Let’s take a look at how we read and write integers. Numbers like eight, negative four, fifteen, negative seventy-six, and zero are all examples of integers. An integer is any number in this set, where the dot dot dots on either side means continues without end. The word “integer” comes from the Latin word that means “whole.” Another way to say that is that an integer is a number that can be written without any fractional parts. Numbers like one-half, one and six-tenths, negative five and four-tenths are not integers; they cannot be written without fractional parts.
Here’s a number line with some integers marked on it. Positive integers are integers that are greater than zero. Negative integers are integers that are less than zero. Zero is neither positive nor negative. Let’s look at some examples of how we use positive and negative integers. Parts of New Orleans, Louisiana, sit below sea level by nearly seven feet. Write the elevation value as an integer. So here’s what we know: we know seven feet and we know below sea level. We know we’re dealing with seven, but should it be a positive seven or a negative seven? If you guess negative seven, you’re right. Since we’re dealing with an area that’s below sea level, negative seven is how we represent the elevation of those parts of New Orleans. Speaking of sea level, if a place is exactly at sea level, what integer would represent that? The answer is zero. Anything that’s neither above sea level nor below sea level sits exactly at sea level and would be at an elevation of zero.
Next up a true or false question, true or false: negative sixty-three is an integer. What do you think? It’s true! Negative sixty-three has no fractional parts or components; so it is by definition an integer. Is seven and two-tenths an integer? Any thoughts? Seven and two-tenths is not an integer. Another way to write seven and two-tenths would be to have a seven with a fraction of two over ten. This fractional piece means we’re not dealing with an integer here. Decimal numbers because they have fractional pieces are not integers.
Let’s quickly summarise the words we’ve been using. An integer is a number written without fractional parts. A positive integer is an integer that is greater than zero. And finally a negative integer is an integer less than zero.