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Integers are whole numbers that cannot be fractions, percentages, or decimals. They include negative numbers and zero. Understanding integers can make math easier. Natural numbers are similar but do not include negative numbers or zero. Integers are important for rounding and practical applications, such as taxes and statistics.
The term “integer” is typically used in mathematics. It is often 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 an integer part of 21, this number is not an “integer” because it contains a decimal of 0.32. Integers are also often referred to as non-negative integers, including zero.
Purpose to identify different types of numbers
While defining an integer may seem pointless to some, it can make it easier for children to understand the properties of integers. Integers and integers are not the same, but all integers are integers. The difference is that integers include negative numbers, while all integers are non-negative. Zero is neither positive nor negative.
Properties that apply to integers include the “zero property of addition” and the “commutative property”. The zero property of addition means that any integer added to zero is equal to that number, for example 0 + 23 = 23. While the commutative property means that the order doesn’t matter when multiplying or adding two integers; which means 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 integers are the “natural numbers,” sometimes referred to as “count numbers.” These are typically the first numbers children learn. Natural numbers may include zero, although count numbers typically do not; zero is not included as a count number because it has no value and therefore cannot really be counted. An integer, a natural number, and a sequence of count numbers would be something like {1, 2, 3, 4,…}, while integers would also include 0.
The importance of integers
Whole numbers matter when teachers ask students to round off their math answers and for some practical applications. At some point in people’s lives, they typically need to figure out simple calculations in their heads. For example, someone considering the price of $29.95 US Dollars (USD) for lunch at a restaurant might need to figure out how to tip on a basic basis. While some diners may want to tip to the exact penny, others simply round up or down to the nearest whole number to determine tip. So a diner can round $29.95 USD up to $30 USD to determine an easier value for the tip.
Even organizations like the Internal Revenue Service (IRS) in the United States prefer to work with whole numbers rather than decimal values. People typically can round up or down when determining deductions, income, and other values when submitting tax information to the IRS. Some people only round when it comes to IRS disbursements and round down to a whole number when estimating their total taxable income, guaranteeing the most beneficial number in each case.
People often laugh at the use of seemingly meaningless decimal numbers in statistical reporting, such as the idea of the average family with 2.5 children. Converting this type of value to an integer, since there is no such thing as 0.5 of a child, makes these statistics more useful. It is more meaningful to consider that “the average family has two or three children”, rather than an impossible decimal.
