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Question

Without actual division, find which of the following rationals are terminating decimals.
(i) 1380
(ii) 724
(iii) 512
(iv) 835
(v) 16125


Solution

(i) Denominator of 1380 is 80.
And,
80 = 24×5
Therefore, 80 has no other factors than 2 and 5.
Thus, 1380 is a terminating decimal.

(ii) Denominator of 724 is 24.
And,
24 = 23×3
So, 24 has a prime factor 3, which is other than 2 and 5.
Thus, 724 is not a terminating decimal.

(iii)  Denominator of 512 is 12.
And,
12 = 22×3
So, 12 has a prime factor 3, which is other than 2 and 5.
Thus, 512 is not a terminating decimal.

(iv) Denominator of 835 is 35.
And,
35 = 7×5
So, 35 has a prime factor 7, which is other than 2 and 5.
Thus, 835 is not a terminating decimal.

(v) Denominator of 16125 is 125.
And,
125 = 53
Therefore, 125 has no other factors than 2 and 5.
Thus, 16125 is a terminating decimal.

Mathematics
RS Aggarwal (2017)
Standard IX

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