 Hello and welcome to the session. Today I will help you with the following question. The question says, without actually performing the long division, state whether the falling rational number will have a terminating decimal expansion or a non-terminating repeating decimal expansion. The given rational number is 64 upon 455. We suppose that let X be equal to p upon q, a rational number such that the prime factorization of q is of the form 2 raised to the power n into 5 raised to the power m where n and m are non-negative integers. Then X has a decimal expansion which terminates but if the prime factorization of q is not of the form 2 raised to the power n into 5 raised to the power m where n and m are non-negative integers then X has a decimal expansion which is non-terminating repeating. This is the key idea we used for this question. Let's move on to the solution. The given rational number is 64 upon 455. Let X be equal to 64 upon 455. This is of the form p upon q. Now here we have q is equal to 455. This is the prime factorization of the denominator that is q that is 455. So we have q equal to 455 is written as 5 multiplied by 7 multiplied by 13. This shows that prime factorization of q is not of the form 2 raised to the power n multiplied by 5 raised to the power m where m and n are non-negative integers. So from the key idea we can say that X equal to 64 upon 455 has a decimal expansion which is non-terminating repeating. So our final answer is non-terminating repeating. So hope you enjoyed the session. Have a good day.