Representation Of Irrational Numbers On Number Line Cuemath

Bonisiwe Shabane

-Oct 30, 2025, 10:40 PM

representation of irrational numbers on number line cuemath

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. Representation of irrational numbers can be done by using the Pythagorean theorem. We break down the number inside the square root into two equal parts, where each part represents the side of the right triangle that we form.

The hypotenuse of the right triangle represents the given irrational number. This length is used to mark the approximate location of the irrational number on the number line. Alt tag: Irrational numbers on number line – understanding the basics Each and every point on a number line represents a unique real number. We can represent each real number with the help of a unique point on the number line. Irrational numbers and rational numbers together form the set of real numbers.

Irrational numbers are the real numbers that cannot be written in the form of a ratio (rational form) $\frac{p}{q}$, where p, q are integers and $q \neq 0$. In simple words, all the real numbers that are not rational numbers are irrational. These numbers include non-terminating, non-repeating decimals. function i3u_Function() { var x = document.getElementById("i3u"); if (x.style.display === "none") { x.style.display = "block"; } else { x.style.display = "none"; } } Hi, and welcome to this review of irrational numbers! Today, we’ll be reminded of what an irrational number is, and look at where they fall on a number line.

Let’s get started! So, first, what is an irrational number? It is easy to determine whether a number is rational or irrational based on the word itself. Look closely… the root word ratio tells us that these numbers can be written as a fraction. Rational numbers include all proper and improper fractions. Decimals that repeat or that terminate can be written as fractions, so they are considered rational.

For example, .3333333 can be expressed as the fraction, 13, so it is a rational number. This diagram clearly shows that there is no overlap between the rational and irrational number sets. Another way of thinking about it is that irrational numbers are those that cannot be written as a fraction. To represent an irrational number on the number line. Theory Pythagoras’ theorem – In a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. We can write √2 = .

So, if the base and the perpendicular of a right-angled triangle measure 1 unit each, the hypotenuse will measure , or √2 units. We shall use this concept to represent the irrational numbers on the number line. Procedure To represent √2 on the number line Step 1: Draw a straight line OX on the sheet of white paper. Starting from point O, mark points 1, 2, 3, … at equal distances of 1 unit (take 1 unit = 1 cm). Then, the line OX can be used as the number line. Step 2: Fold the paper along the line that passes through the point marked T’ and cuts the line OX such that the part of line OX on one side of the fold falls...

Make a crease and unfold the paper. From the point marked T’ draw a line of length 11 unit moving upwards along the crease. Mark the top end of this line as point M. Join OM. Then, clearly OM = √2 units (by Pythagoras’ theorem). Step 3: With O as the centre and OM as the radius, draw an arc cutting the line OX at a point A as shown in Figure 3.1.

Then, the point A represents the number √2 on the number line. Result Any irrational number can be represented on the number line (using the above method). Remarks: The students may be asked to represent other irrational numbers such as 43,45, etc., on the 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 horizontal number line, the numbers increase; as we move towards the left, the numbers decrease.

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. Zero (0) is considered to be the origin of a number line. The numbers to the left of 0 are negative numbers and the numbers to the right of 0 are all positive numbers. So, we can say that on a number line, as we move towards the right, the value of numbers increases. This means that the numbers present on the right are larger than the numbers on the left.

For example, 3 comes to the right of 1, so 3 > 1. Observe the horizontal number line given below. In order to draw a number line or to plot a number on it, we use the following steps. As we discussed above, a number line has positive and negative numbers. The section of the number line to the left side of zero forms a negative number line. While, the section on the right side of zero contains all positive numbers, and it forms a positive number line.

It can be extended to infinity from both ends (right and left). The parts of a number line and some of its properties are given below. Observe the parts of a number line given below to relate to the following features of a number line. Rational numbers are defined as any number that can be represented as the ratio of two integers where the denominator is not equal to zero. Rational numbers on a number line are the way of representing positive and negative rational numbers visually. Let us understand more about rational numbers on a number line in this article.

Rational numbers are defined as a number that can be represented in the form of p/q where p and q are integers and q ≠ 0. Representation of rational numbers on a number line is defined as plotting or graphing positive and negative rational numbers on a number line. Number line helps us to find an infinite number of rational numbers between any two rational numbers by increasing the number of divisions. Representation of rational numbers on a number line is very similar to the representation of negative integers or negative fractions on a number line. On a number line, keeping '0' as the reference, the left-hand side of '0' represents the negative region, and the right-hand side of '0' represents the positive region. Let us look into the steps to represent rational numbers on a number line as shown below.

Example: We will plot 4/5 on the number line. Step I: Draw a number line by marking 0 as the reference.

Representation Of Irrational Numbers On Number Line Cuemath

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