Which of the following are rational numbers? Select all correct answers.

Select all that apply:

0.4141141114…

√5

12/13

−6

5.2481

0.6565565556…

Let's evaluate each number to determine which are rational.

1. **0.4141141114…**
   - This is a non-repeating, non-terminating decimal, meaning it cannot be expressed as a ratio of two integers.
   - **Not rational**.

2. **√5**
   - The square root of 5 is an irrational number because it cannot be expressed as a fraction of two integers and it has a non-repeating, non-terminating decimal expansion.
   - **Not rational**.

3. **12/13**
   - This is a ratio of two integers (a fraction), and it can be expressed exactly as \( \frac{12}{13} \).
   - **Rational**.

4. **−6**
   - This is an integer, and all integers are rational because they can be expressed as a ratio (e.g., \( -6 = \frac{-6}{1} \)).
   - **Rational**.

5. **5.2481**
   - This is a terminating decimal, and terminating decimals are always rational because they can be expressed as fractions (e.g., \( 5.2481 = \frac{52481}{10000} \)).
   - **Rational**.

6. **0.6565565556…**
   - This is a non-repeating, non-terminating decimal, so it cannot be expressed as a ratio of two integers.
   - **Not rational**.

### Final Answer:
- **Rational numbers**: 12/13, −6, 5.2481
- **Not rational numbers**: 0.4141141114…, √5, 0.6565565556…

Would you like more details or clarification?

### Relative questions:
1. What makes a number irrational?
2. Can a repeating decimal be considered rational?
3. How do we convert terminating decimals into fractions?
4. Why is the square root of non-perfect squares irrational?
5. What is the difference between rational and irrational numbers?

### Tip:
Remember, any decimal that either terminates or repeats can always be expressed as a fraction, making it rational.

Which of the following are rational numbers? Select all correct answers.
Select all that apply:
0.4141141114…
√5
12/13
−6
5.2481
0.6565565556…

Discover how to identify rational and irrational numbers from a given set. Learn key concepts like non-terminating decimals, fractions, and integer properties. Suitable for students in Grades 7-9, this exercise provides a detailed breakdown of rational numbers such as 12/13, −6, and 5.2481.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation