Question

Which number is a rational terminating decimal?
Responses

5 over 11

√39

√12

1 over 3

7 over 8

Answer 1

A rational terminating decimal is a decimal representation that comes to an end after a certain number of digits. To determine which of the given numbers is a rational terminating decimal, we can look for fractions whose denominators (when in simplest form) are only composed of the prime factors 2 and/or 5.

Let's analyze each option:

1. **5 over 11**: The fraction 5/11 has a denominator of 11, which is not a product of only the primes 2 and 5. Therefore, it is not a terminating decimal.

2. **√39**: The square root of 39 is an irrational number, so it is not a terminating decimal.

3. **√12**: The square root of 12 can be simplified to 2√3, which is also irrational. Therefore, it is not a terminating decimal.

4. **1 over 3**: The fraction 1/3 has a denominator of 3, which is again not a product of only the primes 2 and 5. Hence, it is not a terminating decimal.

5. **7 over 8**: The fraction 7/8 has a denominator of 8, which can be expressed as 2^3. Since 8 consists only of the prime factor 2, 7/8 is a terminating decimal.

Thus, the answer is **7 over 8**.