How To Use A Number Line

Number Line

A number line is a visual representation of numbers on a straight line. This line is used to compare numbers that are placed at equal intervals on an infinite line that extends on both sides, horizontally or vertically. As we move towards the right side of a number line, the numbers increase; as we move towards the left, the numbers decrease.

1.	What is a Number Line?
2.	Negative and Positive Number Line
3.	Number Line with Decimals
4.	Inequalities on a Number Line
5.	FAQs on Number Line

What is a Number Line?

A visual representation of numbers on a straight line drawn either horizontally or vertically is known as a number line. Writing down numbers on a number line makes it easy for us to compare them and to perform basic arithmetic operations on them. There are three parts of a number line which are - negative side, zero, and positive side. Numbers to the left of 0 are negative numbers and numbers to the right of 0 are all positive numbers. So, we can say that on a number line, the numbers present on the right are larger than the numbers on their left. For example, 3 comes to the right of 1, so 3 > 1. Look at the image of a number line given below.

number line

How to Draw a Number Line?

To make a number line or to plot a number on it, follow the steps given below:

Step 1: Draw a horizontal line with arrows on both ends. [You can also draw a vertical number line]
Step 2: Choose a scale depending on the given number. For example, if you have to plot 5, then you can choose a scale of 1. If you have to plot 50, you can choose a scale of either 5, 10, or 25. [Determining an appropriate scale depends on the factors of the given number]
Step 3: Mark the points at equal intervals. So, if you have chosen 1 as the scale, then mark 0, 1, 2, 3, 4, and so on.
Step 4: Locate the given number. Highlight that point with a circle.

Negative and Positive Number Line

As we discussed above, there are two different types of numbers that can be represented on a number line, which are positive and negative numbers. The section of the number line to the left side of zero is known as a negative number line. While, the section on the right side of zero contains all positive numbers, and therefore it is known as a positive number line. It can be extended to infinity from both ends (right and left). Some of the properties of the negative and positive number lines are given below:

Numbers on the right side are greater than the numbers on their left.
Numbers on the left side are smaller than the numbers on their right.
0 is the point of origin or the middle point of the number line.
Numbers are placed at equal intervals.

Look at the number line graph given below.

negative and positive number line

Number Line with Decimals

We can represent any type of number on a number line such as whole numbers, fractions, decimals, integers, rational numbers, and even irrational numbers. In this section, we are going to learn how to draw a number line with decimals. To represent decimals on a number line, we need to look at the digits starting from the left. For example, if we represent 2.4 on a number line, follow the steps given below:

Identify the whole number part of the given decimal. Here, in 2.4, the whole number part has one digit, i.e. 2.
Now, draw a number line and mark two points on it with a suitable gap in between. 2.4 lies between 2 and 3, so mark 2 and 3 on the line.
Look at the tenths place digit of the given number. In 2.4, the tenths place digit is 4. Make 10 equal intervals between 2 and 3 and mark 2.4 on the fourth bar to the right of 2.

number line with decimals

This is how we draw a number line with decimals.

Inequalities on a Number Line

Inequality is a mathematical statement used for the comparison of quantities. We can show solutions to inequalities on a number line. For example, if x ≥ 5 is given and we have to represent it on a number line, then we can follow the steps given below:

Draw a number line of a suitable length.
In the given inequality x ≥ 5, the value of x can be 5 or greater than 5. So, it will move to the right of 5.
So, mark 0 anywhere on the line and draw equal intervals to the right, starting from 1 to 5.
Place a black circle on 5 and shade the line from 5 to the right arrow.
That will be the required number line inequality.

If we have to show 5 < x, then we will follow the above steps but the circle at point 5 will be left blank. A blank circle shows that 5 is not included in the solution. If we draw a colored circle, it will show that 5 is included in the solution set of x. Look at the figure given below that represents the following inequalities on a number line: x ≥ 5, x > 5, x ≤ 5, and x < 5.

Inequalities on a number line

Number line Tips and Tricks:

Note the following important tips and tricks on a number line.

We can represent various numbers on the number line, according to our requirements. For example, they can be only positive numbers, or integers between -4 and 3, or even fractions between -2 and 2.
Number lines can help us in real-life situations. For example, they read the altitude (height) which is shown on a GPS device's screen, and can tell you how high or low you are below sea level!

► Topics Related to Number Line

Check these interesting pages to know about the number line and its related topics.

Number Line Addition Worksheets
Number Line Multiplication Worksheets
Fractions on Number Line
Multiplication on Number Line
Addition on Number Line
Subtraction on Number Line
Representation of Real Numbers on Number Line

Number Line Examples

Example 1: A flower is hidden behind an integer which is at a position 7 less than the spot where the butterfly is placed. Can you find the integer?

Solution:

From the above number line, it is clear that the butterfly is placed at 4. 7 steps less than 4 means: 7 steps to the left of number 4 will take the butterfly to the flower. This can also be understood as: + 4 − 7 = −3.
This brings us to -3.
Thus, the flower is hidden behind -3.
∴ The integer is -3.
Example 2: Show the following addition on a number line.

Solution:

To perform addition on a number line we first look for the numbers from where we have to start. Here, the starting number is 300 and we need to add 500 to it. The addition of 300 + 500 is shown in the following number line:
Example 3: Represent y ≥ 2 on a number line.

Solution:

y ≥ 2 means that the value of a variable y is 2 or greater than 2. This can be easily represented on the number line as:

The black region on the line represents y ≥ 2.

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Practice Questions on Number Line

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FAQs on Number Line

What is the Definition of a Number Line?

What is a Number Line Model?

A number line model is a representation of numbers plotted on an infinite line that extends at both ends.

What all Operations can be Performed Using Number Line?

The four basic arithmetic operations of addition, subtraction, multiplication, and division can be easily performed using a number line. For addition and multiplication, we move towards the right side and for subtraction, we move towards the left side of the number line.

What all Numbers can be Represented on a Number Line?

We can represent real numbers on the number line. It includes the set of whole numbers, integers, fractions, decimals, rational and irrational numbers.

How to Perform Addition Using Number Line?

When we perform addition using a number line, we count by moving one interval at a time towards the right side. For example, if we need to solve 4 + 5, we start by marking the number 4 on the number line. Since we are adding 4 and 5, we will move 5 steps to the right. This brings us to 9. Hence, 4 + 5 = 9.

What is an Inequality on a Number Line?

We can easily represent inequalities on a number line. To do that, we just need to circle the value and shade the appropriate region on the number line. For example, to represent x > 7 on the line, we have to draw a line and locate point 7 on it with respect to the origin. Then, we have to circle point 7 and shade the region to the right of 7 on the number line. That will represent that x can take any value greater than 7. Make sure that you will draw a blank circle at point 7. We fill the circle when that value is also included in the solution, for example, in the case of x ≥ 7.

How to Put Fractions on a Number Line?

To represent fractions on a number line, we find two whole numbers between which the fraction is lying. Then we make equal intervals between those two whole numbers and appropriately mark the given fraction.

How to Represent Rational Numbers on Number Line?

Rational numbers can be given in the form of integers, fractions, or decimals. To represent rational numbers on the number line, we locate two integers between which the number is lying. And then we mark the point by making equal intervals between those two points. If the rational number is in the form of an integer, then we can simply locate the point with respect to the origin and mark it.