(i) 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 0.098