All decimal numbers are

Options

A. rational number
B. irrational numbers
C. real numbers
D. integers

Answer

To solve the question "All decimal numbers are...", we need to classify decimal numbers into the appropriate category of numbers. Let's break this down step by step.

### Step-by-Step Solution:

1. **Understanding Decimal Numbers**:
- Decimal numbers are numbers that have a decimal point. Examples include 5.2, 3.4, 0.75, etc.

2. **Identifying Types of Numbers**:
- We need to classify decimal numbers into different types of numbers:
- **Rational Numbers**: These are numbers that can be expressed as a fraction \( \frac{p}{q} \), where \( p \) and \( q \) are integers and \( q \neq 0 \). Decimal numbers like 5.2 can be expressed as \( \frac{52}{10} \), which makes them rational.
- **Irrational Numbers**: These are numbers that cannot be expressed as a fraction. They are non-terminating and non-repeating decimals, such as \( \sqrt{2} \) or \( \pi \).
- **Real Numbers**: This category includes all rational and irrational numbers. Therefore, all decimal numbers fall under real numbers.

3. **Conclusion**:
- Since decimal numbers can be expressed as fractions (and thus are rational), and all rational numbers are included in the set of real numbers, we conclude that:
- **All decimal numbers are real numbers**.

### Final Answer:
All decimal numbers are **real numbers**.

---