 Hi and welcome to the session. I am Priyanka and I am going to help you with the following question which says express 0.999 and so on in the form P by Q. Are you surprised with your answer? With your teacher and classmate discuss why the answer makes sense. So first of all let us start with our solution. Let X be equal to 0.999 and so on which we can write as 0.9 bar. Multiplying both the sides by 10 we have 10x is equal to 9.9 bar. Let this be the first equation and this be the second equation. Now on subtracting 1 from 2 we have 9x is equal to 9.9 bar minus 0.9 bar. That gives us the answer as X is equal to 9 divided by 9 which says that X is equal to 1. So the answer is that in P by Q form 0.9 bar is equal to P by Q form 1 divided by 1 which is 1. So this completes the question that was given to us and yes we were surprised with our answer because in fraction form it is converted into 1 and but in decimal form it was looking as a difficult expression. Right? Bye for now.