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Here’s the solution to the classification of the numbers in your image:

### Directions: For each number shown, classify it as either rational or irrational, then tell whether it is terminating, repeating, or neither.

#### a) \(-5\)
- **Rational**: It can be written as a fraction \(-\frac{5}{1}\).
- **Terminating**: It is a whole number with no repeating decimal part.

#### b) \(\sqrt{7}\)
- **Irrational**: The square root of 7 cannot be expressed as a fraction, and its decimal expansion is non-repeating and non-terminating.
- **Neither**: It doesn't terminate or repeat.

#### c) \(\frac{5}{8}\)
- **Rational**: This is a fraction of two integers.
- **Terminating**: \(\frac{5}{8} = 0.625\), which terminates after three decimal places.

#### d) \(\pi\)
- **Irrational**: \(\pi\) cannot be written as a fraction of integers and has a non-repeating, non-terminating decimal expansion.
- **Neither**: Its decimal form is neither terminating nor repeating.

#### e) \(4.333333\ldots\) (repeating decimal)
- **Rational**: Repeating decimals can be expressed as fractions. In this case, \(4.3333\ldots = \frac{13}{3}\).
- **Repeating**: The decimal repeats.

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Would you like further details or explanations on any of these? Here are some related questions to deepen understanding:

1. What is the difference between a terminating and repeating decimal?
2. Can all irrational numbers be written as square roots?
3. Why is \(\pi\) classified as irrational even though it's used in many formulas?
4. How can repeating decimals be converted into fractions?
5. What properties make a number rational or irrational?

**Tip:** Any repeating decimal can be converted to a fraction by algebraic manipulation.

For each number shown, classify it as either rational or irrational, then tell whether or not it is terminating or repeating.

Learn how to classify numbers as rational or irrational and determine whether they are terminating, repeating, or neither. This problem covers key mathematical concepts in number theory, suitable for Grades 8-10.

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