In science, we should know about various numbers. These numbers are ideal squares, surds, non-ending decimals, ending decimals, non-rehashing decimals and rehashing decimals, and so forth. They are regularly isolated into two classes.

The main classification is alluded to as objective numbers, while the subsequent one is considered irrational. Understanding the differentiation between rational and irrational numbers can be somewhat extreme but charming when perceived for understudies. We will endeavour to characterise the contrast among rational and irrational numbers utilising the guide of models.

So, let’s start by learning the difference between Rational and Irrational numbers.

What is a Rational Number?

The number made out of numbers that can be communicated in structures p/q is known as the rational number. It is alluded to by (Q) that is in the genuine number (R), and their member’s numbers (Z) are called normal numbers (N). In this situation, the numbers comprise two sections: denominator q that can’t be zero, just as numerator p.

Every member’s number likewise has a place with reasonable numbers, for example, 7=7/1. Thus, the rehashing or ending decimal series is known as an objective number. Likewise, the duplication and whole numbers of the various quantities of the reasonable number may change into the expression “levelheaded number”.

What is an Irrational Number?

Irrational numbers aren’t rational and belong to real numbers. They cannot be described in terms of an equation of 2 integers. A common illustration of the numbers is √3, √2, etc. The square roots of all natural numbers, except perfect squares, are not rational.

Difference Between Rational and Irrational Numbers

A majority of students cannot comprehend the distinction between rational and irrational numbers by using their definitions. They need more information to comprehend the distinction between rational and Irrational numbers. The main difference between them can be found below:

1. Perfect Squares are Rational Numbers, and Surds are Irrational Numbers

The perfect squares are all rational numbers. The perfect squares are those that correspond to the circumferences and squares of an integer. In other words, you can multiply an integer by the same number of numbers and have the perfect square.

The correct squares are √ 4, √ 49, √ 324, √ 1089 as well as √ 1369. After taking those square roots for these perfect squares, we will get 2, 7,18, 33, and 37. 2, 7, 18, 33, and 37 represent both integers.

However, Surds, in general, are Irrational Numbers. Surds are numbers that do not represent the numbers that are the squares that make up an integer. Also, they aren’t any of the multiplications that a number with the integer. Surds examples comprise 2, 3, and 7. When we take those surds’ square roots, we will get 1.41, 1.73, and 2.64. 1.41, 1.73, and 2.64 aren’t integers.

2. Terminating Decimals are Rational Numbers

All terminable decimals have rational values. These are decimals that have a limited number of digits that follow that decimal mark. For instance, 1.25, 2.34, and 6.94 are all rational numbers.

On the other hand, non-terminating decimals refer to numbers with an infinite number of digits following the decimal mark. For instance, 1.235434 …, 3.4444…, and 6.909090… are all non-terminating decimals. Non-terminating decimals are either rational or irrational. They are discussed in the next section.

3. Repeating Decimals are Rational Numbers, and Non-Repeating Decimals are Irrational Numbers

All repeating decimals are rational numbers. The decimals that repeat are decimals that have digits that repeat on and off. Examples of repeating decimals include 222222, 33333333, and 555555.

On the contrary, all non-repeating decimals are irrational numbers. The non-repeating decimals are the ones that don’t repeat over and. Examples of non-repeating decimals include 3426452, 0435623, and 908612.

Can we be able to find Irrational Numbers Between Two Rational Numbers?

It is simple to discover the irrational number between 2 rational numbers. It is our goal to master this idea with the help of a case study. Find irrational numbers in the range of the numbers 3-4. It is possible to find the irrational numbers that lie between the two numbers using these steps

  1. The first step is to find squares that correspond to the numbers given. In this instance, squares that are 3 and 4 are 9 and 16, respectively.
  2. In the second step, you must look for the prime numbers in their squares. Prime numbers that lie between 9 and 16 are 11 and 13.
  3. When we take their square roots, we can get the necessary irrational numbers. Square roots for 11 and 13 equal 3.316624… as well as 3.6055512… each. In other words, 3. 3.6055512… 316624… and 3.6055512… is a non-repeating decimal. These are therefore irrational numbers.

Practical Examples

After better understanding the distinction between rational and non-rational numbers, we attempt to distinguish rational and irrational numbers from the given numbers. Divide the rational numbers from the next numbers; √5, 6/5, √25, 5/4, √36, √8, 16/3.

5/4 (1.25) is also an arithmetic number. 5 is an irrational number because 5 is an irrational number. After all, it’s a surd, and it isn’t the factor of an integer by itself. However, 25 is considered a rational figure because it is a quadrilateral of an integer 5 on its own.

The number is considered a terminating decimal since it has a finite number of digits following the decimal mark. 6.5% (1.2) can also be considered a rational decimal since a limited number of digits follow that decimal mark.

The number 36 also is a rational one since it is an ideal square. 8 . is an irrational value because it is unsure. The answer to 16.3 is 5.33333… This indicates that it’s the result of a repeating decimal. We are aware that a repetition decimal is also a rational number.

The answer to six-sevenths is 0.85714… This indicates that it’s not a repeating decimal. We are aware that all non-repeating decimals can be considered irrational.


At the final point, you will be able to easily discern the difference between rational and non-rational numbers with the aid of these important factors:

Rational numbers = Perfect squares + Terminating decimals + Repeating decimals

Still have any questions or confusion, please feel free to reach out.


Please enter your comment!
Please enter your name here