decimal and numeric (Transact-SQL)

Decimal and numeric

Numeric data types that have fixed precision and scale.

decimal [ (p[ ,s] )] and numeric[ (p[ ,s] )]

• Fixed precision and scale numbers. When maximum precision is used, valid values are from - 10^38 +1 through 10^38 - 1. The ISO synonyms for decimal are dec and dec(p, s). numeric is functionally equivalent to decimal.

• p (precision)

• The maximum total number of decimal digits that can be stored, both to the left and to the right of the decimal point. The precision must be a value from 1 through the maximum precision of 38. The default precision is 18.

• s (scale)

• The maximum number of decimal digits that can be stored to the right of the decimal point. Scale must be a value from 0 through p. Scale can be specified only if precision is specified. The default scale is 0; therefore, 0 <= s <= p. Maximum storage sizes vary, based on the precision.

Precision Storage bytes

1 - 9       5

10-19     9

20-28    13

29-38    17
As per my understanding NUMERIC(18, 10) column would take 18 decimal digits to the left of the decimal point and 10 to the right.

Example:

SELECT CAST(1234567891234567.34 AS NUMERIC(18,2))  --Works
SELECT CAST(1234567891234567.34 AS NUMERIC(18,10)) --fails with Arithmetic overflow error

it is clear that, in the first case from the statement NUMERIC(18,2) the total digits are 18 and 16 digits are available to the left of decimal, whereas 1234567891234567 are 16 digits. Hence, there is no error.
In the second case, from the statement NUMERIC(18,10), 8 digits are available to the left of decimal, but 1234567891234567 are 16 digits which is more than 8 digits. Hence, Arithmetic overflow error occurs.