 Hello and welcome to the session. In this session we shall discuss the following question and the question says that first part graph 3 upon 8 on the number 9 second which rational number is greater minus of 2.63 bar or minus of 2.67 bar and let us proceed to the solution in this question we shall plot the fraction 3 upon 8 here the denominator tells us how many parts the unit should be divided and here the denominator is 8 so we shall divide the number 9 between 0 and 1 into 8 equal parts that is 0 by 8, 1 by 8, 2 by 8, 2 by 8, 4 by 8, 5 by 8, 6 by 8, 7 by 8 and 8 by 8 which can also be written as 0 by 8 is 0, 1 by 8, 2 by 8, 3 by 8, 4 by 8, 5 by 8, 6 by 8, 7 by 8 and 8 by 8 is 1 also now we know that 3 by 8 lies in between 0 and 1 that is 0 is less than 3 by 8 is less than 1 so we first draw a number line showing 0 and 1 and we label the number line with 0, 1 by 8, 2 by 8, 3 by 8 and so on up to 1 and this number line is divided into 8 equal parts now we draw a dot on the number line at the point 3 by 8 and thus the fraction 3 by 8 is shown on the number line now we move on to the second part of the question here we need to find out which rational number is greater minus of 2.63 bar of minus of 2.67 bar here we have two rational numbers minus of 2.63 bar and minus of 2.67 bar first we draw a number line here minus of 2.6 is same and the change is in the second place decimal so we have minus of 2.63 and minus of 2.67 will lie between minus of 2.60 and minus of 2.69 so we shall choose the number line accordingly the decimals are expressed in tenths so we divide the number line between minus 2.60 and minus 2.70 in tenth parts now minus of 2.63 bar is equal to minus of 2.63333 and so on since it is a non-terminating rational number and it lies in between minus of 2.63 and minus of 2.64 so we label this point between these two points and we get the point as minus 2.63 bar similarly minus of 2.67 bar is equal to minus of 2.67777 and so on since it is also a non-terminating rational number which lies in between minus of 2.67 and minus of 2.68 so we label this point between these two points and we get the point as minus of 2.67 bar now from the graph we notice that minus of 2.63 bar is to the right of minus of 2.67 bar therefore minus of 2.63 bar is greater than minus of 2.67 bar which is our required answer this completes our session hope you enjoyed this session