Question

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

13
1 third

78
7 eighths

511
5 over 11

39−−√
square root of 39

12−−√

Answer 1

A rational terminating decimal is a number that can be expressed as a fraction \( \frac{a}{b} \) where \( b \) has only prime factors of 2 and/or 5 when fully simplified.

Let's analyze the options:

1. **13** - This is a whole number and can be expressed as \( \frac{13}{1} \), which is a terminating decimal.

2. **1 third** (\( \frac{1}{3} \)) - This is a repeating decimal (0.333...), not terminating.

3. **78** - This is a whole number and can be expressed as \( \frac{78}{1} \), which is a terminating decimal.

4. **7 eighths** (\( \frac{7}{8} \)) - This fraction has a denominator of 8 (\( 2^3 \)), which can be written as a terminating decimal (0.875).

5. **511** - This is a whole number and can be expressed as \( \frac{511}{1} \), which is a terminating decimal.

6. **5 over 11** (\( \frac{5}{11} \)) - This is a repeating decimal (approximately 0.4545...), not terminating.

7. **39−−√** (\( \sqrt{39} \)) - This is an irrational number, not a terminating decimal.

8. **12−−√** (\( \sqrt{12} \)) - This can be simplified to \( 2\sqrt{3} \), which is also an irrational number and not a terminating decimal.

Based on this analysis, the numbers that are rational terminating decimals are **13, 78, 7 eighths (0.875), and 511.** The most direct and simplest examples are **13, 78, and 511** as whole numbers.

Choose any of these: **13, 78, or 511**.