 Hello friends welcome to the session I am welcome let's discuss the question that is without actually performing in the long division say whether the colline rational numbers will have a terminating decimal expansion or a non-terminating repeating decimal expansion. Now our given rational number is 13 upon 3125. Now before starting with the solution I would like to tell you the basic idea behind the question x equal to p by q is a rational number characterization q v of the form 2 to the power n and 5 to the power m where negative integers this implies has a decimal expansion which terminates expansion which terminates but if prime characterization q is not of the form 2 to the power n and 5 to the power m this implies x expansion which is non-terminating repeating let's start with the solution our given rational number is 13 upon 3125 so let x equal to 13 upon 3125 here we see that q is equal to 3125 and factors of 3125 is 5 into 5 into 5 into 5 into 5 this implies q is of the form 2 to the power n 5 to the power m this implies the given number has x has a decimal expansion which terminates the given rational number has a terminating decimal expansion hope you understood this solution and enjoyed the session goodbye and take care