The number \( 2.333\ldots \) (often written as \( 2.\overline{3} \)) is a **rational number**. Here's why:

1. **Rational Number**: A rational number is any number that can be expressed as a fraction \(\frac{p}{q}\), where \( p \) and \( q \) are integers, and \( q \neq 0 \). The number \( 2.333\ldots \) can be written as the fraction \(\frac{7}{3}\), which shows it's rational.

2. **Repeating Decimal**: A repeating decimal, like \( 2.333\ldots \), is always a rational number because it can be expressed as a fraction.

3. **Not an Integer or Whole Number**: Since it is not a whole number (like 1, 2, 3) or an integer (like -1, 0, 1), it doesn't fall into those categories.

4. **Not an Irrational Number**: An irrational number cannot be expressed as a fraction and has non-repeating, non-terminating decimals (like \(\pi\) or \(\sqrt{2}\)). 

5. **Not a Real but Non-Rational**: It's definitely a real number but specifically a rational one.

### Would you like more details, or have any other questions?

Here are 5 related questions:
1. What makes a number irrational instead of rational?
2. How can you convert repeating decimals to fractions?
3. Are all repeating decimals considered rational numbers?
4. What is the difference between terminating and repeating decimals?
5. How do you prove that a decimal is rational?

**Tip**: To convert a repeating decimal to a fraction, set the repeating decimal as \( x \), manipulate the equation to isolate the repeating part, and solve for \( x \).

Discover why the number 2.333... is classified as a rational number. This page explains the concept of repeating decimals, their conversion to fractions, and the definitions distinguishing rational and irrational numbers. Suitable for students in Grades 6-8.

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