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What is a Whole Number?

Article Details
• Originally Written By: Tricia Ellis-Christensen
• Revised By: G. Wiesen
• Edited By: O. Wallace
2003-2016
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The term "whole number" is typically used in mathematics. It is frequently defined by what it does not contain: it cannot be a fraction of a number, a percentage, or have a decimal. While a number like 21.32 has a whole number portion of 21, this number is not "whole" because it contains a decimal of 0.32. Whole numbers are also often defined as non-negative integers, including zero.

Purpose for Identifying Different Number Types

While the definition for a whole number may seem unnecessary to some, it can make it easier for children to understand 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.

Properties that apply to whole numbers include the "zero property of addition" and the "commutative property." The zero property of addition indicates that any whole number added to zero equals that number, such as 0 + 23 = 23. While the commutative property means that order does not matter when multiplying or adding two integers; meaning that 3 x 4 = 4 x 3 and 3 + 4 = 4 + 3. These are important concepts that can make other mathematical procedures easier.

Different Types of Numbers

Related to whole numbers are "natural numbers," sometimes referred to as "counting numbers." These are typically the first numbers children learn. Natural numbers may include zero, although counting numbers typically do not; zero is not included as a counting number because it has no value and so it cannot really be counted. A whole number, natural number, and counting number sequence would be something like {1, 2, 3, 4,...}, while whole numbers would also include 0.

The Importance of Whole Numbers

Integers matter when teachers ask students to round their math answers and for some practical applications. At some point in people's lives, they typically need to figure out simple math in their heads. For example, someone considering the price \$29.95 US Dollars (USD) for lunch at a restaurant may need to figure out how to tip according. While some diners might want to tip to the exact penny, others merely round up or down to the nearest whole number to determine the tip. Thus a diner can round \$29.95 USD up to \$30 USD to determine a simpler value for the tip.

Even organizations like the Internal Revenue Service (IRS) in the US prefer to work with integers instead of decimal values. People can typically round up or down when determining deductions, income, and other values while filing tax information with the IRS. Some people round up only when it comes to disbursements from the IRS, and round down to a whole number when estimating their total taxable income, ensuring the most advantageous number in each instance.

People often laugh at the use of seemingly nonsensical decimal numbers in statistical reports, such as the idea of an average family having 2.5 children. Converting this type of value to a whole number, since there is no such thing as 0.5 of a child, makes these statistics more useful. It is more meaningful to considered that "the average family has two to three kids," rather than an impossible decimal.