To determine whether a number is rational or irrational, you need to look at its characteristics. A rational number is any number that can be expressed as the fraction of two integers, that is, in the form p/q, where p and q are integers and q is not zero. This includes whole numbers, fractions, and repeating decimals.
For example, the number 1/2 is rational because it can be expressed as a fraction. Likewise, the number 3 is rational because it can be written as 3/1.
On the other hand, an irrational number cannot be expressed as a simple fraction. These numbers have non-repeating, non-terminating decimal expansions. Classic examples include the square root of 2 (√2), pi (π), and Euler’s number (e). For instance, the decimal representation of pi goes on forever without repeating, which makes it irrational.
To summarize, if you can express the number as a fraction of two integers, it’s rational. If it has a decimal that neither terminates nor repeats, it’s irrational.