Representation Of Real Numbers On Number Line Embibe

Bonisiwe Shabane

-Oct 31, 2025, 1:45 AM

representation of real numbers on number line embibe

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. Access topical questions for focused practice. Detailed analysis of past paper patterns and trends. The number line is a straight, horizontal line where each point corresponds to a real number.

It extends infinitely in both the positive and negative directions, allowing for the representation of all real numbers, including integers, fractions, and irrational numbers. The number line is divided into equal intervals, each representing a unit increment. Real numbers encompass both rational and irrational numbers. Rational numbers can be expressed as the quotient of two integers, such as $\frac{3}{4}$ or $-2$, whereas irrational numbers cannot be expressed as simple fractions, such as $\sqrt{2}$ or $\pi$. On the number line, rational numbers are represented by precise points, while irrational numbers are indicated by their approximate locations. To plot a real number on the number line:

This topic covers concepts such as Algebraic Operations on Real Numbers, Real Numbers, Unique Representation of Real Numbers on Number Line, and Representing Real Numbers on the Number Line by Successive Magnification Method. Check whether their product is a rational number or not? Check whether their product is a rational number or not? One way to visually represent the real numbers $\mathbb{R}$ is by a real number line, a horizontal line such that each point on the line corresponds to a real number and each real number... Since the number line represents all real numbers and since zero is a real number, there is a point on the line that represents zero (called the origin). Then the points on the line to the right of the origin represent positive numbers while the points on the line to the left of the origin represent negative numbers.

In the following visualization of the real number line, the integers are marked as evenly spaced points on the line, but the real number line also represents all real numbers in between the integers... In the problems below, we will assume that the evenly spaced tick marks correspond to integers, and one unit corresponds to the distance between consecutive integers. Solution: Since the evenly spaced tick marks correspond to consecutive integers, we can label the tick marks around point $a$ as follows:

Representation Of Real Numbers On Number Line Embibe

People Also Search

Real Numbers Can Be Represented On A Number Line, Which

The Set Of Real Numbers Is Represented By R. The

All The Positive Numbers Or Integers Are Represented On The

In This Article, We Will Learn About The Representation Of

For Instance, The Real Number 3 Is Positioned Between 2