Expressing Numbers on the Number Line concept is here. Check the various numbers like natural numbers, rational numbers, whole numbers, etc., and how they lie on the number line. Know the steps to mark the numbers on the number line. Follow the various terminology used in marking the numbers on a line. Scroll down to the next sections to check the complete details regarding expressing numbers.

Read More:

- Addition of Integers on a Number Line
- Representation of Integers on a Number Line
- Representing Fractions On Number Line

## Expressing Numbers on the Number Line

The simple number line or a real number generally allows you to display all the numbers like natural, real, rational visually. You have to mark the unique points on the line and the number associated with the point on the line is called coordinate. The real number line which is associated with the coordinate is known as its graph.

### How to Construct a Number Line?

To construct the number line, first, you have to draw the horizontal line mentioning arrows at both the ends which indicates that the line continues without any bound. Then, choose the point which represents the number zero, then this point is called the origin.

To define the scale, you must mark the consistent lengths on both sides considering origin as the middle point, and label each of the tick marks to define the scale. To the right of the origin, including all the positive real numbers, and to the left of the origin include all the negative real numbers. As zero is neither positive nor negative, it is included in the middle of the line. Each tick label on the line represents one single unit.

We use many symbols which help us efficiently and communicate the relationships between each number on a number line. The following are the symbols used that describe an equality relationship between the numbers.

= represents “is equal to”

≠ represents “is not equal to”

≈ represents “is approximately equal to”

**Expressing Whole Numbers on the Number Line**

**Expressing Decimals and Fractions on the Number Line**

### Logarithmic Scale

You can easily learn how to express numbers on a number line. With the help of the number line, you can understand the natural, rational, whole, fractions which represent the numbers that are in the expanded forms. the distance between two points on the number line is called the unit length and the difference of the numbers equal to 1.

A logarithmic scale is the most common choice where the positive numbers on the number line where the unit length. Consider the ratios of the represented numbers on the number line that has the fixed values. In the logarithmic scale, the origin of the number line represents 1.

### Combining Number Lines

Imaginary numbers are represented by a line that is drawn through the origin at the right angle to the real number. This is called the imaginary number. We can combine the number lines if we have to plot various numbers like decimal, positive and negative values, etc.

### Use of Number Lines

We can number lines for various operations like addition, subtraction, etc.

#### Number Line Addition

Let’s assume that you have 3 chocolates and your friend gave 3 more. Find the total number of chocolates you have with you. Plot the number of chocolates on a number line?

As we know that the numbers on the number line increase as we go to the right, we started at 2 and then take 3 steps to the right of the line to get the answer. Therefore, you have 5 chocolates in total.

#### Number Line Subtraction

Let’s say that you have 7 chocolates with you and you gave 3 chocolates to your friend. Find the number of chocolates you have now. Solve the above equation on a number line?

As we know that the numbers decrease on the number line as we go to the left, we start from 7 and take 3 steps on the line to the left to get the final solution.

Therefore, there are 4 chocolates left.

#### Solving Negative Numbers

The number line gives us a clear understanding of negative numbers and solves many questions.

Find how much 3 is more than -1?

**Solution:**

Represent the given problem on the number line.

We can understand the position of the number “-1” and also its movement of reaching towards the number “3” which is moving 3 steps to the right.

### Expressing Numbers on Number Line Examples with Answers

**Problem 1:**

Mary has 4 books. She bought 5 more books from the library. How many books does she have in total?

**Solution:**

As given in the question,

No of books Mary has = 4

No of more books she bought from the library = 5

As we know that the numbers on the number line increase as we go to the right, we started at 4 and then take 5 steps to the right of the line to get the answer. Therefore, she has 9 books in total.

**Problem 2:**

In the next week, Mary returned 7 books to the library. She did not finish reading all the books. How many books did she keep with her in total?

**Solution:**

As given in the question,

Total no of books = 9

No of books she returned to the library = 7

As we know that the numbers decrease on the number line as we go to the left, we start from 9 and take 2 steps on the line to get the value 7.

Therefore, the result value is 9 – 7 = 2

### FAQs on Expressing Numbers on the Number Line

**1. What is the number line in maths?**

In maths, the number line is the straight line which has the numbers noted at equal segments or intervals along with the length. The number line is represented horizontally and can be extended in any of the directions needed.

**2. How do you note the numbers on a number line?**

On the horizontal line, we mark the middle value as o. Start the number line with the number zero. Mark hash marks at regular intervals and write each number at regular intervals. Note all the positive numbers on the right side of the number line and all the negative numbers on the left side of the number line.

**3. Why do we use number lines?**

Number lines are really important as they represent the numbers in the real life. They enable negative numbers which are represented in the way they make sense. The result of the number line becomes a powerful visual tool and versatile to help all the students understand the numbers easily.