Check all the sets of the real number system that this number belongs to:

-4.101101110...
Question 3Select one or more:

a.
irrational


b.
whole


c.
integers


d.
natural


e.
rational

The number in question is \(-4.101101110...\), which appears to be a repeating or non-terminating decimal. To classify this number, let's go over the different sets of the real number system:

### 1. **Natural Numbers (d)**
   - Natural numbers are positive whole numbers (1, 2, 3, ...).
   - **\(-4.101101110...\)** is negative and not a whole number.
   - **Does not belong to the natural numbers.**

### 2. **Whole Numbers (b)**
   - Whole numbers are non-negative integers (0, 1, 2, 3, ...).
   - \(-4.101101110...\) is negative and not a whole number.
   - **Does not belong to the whole numbers.**

### 3. **Integers (c)**
   - Integers include positive and negative whole numbers and zero (e.g., -3, -2, -1, 0, 1, ...).
   - \(-4.101101110...\) is not a whole number; it's a decimal.
   - **Does not belong to the integers.**

### 4. **Rational Numbers (e)**
   - Rational numbers are numbers that can be expressed as the ratio of two integers (fractions). They either terminate or have a repeating pattern.
   - Since the decimal \(-4.101101110...\) appears to have a repeating or predictable pattern, it can be expressed as a fraction.
   - **Belongs to the rational numbers.**

### 5. **Irrational Numbers (a)**
   - Irrational numbers are non-terminating, non-repeating decimals (e.g., \(\pi\), \(\sqrt{2}\)).
   - Since \(-4.101101110...\) is repeating, it cannot be irrational.
   - **Does not belong to the irrational numbers.**

### Conclusion:

The number **belongs to the rational numbers** but not to any of the other sets.

### Correct Answer:
- **e. Rational**

Would you like more details on this? 

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Here are five questions that expand on this:

1. What is the difference between rational and irrational numbers?
2. How can you prove that a repeating decimal is rational?
3. Can a negative number ever be a natural number?
4. How do whole numbers relate to integers?
5. What is a real-world example of an irrational number?

**Tip:** Repeating decimals can always be expressed as a fraction, making them rational numbers!

Check all the sets of the real number system that this number belongs to: -4.101101110... Question 3 Select one or more: a. irrational b. whole c. integers d. natural e. rational

Discover how to classify the number -4.101101110... in the real number system. Learn why this repeating decimal belongs to rational numbers and does not fit in other categories like whole, integers, or natural numbers. Suitable for students in Grades 6-8.

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