 Hello and welcome to the session. Today I will help you with the following question. The question says write down the decimal expansion of those rational numbers in question one which have terminating decimal expansion. These are the rational numbers given in question one of these. This is terminating. This is terminating. This is terminating. This is terminating and this is also terminating. These six rational numbers have terminating decimal expansions. Now we are supposed to write their decimal expansions. Let's move on to the solution. Consider the first rational number given that is 13 upon 3125. This has terminating decimal expansion. Now we will write the decimal expansion of this rational number. As you can see this is of the form p upon q. Now to write the decimal expansion of this rational number we will convert this p upon q form in the form a upon b where b is the power of 10. This is the prime factorization. As you can see this is the prime factorization of 3125. So the number 13 upon 3125 can be written as 13 upon 5 to the power 5. Now we are supposed to make this denominator as the power of 10. So for this we will multiply the numerator and the denominator by 2 raised to the power 5. Thus we get 416 upon 10 to the power 5. That is this becomes equal to 0.00416. So the rational number 13 upon 3125 has a decimal expansion 0.00416. Next rational number which has a terminating decimal expansion is 17 upon 8. This is also of the form p upon q. Again we will convert this to the form a upon b where b is the power of 10. This is the prime factorization of the denominator 8 of the rational number 17 upon 8. So we can say 17 upon 8 is written as 17 upon 2 to the power 3. Now we have to convert this denominator to the power of 10. So for this we will multiply both the numerator and denominator by 5 to the power 3. Thus this is equal to 2125 upon 10 to the power 3. That is this is equal to 2.125. That is the rational number 17 upon 8 has the decimal expansion as 2.125. Next rational number is 15 upon 1600. This also has a terminating decimal expansion. This is the prime factorization of the denominator 1600. So the rational number 15 upon 1600 is written as 15 upon 2 to the power 6 multiplied by 5 to the power 2. Now again we have to convert this denominator to the power of 10. So for this we will multiply the numerator and denominator by 5 to the power 4. Thus we get 9375 upon 10 to the power 6 which is equal to 0.009375. That is the rational number 15 upon 1600 has the decimal expansion 0.009375. Next rational number given is 23 upon 2 to the power 3 into 5 to the power 2. We have to convert this denominator as the power of 10. So for this we will multiply the numerator and the denominator by 5. So this becomes equal to 115 upon 10 to the power 3. That is this is equal to 0.115. Thus we have the rational number 23 upon 2 to the power 3 multiplied by 5 to the power 2 has a decimal expansion 0.115. Next is 6 upon 15. This is the prime factorization of the denominator 15. So the rational number 6 upon 15 is written as 6 upon 3 multiplied by 5 or this could be equal to 2 upon 5. Now to convert the denominator as the power of 10 we will multiply the numerator and the denominator by 2. So we get 4 upon 10 that is 0.4. Thus we have the rational number 6 upon 15 has a decimal expansion 0.4. Next rational number is 35 upon 50. Now this is the prime factorization of 50. So this can be written as 35 upon 2 multiplied by 5 to the power 2. We have to convert the denominator as the power of 10 so we will multiply both the numerator and the denominator by 2. This gives us 70 upon 10 to the power 2 which is further equal to 0.70. Hence the rational number 35 upon 50 has the decimal expansion 0.70. Thus this is the final answer. For the first part it is 0.00416. For the second part it is 2.125. Fourth it is 0.009375. For the sixth part it is 0.115. For the eighth part it is 0.4. For the ninth part it is 0.7. So hope you enjoyed the session. Have a good day.