 Hello and welcome to the session. In this session we discussed the following question which says if A upon B is a rational number with B not equal to 0, what is the condition on B so that the decimal representation of A upon B is terminated. So we are given a rational number A upon B where the denominator is not equal to 0. We have to find the condition on the denominator B such that the decimal representation of the rational number A upon B is terminating. Let's see its solution now. We have that A upon B is a rational number and we are given that the denominator B is not equal to 0. Let's try to find out the condition on B such that the decimal expansion of A upon B is terminating. For this let's consider an example where we take, let's consider the decimal expansion of a real number that terminates. So let's take this 0.0875. Now we express this as a rational number. So this can be written as 0.0875 upon 10 to the power 4. Now as you can see we have factorized 0.0875. So we can write 0.0875 that is the numerator as 5 to the power 3 multiplied by 7 and now denominator that is 10 to the power 4 and we know that since the powers of 10 can only have powers of 2 and 5 as factors so 10 to the power 4 can be written as 2 to the power 4 multiplied by 5 to the power 4. Now we will cancel out the common factors between the numerator and the denominator. So we would get this is equal to 7 upon 5 into 2 to the power 4. So we have 0.0875 can be written as 7 upon 5 into 2 to the power 4. So we have expressed this as a rational number 7 upon 5 into 2 to the power 4. Now as you can see that the prime factorization of the denominator is of the form 2 to the power n into 5 to the power m where we have n and m are non-negative integers. So this is the denominator it is of the form 2 to the power 4 into 5 that is of the form 2 to the power n into 5 to the power m where n and m are non-negative integers. So we get the result that for any rational number a upon b where b is not equal to 0 and where a and b are co-prime then the decimal representation of the rational number a upon b is terminating if the prime factorization of the denominator that is b 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. So this is our final answer that the prime factorization of the denominator should be of the form 2 raised to the power n into 5 raised to the power m where m and n are non-negative integers. So this completes the session hope you have understood the solution for this question.