# How to Identify Rational and Irrational Numbers?

In this post blog, we teach you the definition of rational and irrational numbers and how to identify them.

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**A step-by-step guide to rational and irrational numbers**

Different types of numbers depend on their properties. For example, rational and irrational numbers are as follows:

**Rational numbers**

A rational number is a number in the form \(\frac{p}{q}\) where \(p\) and \(q\) are integers and \(q\) is not equal to \(0\). The set of rational numbers is denoted by \(Q\).

**How to identify rational numbers?**

Rational numbers can be easily identified with the help of the following properties.

- All integers, whole numbers, natural numbers, and fractions with integers are rational numbers.
- If the decimal form of the number is terminating or repeating, such as \(5.6\) or \(3.151515\), we know that they are rational numbers.
- If the decimal numbers seem never-ending or non-repeating, they are called irrational numbers.
- Another way to identify rational numbers is to see if the number can be expressed as \(\frac{p}{q}\), where \(p\) and \(q\) are integers and \(q\) is not equal to \(0\).

**Irrational numbers**

Irrational numbers are the set of real numbers that cannot be expressed as fractions, \(\frac{p}{q}\) where \(p\) and \(q\) are integers. The denominator \(q\) is not equal to zero \((q≠0)\). The set of irrational numbers is represented by \(Q´\).

**How to identify an irrational number?**

We know that irrational numbers are just real numbers that cannot be expressed as \(\frac{p}{q}\), where \(p\) and \(q\) are integers and \(q≠0\). For example, \(\sqrt{5}\) and \(\sqrt{3}\), etc. are irrational numbers. On the other hand, numbers that can be represented as \(\frac{p}{q}\), such that \(p\) and \(q\) are integers and \(q≠0\), are rational numbers.

**Rational and Irrational numbers**–**Example 1**

Determine the rational numbers among the following. \(\sqrt{16},\:\sqrt{3},\:-\frac{4}{5},\:\pi ,\:2.3137134623730860…..\)

**Solution:** \(\sqrt{16},-\frac{4}{5}\) are rational numbers.

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