Representation Of Real Numbers On Number Line Cuemath

Bonisiwe Shabane

-Oct 30, 2025, 8:12 PM

representation of real numbers on number line cuemath

Real numbers can be represented on a number line, which is a straight line that represents the integers in equal intervals. Both positive and negative integers can be represented on a number line in a sequence. This line extends indefinitely at both ends. Number lines represent real numbers i.e natural numbers, whole numbers, integers, rational numbers, and irrational numbers, and are used as a reference for comparing and ordering numbers. The set of real numbers is the union of the set of rational numbers Q and the set of irrational numbers Q'. Therefore, all the numbers such as natural numbers, whole numbers, integers, rational numbers, and irrational numbers are subsets of the set of real numbers.

The set of real numbers is represented by R. The table below represents the number set included in the set of real numbers. Since we know that real numbers can be rational numbers or irrational numbers, every real number can be represented by a unique point on the number line. A real number line simply called a number line, represents real numbers with unique points associated with each number on the line. The point associated with real numbers is called a coordinate. In the number line, the number 0 is called the origin.

All the positive numbers or integers are represented on the right side of the origin, and the negative numbers or integers are represented on the left side of the origin. Here is an image that represents both the negative and positive numbers on a number line. Real numbers include natural numbers, whole numbers, as well as rational and irrational numbers. On a straight number line, each integer is placed at equal intervals. The number line extends infinitely in both directions. We can organize and compare numbers using a number line.

In this article, we will learn about the representation of real numbers on the number line in detail. The set of rational numbers Q and the set of irrational numbers Q’ together make up the set of real numbers. It is denoted as R. Whole numbers, natural numbers, integers, rational, and irrational numbers are all real numbers. Therefore, $R = Q ∪ Q′$ On a number line, each number has a unique point known as a coordinate and has a distinct position.

For instance, the real number 3 is positioned between 2 and 4. On a number line, two numbers cannot share the same position. The origin of a number line is at 0. On the right side of the origin are the positive numbers, while on the left side are the negative numbers. The visual representation of a real number line is: Following the given steps will help us to easily indicate real numbers on a number line using graphs and coordinates.

Step 1: Draw a straight line, mark the origin at 0, and draw arrows on both sides of the origin point. The number line is a fundamental visual tool used in mathematics to represent numbers geometrically. It is a straight line that extends infinitely in both directions and provides a graphical representation of the set of real numbers ($\mathbb{R}$). There is a perfect one-to-one correspondence between every point on this line and every real number; meaning each real number corresponds to a unique point on the line, and each point on the line... A standard number line is constructed with the following key features: The number line helps in visualizing the order of numbers, comparing numbers, and understanding operations like addition and subtraction geometrically.

Integers ($\mathbb{Z} = \{..., -3, -2, -1, 0, 1, 2, 3, ...\}$) are discrete points on the number line. Since they are whole units (positive, negative, or zero), representing them on the number line is straightforward and foundational to understanding the positions of other numbers. To represent integers on the number line, follow these steps: Real Numbers are continuous quantities that can represent a distance along a line, as Real numbers include both rational and irrational numbers. Rational numbers occupy the points at some finite distance and irrational numbers fill the gap between them, making them together to complete the real line. So, in other words, real numbers are those numbers that can be plotted on the real line.

Real numbers include rational numbers including positive and negative integers, fractions, and irrational numbers. Basically, any number that we can think of is a real number. Examples of Rational Numbers are 2, 3.5, 6/7, √5, 0.35, -67, \pi, e, etc. In this article, we will discuss real numbers in detail, including their properties, representation on the number line, and decimal expansion and we will also check if 0 is a real number. Real numbers are all the numbers that can be found on the number line. This includes both rational numbers (like 7, -3, 0.5, and 4/3) and irrational numbers (like √2) .

They encompass integers, fractions, and decimals, representing a continuous, unbroken set of values. The collection of all rational numbers contains all the other numbers like natural numbers, integers, rational as well as irrational. Some examples of real numbers are 3 (a whole number), -1 (an integer), 1/2 (a rational number), √2 (an irrational number), π (an irrational number), 2.5 (a decimal number), etc. The number line is a fundamental concept in mathematics, illustrating how numbers are arranged in a specific order. It is a straight line that extends to infinity in both positive and negative directions and is marked at regular intervals, representing integers. In this article, we will delve into the process of representing real numbers on a number line.

Representation of irrational numbers on a number line can be done by first identifying the origin point and then moving towards the positive or the negative numbers. A number line is a straight line with both positive and negative numbers visually represented. Positive, negative, zero, and decimal numbers can be represented on a number line. In this article, we are going to learn the steps of representation irrational numbers on a number line and solve a few examples to understand the concept better. Irrational numbers are real numbers that cannot be represented as a simple fraction. These cannot be expressed in the form of ratio, such as p/q, where p and q are integers, q≠0.

It is a contradiction of rational numbers. Some of the commonly known examples are π, √2, √5, etc. Irrational numbers consist of non-terminating and non-recurring decimals. Addition, subtraction, multiplication, and division of two irrational numbers may or may not be a rational number. 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. Real numbers can be considered as rational numbers or irrational numbers.

Hence, a unique point is considered to represent them on the number line. Some irrational numbers in the form of √n, where n is a positive integer can be represented on a number line by using the following steps. Let us look at an example to understand this better. Represent √2 on a number line. Grade 10 → Number Systems → Real Numbers ↓ In mathematics, it is important to understand where real numbers lie on the number line.

It is a fundamental concept for many mathematical operations, calculations, and distinctions between numbers. Real numbers consist of all the numbers on the number line, whether positive or negative, and include zero. In this document, we will explore what real numbers are, how they are organized, and how they are represented on the number line. Real numbers are all the numbers you can find on the number line. They include both rational numbers and irrational numbers. Rational numbers are numbers that can be expressed as the fraction a/b, where a and b are integers and b ≠ 0 Examples include 1/2, 4, -3.5, etc.

Irrational numbers are numbers that cannot be written as simple fractions, have non-repeating and non-terminating decimals. Examples are π (pi) and √2 (square root of 2). The number line is a straight line where each point corresponds to a real number. To identify and visualize real numbers more easily, imagine a horizontal line:

Representation Of Real Numbers On Number Line Cuemath

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