Floating-point to decimal
When a single precision floating-point number is assigned to a decimal column or variable, the number is first converted to a temporary decimal number.
When a single precision floating-point number is assigned to a decimal column or variable, the number is first converted to a temporary decimal number of precision 6 by rounding on the seventh decimal digit. Twenty five zeros are then appended to the number to bring the precision to 31. Because of rounding, a number less than 0.5×10-6 is reduced to 0.
When a double precision floating-point number is assigned to a decimal column or variable, the number is first converted to a temporary decimal number of precision 15, and then, if necessary, truncated to the precision and scale of the target. In this conversion, zeros are added to the end of the number, if necessary, to bring the precision to 16. The number is then rounded (using floating-point arithmetic) on the sixteenth decimal digit to produce a 15-digit number. Because of rounding, a number less in magnitude than 0.5×10-15 is reduced to 0. If the decimal number requires more than 15 digits to the left of the decimal point, an error is reported. Otherwise, the scale is given the largest possible value that allows the whole part of the number to be represented without loss of significance.
The following examples show the effect of converting a double precision floating-point number to decimal:
Example 1: The floating-point number, .123456789098765E-05 in decimal notation is, .00000123456789098765. Rounding adds 5 in the 16th position, so the number becomes .00000123456789148765 and truncates the result to .000001234567891. Zeros are then added to the end of a 31-digit result, and the number becomes .0000012345678910000000000000000.
Example 2: The floating-point number, 1.2339999999999E+01 in decimal notation is, 12.33999999999900. Rounding adds 5 in the 16th position, so the number becomes 12.33999999999905 and truncates the result to 12.3399999999990. Zeros are then added to the end of a 31-digit result and the number becomes 12.33999999999900000000000000000.