Which of the following rational numbers have terminating decimal?(i) 1

1.	Which of the following rational numbers have terminating decimal?(i) 16/225(ii) 5/18(iii) 2/21(iv) 7/250A. (i) and (ii)B. (ii) and (iii)C. (i) and (iii)D. (i) and (iv)
Answer» Let x = p/q be a rational number, such that the prime factorization of q is of the form 2ⁿ 5^m, where n, m are non - negative integers. Then x has a decimal expansion which terminates. (i) Here q = 225 225 can be written as 3²×5² Since it is in the form of 5^m, it is a terminating decimal. (ii) Here q = 18 18 can be written as 2 × 3² Since 3 is also there and it is not in the form of 2ⁿ5^m, it is not a terminating decimal. (iii) Here q = 21 21 can be written as 3 × 7 Since it is not in the form of 2ⁿ5^m, it is not a terminating decimal. (iv) Here q = 250 250 can be written as 2 × 5³ Since it is in the form of 2ⁿ5^m, it is a terminating decimal.

Which of the following rational numbers have terminating decimal?(i) 16/225(ii) 5/18(iii) 2/21(iv) 7/250A. (i) and (ii)B. (ii) and (iii)C. (i) and (iii)D. (i) and (iv)

Answer»

Let x = p/q be a rational number, such that the prime factorization of q is of the form 2ⁿ 5^m, where n, m are non - negative integers.

Then x has a decimal expansion which terminates.

(i) Here q = 225

225 can be written as 3²×5²

Since it is in the form of 5^m, it is a terminating decimal.

(ii) Here q = 18

18 can be written as 2 × 3²

Since 3 is also there and it is not in the form of 2ⁿ5^m, it is not a terminating decimal.

(iii) Here q = 21

21 can be written as 3 × 7

Since it is not in the form of 2ⁿ5^m, it is not a terminating decimal.

(iv) Here q = 250

250 can be written as 2 × 5³

Since it is in the form of 2ⁿ5^m, it is a terminating decimal.