The Real Number Line
We can visualize all numbers in the real number set (and their locations within it) with the real number line. Starting at the origin (or at the number zero), the line expands indefinitely in either direction. We determine the locations of different numbers on the line with labeled tick marks. To focus on a particular number on the line, we plot its coordinate.
![The Number Line [(-5),5]](/assets/images/number_line/real_number_line.svg)
Plotting Coordinates
To plot a coordinate, place a heavy dot on its location on the number line as indicated by the tick marks.
Example 1
- Plot the coordinate of the number 5 on the number line below:
Checkpoint 1
- Count the number of dots in the picture below, then plot the number on the number line:
Checkpoint 2
- Count the number of squares in the picture below, then plot the number on the number line:
Checkpoint 3
- Count the number of triangles in the picture below, then plot the number on the number line:
Click for solutions...Plotting Sets
We use sets to group together multiple quantities of interest. We graph sets on a number line by plotting the coordinate of each value together on the same line. The not only allows us to see each value altogether, but also allows us to quickly compare each value to the others. This allows us to see which values are greater (or less) and by how much.
Example 2
- A local pet store owner wants help visualizing his the number of animals he has in his store. To help him, plot the coordinates of the number of each animal in stock.
Puppies: 4
Cats: 8
Rabbits: 3
Guinea Pigs: 5
Parakeets: 6
Lizards: 1
Checkpoint 4
- A local neighbor has a garden, and she would like a graph to better visualize the number of each type of vegetable the garden produced this season.
Corn: 13
Carrots: 8
Cabbage: 4
Lettuce: 5
Tomatoes: 10
Green Beans: 19
- Use the number line below to graph the number of vegetables. Label each plot with the name of the vegetable.
Click for solutions...The number line can also be rotated to the up/down position to show vertical data.
Checkpoint 5
- The coach for the local archery club would like your help visualizing the performance of one of her star athletes.
- To key-in on his vertical performance, she has him line up and shoot 5 arrows at the target. Then, she recorded the number of centimeters above or below the bullseye each arrow landed. Graph each point on the number line.
a. 2 cm
b. 4 cm
c. -1 cm
d. 0 cm
e. 1 cm
- Extra Credit: Give the archer a tip to help him do better based on his performance.
Exercises
Exercise Set 1 - Whole Numbers (1-10)
- Whole numbers are positive numbers which have no fractional or decimal parts.
1. Write the number plotted on each number line:
1-1.)
1-2.)
1-3.)
1-4.)
1-5.)
2. Plot the following numbers on the number line:
2-1.) a. 4, b. 8, c. 9, d. 10
2-2.) a. 1, b. 5, c. 6, d. 7
2-3.) a. 0, b. 3, c. 4, d. 9
Exercise Set 2 - Whole Numbers (1-100)
- As we plot larger numbers, we need larger plots in which to fit them. Another useful trick is to cut off the ends of the number line and only focus on surrounding values when graphing.
1. Write the number graphed on each line:
1-1.)
1-2.)
1-3.)
1-4.)
1-5.)
1-6.)
1-7.)
1-8.)
1-9.)
1-10.)
2. Plot the following numbers on the number line:
2-1.) 50
2-2.) 12
2-3.) 42
2-4.) 39
2-5.) 88
2-6.) 21
2-7.) 13
2-8.) 74
2-9.) 97
2-10.) 3
Exercise Set 3 - Complete the Number Line
- A classmate has 2 CUTE gerbils. Last night, they both escaped their cage and nibbled on her homework. She still has some of the assignment, and she wants you to help her complete the rest.
1. Complete each number line by filling in the missing values:
1-1.)
1-2.)
1-3.)
1-4.)
2. Use the number line to find the answer to each question.
a. If B=1 and D=3, what is A?
b. If A=4 and E=8, what is C?
c. If A=-13 andE=-9, what is C?
d. If A=-4 and C=-2, what is E?
e. If B=-2 and E=1, what is D?
Exercise Set 4 - Word Problems
1. Car Dealership
A local car dealership wants a graph that illustrates the number of cars they've sold based on their color. Plot and label each quantity of car sales (by color):
black: 8
red: 4
green: 1
blue: 3
gray: 10
white: 6
- Extra Credit: Identify a trend for the cars that are selling.
2. Long Jump Competition
A track & field team would like your help visualizing the data from the long jump competition at the last meet. Plot each jump on the number line (which is in feet) and label each coordinate with the name of the athlete.
Christopher: 17ft
Fahim: 16ft
David: 13ft
Adam: 21ft
Omar: 20ft
Felix: 19ft
- Extra Credit: Highlight any athletes doing well or poorly based on their performance.