How do we know some numbers, like Pi are endless, instead of just a very long number?

Thank you for asking ! Pi ( π ) is an ir r ational number , which means that it cannot be expressed as a finite decimal or fraction . In other words , it has an infinite number of digits and cannot be written as a simple , fixed - length value . \n The reason we know that Pi is end less is because of the way it is defined . Pi is the ratio of a circle ' s circum ference to its diameter . This ratio is an ir r ational number because it cannot be expressed as a simple fraction , such as 3 / 4 or 2 2 / 7 . Instead , Pi is an infinite , non - re pe ating decimal that goes on forever without repeating itself . \n For example , the first 1 0 digits of Pi are 3 . 1 4 1 5 9 2 6 5 3 , but there are an infinite number of digits beyond that . In fact , the number of digits of Pi is infinite and non - re pe ating , which means that there is no way to write down all of its digits exactly . \n So , to answer your question , we know that Pi is end less because it is an ir r ational number that cannot be expressed as a finite value . Its infinite nature is a fundamental property of the mathematical concept of Pi , and it has been known and studied for thousands of years by mathemat icians and scient ists . </s>