Question

Which number is a rational terminating decimal?
Responses

511
5 over 11

√39

12−−√
square root of 12

1 over 3

7 over 8

Answer 1

A rational terminating decimal is a decimal that ends after a certain number of digits. This occurs when a fraction is simplified and its denominator has only the prime factors 2 and/or 5.

Let's analyze the provided options:

1. **511**: This is an integer and can be written as \( \frac{511}{1} \). It is a terminating decimal.

2. **5 over 11**: This fraction does not have a denominator that consists solely of the prime factors 2 and 5. It results in a repeating decimal (approximately 0.4545...).

3. **√39**: The square root of 39 is an irrational number, so it’s not a terminating decimal.

4. **√12**: This can be simplified to \( 2\sqrt{3} \), and since it is also irrational, it's not a terminating decimal.

5. **1 over 3**: This fraction results in a repeating decimal (approximately 0.333...), so it’s not a terminating decimal.

6. **7 over 8**: The denominator (8) can be expressed as \( 2^3 \), which consists solely of the prime factor 2. Therefore, it is a terminating decimal (0.875).

From this analysis, the rational terminating decimals are **511** and **7 over 8**.