Question

Which number is a rational terminating decimal?(1 point)
Responses

7/8
7 eighths

12−−√
square root of 12

5/11
5 over 11

39−−√
square root of 39

1/3
1 third

Answer 1

A rational terminating decimal is a fraction that can be expressed as a decimal that ends after a finite number of digits. This occurs when the denominator (in its simplest form) contains only the prime factors 2 and/or 5.

Let's analyze each option:

1. **7/8**: The denominator is 8, which is \(2^3\). This fraction is a terminating decimal (0.875).

2. **12−−√**: The square root of 12 is not a rational number. It is approximately 3.464, which is non-terminating and non-repeating.

3. **5/11**: The denominator is 11, which has prime factor 11. This fraction is a non-terminating repeating decimal (approximately 0.4545...).

4. **39−−√**: The square root of 39 is not a rational number. It is approximately 6.244, which is non-terminating and non-repeating.

5. **1/3**: The denominator is 3, which has the prime factor 3. This fraction is a non-terminating repeating decimal (approximately 0.3333...).

From the options provided, the only rational terminating decimal is **7/8**.