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 an online tool that identifies the given number is rational or irrational. It takes a 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 number that can be expressed 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 integers 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 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 into 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 depending 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:
- Roberts, D. Rational, and Irrational Numbers - MathBitsNotebook(A1 - CCSS Math).
- Classifying numbers: Rational & Irrational | Algebra (video) | Khan Academy.