Which of the following rational numbers have terminating decimal?

Question

3 Answers

kritika · Answer 1 · 2021-12-19T12:58:42+0000

Let

$x=p / q$ be a rational number, such that the prime factorization of

$q$ is of the form

$2^{n} 5^{m}$ , where

$n, m$ are non - negative integers.
Then

$\mathrm{x}$ has a decimal expansion which terminates.
(i) Here

$q=225$
225 can be written as

$3^{2} \times 5^{2}$
Since it is in the form of

$5^{m}$ , it is a terminating decimal.
(ii) Here

$q=18$
18 can be written as

$2 \times 3^{2}$
Since 3 is also there and it is not in the form of

$2^{n} 5^{m}$ , it is not a terminating decimal.
(iii) Here

$q=21$
21 can be written as

$3 \times 7$
Since it is not in the form of

$2^{n} 5^{m}$ , it is not a terminating decimal.
(iv) Here

$q=250$
250 can be written as

$2 \times 5^{3}$
Since it is in the form of

$2^{n} 5^{m}$ , it is a terminating decimal.