 Hello friends, welcome to the session I am Malka. We are going to discuss real numbers. Our given question is without actually performing the long division state whether the following rational numbers will have a terminating decimal expansion or a non-terminating repeating decimal expansion. Our given rational number is 6 upon 15. So let's start with the solution. Let X be a rational number which is equal to 6 upon 15. Now we can express 6 upon 15 to its lowest term. So X can also be written as 2 upon 5. We see that here Q is 5 which is of the form 2 to the power n and 5 to the power m. This implies that the given rational number X has a terminating decimal expansion. Hope you understood this solution and enjoyed the session. Goodbye and take care.