Question

Check whether following rational fractions are terminating or non- terminating. If they are terminating convert them into decimal number:
(i) 1/3
(ii) 2/5
(iii) 3/6
(iv) 8/13​

Answer 1

Step-by-step explanation:

13/125 = 13/(5 x 5 x 5) = 13/53 = 13/(20 x 53) Denominater is of the form of 2m x 5n. Hence, 13/125 is the decimal terminating expansion Representing in decimal form 13/125 = 13/53 Multiply (2)3 for making in power of 10 to denominator. 13/125 = (13 x 23)/(23 x 53) = (13 x 8)/(2 x 5)3 = 104/103 = 104/1000 = 0.104 Hence, decimal expansion of 13/125 is 0.104 (ii) 14588/625 = 14588/(5 x 5 x 5 x 5) = 14588/(20 x 54) denominator is of the form 2m x 5n. So, 14588/625 is the decimal terminating expansion. Representing in decimal form 14588/625 = 14588/54 Multiply 24 in numerator and denominator So, decimal expansion of given number is 23.3408. (iii) 59/500 = 49/(2 x 2 x 5 x 5 x 5) = 49/(22 x 53) Since, denominator is in the form 2m x 5n. So, 49/500 is decimal terminating expansion Representing in the decimal form 49/500 = 49/(22 x 53) Multiply 2 in numerator and denominator = (49 x 2)/(23 x 53) = 98/(2 x 5)3 = 98/103 = 98/1000 = 0.098 So, decimal expansion of given number is 0.098Read more on Sarthaks.com - https://www.sarthaks.com/746498/write-down-decimal-expansion-following-rational-numbers-show-whether-these-terminating