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Rational or Irrational Calculator

Rational or Irrational Calculator

Select the operation and provide inputs according to it. The calculator will immediately figure out whether it is rational or irrational.


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Use this free online rational or irrational calculator to know whether the entered value is rational or irrational by applying a certain operation. Let us further discuss rational and irrational terminologies.

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What Are Rational And Irrational Numbers?

Let us have a look of the divisible and non-divisible numbers below:

Rational Numbers:

Any number that can easily be written in the form of p/q, where p, q are any integer numbers and q is not equal to zero (q ≠ 0).

For example:

2, 2/4, 7/7, \(\sqrt{4}\), and 4/2 are considered as the rational numbers and could also be checked by using this free rational number calculator.

Identification of Rational Numbers:

  • Every integer number is rational. This is because we can consider 1 in its denominator which attains the form of p/q
  • When it comes to under root, then the number whose perfect root is possible is considered a rational number

The free rational number checker instantly lets you know whether the number you entered is rational or not. How does it sound?

Types of Rational Numbers:

Rational numbers are of two types that are enlisted as below:

Terminating Rational Numbers:

If the number of digits after the decimal point are finite, then it is called the terminating rational number.

For example:

1/4 = 0.25,

2/4 = 0.5, and

2/7 = 0.2857142857

All above are terminating rational numbers as all have finite decimal places. You can also go for verification by relying on our best rational or irrational calculator.

Recurring Rational Numbers:

The numbers that are not terminating but contain a single number or group of numbers that go on repeating them again and again for indefinite times are recurring rational numbers.

For example:

4/9 = 0.444444444…

4/9 = 0.4

The following table shows various rational numbers that are often used in calculations:

Is 0 a rational number Yes
is 3/5 a rational or irrational number Rational 
is 6.7234724 irrational Yes
is 3.587 a rational or irrational number Rational
is 2.72135 rational or irrational Rational
3.587 rational or irrational Rational
is 0.684 a rational number Yes
is 3.587 a rational number Yes
is 0.1875 a rational number Yes
Is 74.721 a rational number? Yes
Is 1.345 a rational number? Yes 
is 6.5 rational or irrational Rational
is 21.989 an irrational number Yes
Is 3.444 a rational number? Yes
Is 2.3333 a rational number? Yes
Is 5 a rational number Yes
Is 2 a rational number Yes
is 1/2 a rational number Yes
is 5/2 rational or irrational Rational
Is 4.567 a rational number? Yes


Irrational Numbers:

The numbers that can never be written in the form of p/q are known as irrational numbers. You can get to know if a number is irrational or not by using a rational and irrational numbers calculator in a fragment of seconds.

For example:

22/7, \(\sqrt{3}\), \(\sqrt{5}\), and \(\sqrt{10}\) are irrational numbers.

Identification of Irrational Numbers:

  • The numbers whose under root does not yield a perfect square are irrational number
  • \(\pi\) is an irrational number
  • Irrational numbers are non-terminating and non-recurring

All of the above mentioned conditions are also fulfilled by our best irrational number calculator to determine accurate output against any number.

Special Condition:

If there comes a zero in the denominator, then it is neither a rational number nor an irrational number. Even our free online rational or irrational calculator also denies such an input as it is against the mathematical laws.

Rules of Rational and Irrational Numbers:

The following rules imply on the rational and irrational numbers as defined below:


  • If you add two rational numbers, you will always get a rational number
  • If you add two irrational numbers, the result may or may not be an irrational number


  • The multiplication of two rational numbers is always a rational number
  • If you multiply two irrational numbers, the resulting number may or may not be irrational

How To Identify Rational And Irrational Numbers?

Let us resolve a couple of examples to understand the maths of rational and irrational numbers. Let us go!

Example # 01:
Check whether the number \(\sqrt{8}\) is a rational number or not.

$$ \sqrt{8} $$

$$ \sqrt{2*4} $$

$$ \sqrt{2*2^{2}} $$

$$ 2\sqrt{2} $$

As the square root of 2 is irrational, so the whole number will become irrational too. In case of any doubt, let the free rational irrational calculator fade it away.

Example # 02:
Whether the given number is rational or irrational?
$$ 0/456676 $$

As the given number is in the form of p/q, you can consider it as a rational number. For further instance, you can also commence our free number set calculator that will also validate this answer.

How Rational or Irrational Calculator Works?

Let this free real numbers calculator determine if the real number entered are rational or irrational. Want to know how it works? Let’s move ahead!


  • From the first drop-down list, select the operation you want to apply to number
  • After that enter the numbers in their designated fields
  • Now tap the calculate button


  • The free rational and irrational calculator displays if:
  • The given number is rational
  • The given number is irrational


What is a simple trick to determine the rational number in between the two rational numbers?

The simplest way to find the rational number in between any two rational numbers is to divide the sum of both the numbers by 2. At last, you can verify the answer with the help of our free online rational or irrational calculator.

What are two rational numbers between 4 and 5?

We can write the given numbers as 4/1 and 5/1.
Now we have:
4/1 * 10/10 = 40/10
5/1 * 10/10 = 50/10
So now we have the two numbers as follows:
40/10, 41/10, 42/10, 50/10

The above two bold numbers are the two rational numbers between 4 and 5. Rest of the verification can be performed by using a free real number calculator.


Rational and irrational numbers are very important as there are many calculations in mathematical analysis that may not be completed with only real numbers. That is why we have developed this free rational or irrational calculator to make you people feel at ease while doing various mathematical computations.


From the source of wikipedia: Rational number, Terminology, Arithmetic, Continued fraction representation, Properties

From the source of khan academy: Ordering negative numbers, Ordering rational numbers

From the source of lumen learning: Identifying Rational and Irrational Numbers, Classifying Real Numbers