Question

Which of the following rational number has terminating decimal?

• A. \(\frac{7}{250}\)
• B. \(\frac{16}{225}\)
• C. \(\frac{5}{18}\)
• D. \(\frac{2}{21}\)

Hint:

For a terminating decimal, ensure that the denominator (in its simplest form) only contains the prime factors 2 and 5.

Answer 1

The Correct Option is A

A rational number has a terminating decimal if and only if the denominator, when reduced to its simplest form, contains no prime factors other than 2 and 5. Let's analyze each option:
- \(\frac{7}{250}\): The prime factorization of 250 is \(2 \times 5^3\), which contains only 2 and 5. Therefore, this number has a terminating decimal.
- \(\frac{16}{225}\): The prime factorization of 225 is \(3^2 \times 5^2\), so it has a factor of 3, making it a non-terminating decimal.
- \(\frac{5}{18}\): The prime factorization of 18 is \(2 \times 3^2\), and since 3 is involved, it will not terminate.
- \(\frac{2}{21}\): The prime factorization of 21 is \(3 \times 7\), so it also does not terminate.
Thus, the correct answer is \(\frac{7}{250}\).