 Hello and welcome to the session. In this session we discussed the following question which says the decimal expansion of the rational number 43 upon 2 raised to the power 4 into 5 raised to the power 3 will terminate after how many places of decimal. Let's consider x equal to p upon q be a rational number. Now if the denominator of this rational number that is q can be written as 2 raised to the power n into 5 raised to the power m where we have m and n are non-negative integers. Then we can say x that is the rational number p upon q has a decimal expansion which terminates. So for a given rational number p upon q if it's denominator can be factorized in the form of 2 raised to the power n into 5 raised to the power m then we can say that the rational number x equal to p upon q has a decimal expansion which terminates. This is the key idea that we use for this question. Let's proceed with the solution now. The given rational number is 43 upon 2 raised to the power 4 into 5 raised to the power 3. Now as you can see that the denominator of this rational number is expressed as 2 raised to the power n into 5 raised to the power m. So this means that the given rational number has a decimal expansion which terminates. But we have to find out that the decimal expansion of the given rational number will terminate after how many places of decimal. Consider the rational number 43 upon 2 raised to the power 4 into 5 raised to the power 3. Now we multiply its numerator and denominator by 5. So this would be equal to 43 into 5 upon 2 raised to the power 4 into 5 raised to the power 4. Further this is equal to 215 upon 2 into 5 raised to the power 4. Further this is equal to 215 upon 10 to the power 4 which is further equal to 215 upon 10,000. So this is equal to 0.0215. This is the decimal expansion of the given rational number. That is we have the rational number 43 upon 2 raised to the power 4 into 5 raised to the power 3 is equal to 0.0215. So as you can see from this decimal expansion we have that this rational number will terminate after 4 places of decimal. That is 43 upon 2 raised to the power 4 into 5 raised to the power 3 will terminate after 4 places of decimal. So this is our final answer. This completes the session but we have understood the solution of this question.