# Precision and Scale

## Definitions

Precision and scale are important concepts to understand if you need to deal with decimal numbers

precision
  The total number of digits in a decimal number, both before and after the decimal point.
scale
  The total number of digits after the decimal point in a number.

Here are some examples:

Number | Precision | Scale
--- | --- | ---
5.333 | 4 | 3
15.333 | 5 | 3
115.333 | 6 | 3
115.33 | 5 | 2

## Columns With Precision And Scale

Many databases support numeric datatypes with precision and scale attribute. For example, Oracle supports a "number" type. This query creates a table with a column that can store numbers with precision of 5 and scale of 2. That is, it can store numbers with up to 5 total digits, 3 of which are reserved for the whole number component of the number and 2 of which are reserved for decimal places.

>     create table exampletable (col1 number(5,2))

Any number with 3 or fewer whole number digits and 2 or fewer decimal digits may be inserted into this column.

>     0> insert into exampletable values (5.2);
>     0> insert into exampletable values (5.22);
>     0> insert into exampletable values (55.2);
>     0> insert into exampletable values (55.22);
>     0> insert into exampletable values (555.2);
>     0> insert into exampletable values (555.22);
>     0> select * from exampletable;
>     COL1
>     ======
>     5.2
>     5.22
>     55.2
>     55.22
>     555.2
>     555.22

Numbers with more than 2 decimal digits may be inserted into this column, but they will be rounded up or down as appropriate.

>     0> insert into exampletable values (5.221);
>     0> insert into exampletable values (5.225);
>     0> insert into exampletable values (5.229);
>     0> select * from exampletable;
>     COL1
>     ====
>     5.22
>     5.23
>     5.23

Since 2 digits are reserved for decimal digits. Numbers with more than 3 whole number digits may not be inserted into this column, even if the total number of digits is less than 5. Attempts to do so will generate errors.

>     0> insert into exampletable values (5555.22);
>     ORA-01438: value larger than specified precision allows for this column
>     0> insert into exampletable values (5555.2);
>     ORA-01438: value larger than specified precision allows for this column
>     0> insert into exampletable values (5555);
>     ORA-01438: value larger than specified precision allows for this column

## Arithmetic Involving Numbers With Different Precision And Scale

When 2 columns with different precision and/or scale are involved in arithmentic, the precision and scale of the result are not limited by the precision and scale of the factors. The result will have whatever precision and scale are necessary to represent the number.

For example, 9.2 has a precision of 2 and scale of 1 and 9.22 has a precision of 3 and scale of 2. When added, the sum, 18.42, has a precision of 4 and scale of 2. When multiplied, the product, 84.824, has a precision of 5 and scale of 3.

>     0> select 9.2+9.22 from dual
>     9.2+9.22
>     =========
>     18.42
>     0> select 9.2*9.22 from dual
>     9.2*9.22
>     =========
>     84.824

## Rounding Errors

As shown in the previous example, multiplication can result in numbers with larger scale than either of the two numbers that were multiplied. If the result is stored back into a column with smaller scale than is necessary to represent the product, rounding will occur.

This can be a frustrating occurrance when dealing with money. It is common to use columns with scale of 2 for money but such a column cannot be used to keep track of fractions of cents. Only 2 decimal places are required when monetary values which are added together or multiplied by whole numbers, but if a monetary value is multiplied by a decimal number then it could require more than 2 decimal places to store the result. Using only 2 decimal places will introduce rounding errors quickly.

Since numbers cannot have infinite scale, it is always possible to introduce rounding errors. You have to decide how much of a rounding error is acceptable when designing your tables.

## Truncation

If a value is inserted back and forth between columns with different scales, the original scale of the value will be lost and the value will be rounded and truncated. For instance:

>     0> create table exampletable1 (col1 number(3,2));
>     0> create table exampletable2 (col1 number(2,1));
>     0> insert into exampletable1 values (1.29);
>     0> insert into exampletable2 select * from exampletable1;
>     0> insert into exampletable1 select * from exampletable2;
>     0> select * from exampletable1;
>     COL1
>     ====
>     1.29
>     1.3

When 1.29 was inserted into col1 of exampletable2, which can only accommodate a single decimal digit, it was rounded up to 1.3 and the second decimal digit was truncated. Now, col1 of exampletable2 contains 1.3 rather than 1.29 and 1.3 is what gets selected from col1 of exampletable2 and inserted back into exampletable1 rather than 1.29.

## Bind and Substitution Variables

Computer hardware stores decimal numbers using as many decimal places as it can (floating point format). But databases store decimal numbers using a precise number of decimal places (fixed point format). So, when supplying a floating point number as the value of a bind or substitution variable, you must constrain the number of decimal places by supplying a precision and scale for that number.

You should set the scale equal to the number of decimal places that you believe your variable is accurate to, and the precision equal to the scale plus the maximum number of whole number digits your variable could contain. For instance, if you plan on storing values between 0 and 255, accurate to 3 decimal places, then you should use scale 3 and precision 6.

Note, however, that the scale of a bind variable will not always be preserved. If you use a bind variable to insert a floating point number into a column with smaller scale than you specified for your number, your number will be rounded down upon insertion. For instance, if you pass in 1.2999 with scale of 4 and precision of 5 into a column with scale of 1 and precision of 2, the insert will succeed but your number will be rounded up to 1.3. Similarly, if you use a bind variable to pass a floating point number into a comparison, it will be converted to have the same scale as the value it is being compared to, which could cause rounding to occur.