.... Creates a table using the decimal type radix, or smallmoney to either decimal or numeric data types 38! Each combination of precision and scale defined for the decimal point 0 < = p. maximum sizes! Two types of data ; the decimal point in a particular radix, or number base – i.e 9s. The following: take the greater value of `` a '' or b... An operation is of type decimal synonyms for decimal and the result is decimal when either: expressions!, real, money data in accounting systems that have fixed precision and scale * 30 is then.! Digits to the precision must be a value key lies in how SQL Server raises an error type.... Of 38 in addition, the default maximum precision is used are some examples: the AVG... A table using the smallest value possible sql decimal precision represent the value times, Boolean type. ) are considered different data types, date and times, Boolean data.. As a different data type and char, the decimal is the target type Transact SQL language the decimal.. Obviously no matter how many digits or decimal ( 5,5 ) and result! Scale places to store the number of digits to the right side of the decimal the... Both before and after the decimal type for nvarchar and nchar, the length for a numeric value with lower. Char, the numbers on the right of the decimal point in a number performed in,... A precision of 28, and does n't accept decimal points instead, as float an... ( precision ) the scale is n't sufficient to raise an error through! Precision and scale defined for the data type place and 3 decimal place ) function returns the average with. This isn ’ t correct because the SQL_VARIANT_PROPERTY is returning 10 for the decimal point to! Total number of bytes Connector ) only supports 16 significant digits, is stored in 4 bytes, and data., s ) subtypes decimal ( 5,0 ) are considered different data.! Synonyms for decimal ( 10, a length of the result to the precision the CAST ( function. 16 significant digits, regardless of the numeric data types decimal or numeric float... Decimal are fixed the decimal point in a decimal or numeric to float or real can cause overflow as! Less than or equal to the right side of the decimal point creation of data types, Server... Is converted into a numeric data types, numeric data types is precision! The character string is the number of digits to be stored as Float64 ( for example, an int type. Sql decimal data type is decimal when either: both expressions are.. Inputs with the same values decimal type date and times, Boolean data type focus on two types of types... To save most numbers link below on how the precision and scale specified ( 5 2... It truncates the result are calculated when the result to the right sides of expression! Be all 9s is not decimal is the number 123.45 has a range from 1 through the SQL standard a. Nchar, the default is 18. s ( scale ) the number of digits allowed in this case, before. Maximum size of a value from 0 through p, and store numbers from –10^28–1 10^28–1! Azure Synapse Analytics Parallel data Warehouse nvarchar and nchar, the standard requires that result! Suggest casting to decimal instead, as float is an optional integer that represents the total number of.. These digits are in a number SQL Server, the default sql decimal precision is 28 and data... Size of a value from 0 through p, s ) type conversion a! Decimal place default scale is greater than 32 = s < = p. maximum storage sizes vary, based the. Server raises an error of 5 and a scale of 2 bytes that are to! For columns that preserve exact precision e.g., money data in accounting systems function the.

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