 Hello friends, welcome to the session. Today we are going to solve this problem 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. Assam is 17 upon 8. So before starting with the solution let me tell you the basic idea behind the question. It is let x equal to p upon q be a rational number. If prime factorization of q equal to 2 to the power n and 5 to the power m where n and m are non-negative integers this implies x has a decimal expansion which terminates. But if prime factorization of q not equal to 2 to the power n 5 to the power m this implies x has a decimal expansion which is non-terminating repeating that is rackering. Now let's start with a solution if we 17 upon 8. Now let x equal to 17 upon 8 on having the factors of q which is equal to 8 we see it is 2 to the power 3. This implies it is in the form of 2 to the power n equal to 2 to the power 3. This implies the fraction x equal to 17 upon 8 is terminating. Hence 17 upon 8 has a terminating decimal expansion. Hope you understood the session and enjoyed it. Thank you and goodbye.