There is a confusion here. “Decimal” is not a number set. “Whole numbers” is.
“Decimal” has been used to mean three different things about the representation of numbers:
- Numbers written using a base 10 place value system
- The decimal point that separates the integer and fractional parts of a number written in base 10. (Some countries use a comma. Some folks refer to the point used for this purpose in other bases as a decimal too for extra confusion.)
- A number written in the above form that has some numerals, probably nonzero, written to the right of the point. In other words, a number written in decimal form with a nonzero fractional part.
I'm guessing that the usage in this question is referring to the third meaning of “decimal” and will interpret the question as being not about representation of numbers but about transformation of numbers.
To wit, “What are some popular ways real numbers with nonzero fractional parts can be mapped to integers?”
I hope this is the correct interpretation.
There are a few common ways:
- Round towards zero: Ignore the fractional part and keep only the integral part.
- Floor: Take the greatest integer less than the number in question.
- Ceiling: Take the least integer greater than the number in question.
- Round to the nearest integer: Ignore the fractional part if it's less than a half. Otherwise, round away from zero.
These are the main ways of picking integers close to the number in question, but obviously, there are infinitely many ways to map sets of real numbers to mergers, so it is unclear if any of these are what the asker was looking for.
