 Hello and welcome to the session. In this session we shall discuss the following question and the question says that Right fractions as repeating or terminating decimals first minus 5 upon 8 second 2 and 4 by 11 We know that if the division ends or terminates when the remainder is 0 then the decimal is terminating decimal And if the division does not end and digit, group of digits repeats when it is a non-terminating decimal With this key idea let us proceed to the solution In this question we shall find which fraction is terminating and which is non-terminating And first we have the fraction minus 5 upon 8 so we divide 5 by 8 Since 5 is smaller than 8 so we put a decimal point in quotient and lx0s and divide as we do with whole numbers Now 5 is smaller than 8 so we put decimal in quotient so that we can put 0 with 5 Then 50 is greater than 8 and 8 into 6 is 38 and we get the remainder as 2 which is again smaller than 8 So we again put 0 because we have already put decimal in quotient and we get 20 Now 8 into 2 is 16 and we get the remainder as 4 which is again smaller than 8 So we put a 0 and we get 30 Now 30 is greater than 8 and 8 into 5 is 30 so we get the remainder as 0 and the division ends here So we get 5 by 8 as 0.625 which implies that minus of 5 by 8 will be equal to minus of 0.625 Here remainder is 0 so division ends Therefore we can say 8 is a terminating decimal and second we have 2 and 4 by 11 We have a next fraction first we shall simplify it and we get 11 into 2 plus 4 in the numerator That is 22 plus 4 which is equal to 26 and denominator remains same that is 11 So we have the fraction 26 by 11 so now we divide 26 by 11 Here numerator is greater than denominator so we start with normal division 11 into 2 is 22 and we get 4 as remainder which is smaller than 11 So now we put a decimal in quotient after 2 and vls0 that is we put a 0 after 6 and we get 40 which is greater than 11 so we have 11 into 3 is 33 and we get 7 as remainder Now 7 is smaller than 11 so we put 1 more 0 as we have already put a decimal in quotient and we get 70 and now 11 into 6 is 66 and we get 4 as remainder Here we notice that the remainder is alternately 4 and 7 and in quotient we are having repetition of 3 and 6 So here division is endless and thus digits in quotient repeat thus we have 2 and 4 by 11 is equal to 2.363636 and so on which can also be written as 2.36 bath and therefore we conclude that it is a non-terminating decimal This completes our session hope you enjoyed this session