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Rational or Irrational Number Calculator

Select the operator and enter the required values to identify a number using a rational or irrational calculator.

Rational and Irrational

The rational number calculator is online tool that identifies the given number as rational or irrational. It takes numerator and denominator to check a fraction, index value and a number in case of a root value.

Rational or irrational checker tells us if a number is rational or irrational and shows the simplified value of the given fraction.


What is a rational number?

Rational number is a numbers that can be express as the ratio of two integers. Generally, it’s written in the form of p/q where the condition must be q ≠ 0.

For example,

4/5, 2/3

All the integers, whole numbers, even and odd numbers are rational numbers. This is because the integer numbers are considered of having the denominator of 1.

3 = 3/1


What is an irrational number?

An irrational number is a number that cannot express the ratio between two numbers. We can say that the numbers that are not divisible to the simplest form are considered an irrational number.

For example,

√7, 54.72410, π


How to identify a rational and irrational number?

The following conditions should be followed to identify a rational or irrational number.

Conditions for rational number

Conditions for Irrational number

It is written in the form of “p/q” and the q is not equal to 0 (q ≠ 0).

The square roots that are not perfectly square to any of the integer e.g. √8, √20.

The p/q value can be further shortened through division and it can be converted into the decimal form

The decimals that don’t stop or repeating are irrational number.

The set of rational numbers can include the positive, negative integers and a zero where it can be written in the fraction.

“π”, which is also known as the “pie.”

If you don’t want to dive in these conditions to check a number, use our rational and irrational numbers calculator above.


Is the square root of a number a rational number?

The square root of a number can be a rational or irrational number depends on the condition and the number.

If the square root is a perfect square, then it would be a rational number. On the other side, if the square root of the number is not perfect, it will be an irrational number. i.e., √10 = 3.16227766017.

Examples:

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

References:

  1. Roberts, D. Rational, and Irrational Numbers - MathBitsNotebook(A1 - CCSS Math).
  2. Classifying numbers: Rational & Irrational | Algebra (video) | Khan Academy.