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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

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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.

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