1.06 Identify and represent integers
Introduction
So far in mathematics we have identified positive whole numbers, fractions, and decimals. In this lesson, we are going to explore whole numbers that are negative. You've probably already had real-life experience with this, like when the temperature goes below 0. Let's learn what this type of number is called and how to identify them.
Identify integers
Integers are made up of positive and negative whole numbers, as well as the number 0. The positive sign (+) indicates a quantity that is greater than zero, while the negative sign (-) indicates a quantity that is less than zero. These signs are important in mathematics for determining the direction and value of quantities. Here is a partial list of the set of integers, which continues up toward positive infinity and down toward negative infinity.
\left\{\ldots ,-3,\,-2,\,-1,\,0,\,1,\,2,\,3,\,\ldots\right\}
We know that 1 is less than 2, that 2 is less than 3, and so on. We can apply that to negatives as well, for example -3 is less than -2.
When we are asked to identify if a number is an integer or not, we can ask ourselves, is it a positive or negative whole number, or 0? If the answer is yes, then the number is an integer.
Examples
Example 1
Is the following number an integer?
+19
Example 2
State whether each of the following numbers is an integer: -2, \, \dfrac{1}{2}, \, 0.4
When we are asked to identify if a number is an integer or not, we can ask ourselves, is it a positive or negative whole number, or 0?
Location of integers on the number line
We can identify and represent integers using a number line. A number line is a visual representation of numbers on a straight line. The straight line can be horizontal or vertical and can be extended to both directions. Number lines can be used to compare numbers and perform operations.
We can identify an integer on the number line by plotting a point at that integer. On the number line below we can see that the point is at the mark labeled with the integer -3. This means that the point on the number line is at -3.
However, not every number line has labels for all the marks. On the number line below, the location of the point on the number line has not been labeled.
In order to find the missing label we need to find the distance between each mark. We can do this by comparing the number of gaps between the existing labels with the distance between the integer labels.
In this case, we can see that there are three gaps between the labels of 0 and 3. This means that there is a distance of 3 units shared between three gaps, so each gap will be equal to 1 unit. Since the point is located one mark to the right of 3, the integer we are looking for is 1 unit greater than 3. So the location of the point is 4.
Examples
Example 3
Determine if the following number is an integer:
Example 4
Where is the point plotted on the number line?
To locate an integer on the number line, plot the labeled point of the integer. If the point is not labeled, find the distance between each mark.