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.
