How can I determine if a number is rational or irrational?

To determine if a number is rational or irrational, you first need to understand the definitions of both types of numbers.

A rational number is any number that can be expressed as the quotient or fraction of two integers, where the denominator is not zero. This means that if you can write a number in the form of p/q, where p and q are integers and q ≠ 0, then it is a rational number. Examples of rational numbers include 1/2, -3, and 0.75.

On the other hand, an irrational number cannot be expressed as a simple fraction. These numbers go on forever without repeating in their decimal form. Common examples of irrational numbers include √2, π (pi), and e (Euler’s number). To check if a number is irrational, look at its decimal representation:

• If the decimal is terminating (like 0.5), it is rational.
• If the decimal is repeating (like 0.333…), it is also rational.
• If the decimal goes on forever without repeating (like 3.14159... for π), it is irrational.

In summary, to tell if a number is rational or irrational, check if it can be expressed as a fraction of two integers:

• If yes, it is rational.
• If no, observe its decimal form—if it’s non-repeating and non-terminating, it’s irrational.

This method will help you easily categorize most numbers you encounter!