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

The number π ( pi ) is a mathematical constant that represents the ratio of a circle ' s circum ference to its diameter . It is an ir r ational number , which means that its decimal representation goes on forever without repeating . This means that π is not just a very long number , but rather an infinite number . \n \n We know that π is infinite because we can calculate its decimal representation using a formula , and the decimal representation goes on forever without repeating . For example , the first decimal places of π are : \n \n 3 . 1 4 1 5 9 2 6 5 3 5 8 9 7 9 3 2 3 8 4 6 2 6 4 3 3 8 3 2 7 9 5 0 2 8 8 4 1 9 7 1 6 9 3 9 9 3 7 5 1 0 5 8 2 0 9 7 4 9 4 4 5 9 2 3 0 7 8 1 6 4 0 6 2 8 6 2 0 8 9 9 8 6 2 8 0 3 4 8 2 5 3 4 2 1 1 7 0 6 7 9 \n \n As you can see , the decimal representation of π goes on forever without repeating any pattern . This shows that π is an infinite number . \n \n In addition to π , there are other mathematical constants that are also infinite , such as e ( the base of the natural log arith m ) and φ ( the golden ratio ). These constants are important in mathematics and have many practical applications in fields such as physics , engineering , and computer science . </s>