What Is a Whole Number?
The term whole number is one you'll find often in mathematics. Essentially the definition of a whole number is based around what it doesn't contain. A whole number can't be a fraction of a number, a percentage, or have a decimal. If you have a number like 21.32, it has a whole number portion (21), but in itself, this number is not a whole number because it contains a fraction (.32). Whole numbers are usually defined as non-negative integers, including zero, although not everyone agrees on this definition.
The definition for whole number may seem unnecessary to some, but in fact in early math we soon begin teaching children the properties of integers. Integers and whole numbers are not the same, but all whole numbers are integers. The difference is that integers include negative numbers, while all whole numbers are non-negative. Zero is neither positive nor negative.
Other properties applying to whole numbers with addition and multiplication include the following:
Identity property: Any whole number added to zero equals that number (0 + 23 = 23)
Commutative property: Order doesn't matter when multiplying or adding two integers (3 x 4 = 4 x 3) (3 +4 = 4 + 3).
Related to whole numbers are natural numbers, sometimes referred to as counting numbers. They're really the first numbers children learn. Natural numbers may include zero, although counting numbers typically do not; zero isn't included as a counting number because it cannot really be counted. The sequence 1, 2, 3, 4 ... is a whole number, natural number, and counting number sequence.
Integers also matter when we ask students to round answers. At some point in our lives, we all need to figure out a little math in our heads, especially when we buy things. If we look at a number with a fraction, for instance the price $29.95 for lunch at a restaurant, we may need to figure out how to tip according. While some people may just want to tip to the exact penny, others merely round up or down to the nearest counting number to figure tip. Thus $29.95 is rounded up to $30. If we tip 20%, we tip $6. It's sometimes more practical and simpler to use whole numbers in everyday applications of math.
Even organizations like the Internal Revenue Service (IRS) would prefer to work with integers instead of decimal amounts. You'll note you can round up or down when your deductions, income, and et cetera aren't whole numbers. You might also discover that some people employ rounding up only when it comes to disbursements from the IRS, and only round down to a counting number when estimating their total taxable income.
While many children contend that mathematics is a worthless pursuit, we find ourselves lost without a basic understanding of the counting number. We use these constantly, no matter what our occupation. Real numbers answer such basic questions as how many people are coming to dinner, or how many hours in a day, days in a year, or minutes in an hour. We consider whole numbers as they relate to how many apartment complexes are in a building, the number of available parking spaces, or the cartons of milk we need to buy.
People often laugh at the use of decimal numbers in various statistical reports, such as in the following: the average family has 2.5 children. Our minds immediately convert this to a counting number, since there is no such thing as a 0.5 child. We read this in whole numbers too, as the following: the average family has two to three kids.
Written by Tricia Ellis-Christensen
