Graphing Real Numbers on a Number Line

Instructor: David Karsner

David holds a Master of Arts in Education

The number line is a one-dimensional graph that can display all of the rational numbers (whole numbers, integers, and rational numbers). Irrational numbers cannot be placed accurately on a number line.

The Vague Text Message

Times Square
TimesSquare

I was standing in Times Square in New York City waiting on friend and got a text saying she was four blocks away from Times Square, and I should meet her there. If you are familiar with Times Square, you might already see the problem. There are several streets that come into Times Square and all of them have a place that is four blocks away. If she had said I am four blocks away from Times Square on Broadway, it would have reduced the places to look to two. With only two options, the scenario resembles a number line. This lesson is about how to construct a number line and how to place numbers on the number line.

The Number Line

All rational numbers can be placed on a number line to signify their position. Every spot on the number line shows how many units away from zero a number is and in what direction. For example, the spot labeled -3 on the number line is 3 units to the left of zero. Zero is the most important spot on the number line. All of the other spots on the number line give their location based on zero. If you move to the right from zero on the number line, the numbers become larger positive numbers. As you move to the left from zero, the numbers become larger negative numbers.

Placing the Whole Numbers

To create a number line with whole numbers (0,1,2,3,,,,etc), draw a line segment with arrows on each end signifying that it goes on forever in both directions. Place a tic mark on the line segment and label this tic mark as zero. Move to the right a little bit and place another tic mark. This tic mark should be labeled as one. Continue to place tic marks along the line segment. Be sure to keep the same distance between each of the subsequent tic marks as you did between 0 and 1. Label the rest of the tic marks as 2,3,4,,,,etc. The location on the line segment of the zero and the distance between tics will be determined by the situation for which you have to draw a number line.

Whole Numbers on a Number Line
NumberLineWhole

Placing the Integers

Integers are the whole numbers plus their negative counterparts. To create a number line that has integers on it: begin by creating a number line for whole numbers, but place the zero so that you have room to the left. The negative numbers will be to the left of the zero. Whatever distance you move to the right from zero to one, move to the left and place -1. Continue the process with -2,-3,-4,,,,,etc.

Integers on a Number Line
NumberLineIntegers

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