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.

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.