Representation of Real Numbers on a Line

In mathematics, numbers play a significant role. A number line is a straight line representing all integers at equal intervals. This line extends to infinity from both directions, and has both negative and positive integers. A number can be expressed as a mathematical value that helps in counting and measuring objects by performing several mathematical calculations. 

 This article talks about the representation of real numbers on a line. It gives an explanation of the concept of the number system in maths, a thorough explanation of real numbers, representation of real numbers on a line, and other related topics. So, let’s start by describing the representation of real numbers on a line in the maths study material.

Concept of the number system 

A number system is a major term of mathematics that mainly deals with the process of writing and expressing numbers. It is often referred to as a mathematical representation of numbers using a given set of digits or numbers in a consistent manner. The value of the digit can be determined in three major ways: the digit; the base of the number system; and the position of the digit in the number. 

 There are four types of numbers in a number system. These include: 

• Octal numbers with base 8

• Binary numbers with base 2

• Decimal numbers with base 10

• Hexadecimal numbers with base 16.

 What are real numbers? 

In simple terms, real numbers can be described as the set of rational and irrational numbers. These include natural numbers, whole numbers, integers, and rational and irrational numbers. All these types of numbers can be easily represented on the number line. All the arithmetic operations, including addition, multiplication, subtraction, and division, can be easily performed on real numbers. Also, imaginary numbers are not real numbers, and hence they cannot be plotted on the number line. Some common examples of real numbers are 23, -12, 6.99, 5/2, π, and so on. 

Set of real numbers 

The set of real numbers includes several types of numbers such as natural and whole numbers, integers, and rational and irrational numbers.  

Real number line 

The number line is mainly a simple line with different points called coordinates. On the number line, ‘0’ is termed as the origin. The right side of the number line has all positive numbers, whereas the negative numbers are plotted on the left-hand side of the number line.

Representing real numbers on the number line 

Here are the steps to represent real numbers of the number line – 

 Step 1: Draw a horizontal line with arrows on both sides. Mark point ‘0’ anywhere on the line. 

Step 2: Using a scale, start marking the real numbers of the number line at equal distance. 

Step 3: Make sure you’re marking the positive numbers on the right side of the point ‘0’ and the negative numbers on the left side. 

Step 4: In case the given point appears to be larger, adjust your scale accordingly. 

Step 5: In case the given number is an irrational or a rational number, change them into the decimal form and start plotting on the number line. 

Using these steps, you can easily represent real numbers on a number line. 

Conclusion 

Now you understand the representation of real numbers on a line. A number line is a straight line representing all integers at equal intervals. This line extends to infinity from both directions, and has both negative and positive integers. On the number line, the right side of the number line has all positive numbers, whereas the negative numbers are plotted on the left-hand side of the number line.

In this article describing the representation of real numbers on a line, we studied the concept of the number line in length. We also covered several other topics, such as real numbers, and representation of real numbers on a line. We hope this study material helped you better understand the representation of real numbers on a line.