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Here are the correct answers for each question on the worksheet, with clear reasoning:

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1. Number: 9

- Is it a rational number? → Yes, because 9 = 9/1 (can be written as a fraction).
- Is it an integer? → Yes, integers include positive and negative whole numbers and zero.
- Is it a whole number? → Yes, whole numbers are 0, 1, 2, 3, ... — no negatives or fractions.

✔ So, all three apply: Rational number, Integer, Whole number.

But since the question says “identify whether... and/or”, and gives separate radio buttons, you should select all that apply. However, in many worksheets like this, if only one button can be selected per question, they may expect the most specific category — but here, since all are true, and the format allows multiple selections (radio buttons usually mean single choice, but context suggests checking all correct), we’ll assume you check all correct options.

Wait — looking at the layout: each question has 3 radio buttons. Radio buttons typically allow only ONE selection. But that doesn’t make sense for Q1 and Q2, because 9 is ALL THREE.

Actually, re-examining: In standard math classification, every whole number is also an integer and a rational number. So if the test expects you to pick the *most specific* category, it would be “Whole number”. But the instruction says “and/or”, meaning possibly more than one.

However, since these are radio buttons (circles, not checkboxes), likely only one answer is expected per question. That’s confusing.

Let me check common curriculum practice: Often in such worksheets, when they say “identify whether... and/or”, and give radio buttons, they actually intend for students to recognize that some categories contain others — so for 9, since it’s a whole number, and whole numbers are a subset of integers, which are a subset of rationals, the *most precise* label is “Whole number”.

But wait — let’s look at Question 3 and 4: they say “Choose the integers” and list multiple options with radio buttons — again, radio buttons imply single choice, but that can’t be right because there are multiple integers in the list.

Ah! I think there’s a formatting issue in the original worksheet. The circles might actually be meant to be checkboxes (squares) but are drawn as circles. Or perhaps in the digital version, they’re clickable independently.

Given that, and to match educational standards, I will treat each option as independently selectable — i.e., you can choose multiple correct answers per question, even if drawn as radio buttons.

So for accuracy:

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Question 1: 9

→ Rational number: ✔
→ Integer: ✔
→ Whole number: ✔

Question 2: 27

Same logic: 27 is positive, no decimal, no fraction.

→ Rational number: ✔
→ Integer: ✔
→ Whole number: ✔

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Question 3: Choose the integers.

List:
- −33 → integer ✔
- −0.3810964... → decimal, not integer ✘
- 30 → integer ✔
- 38 → integer ✔
- −5/4 → fraction, equals -1.25 → not integer ✘
- −3 → integer ✔

So integers are: −33, 30, 38, −3

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Question 4: Choose the integers.

List:
- 34 → integer ✔
- 4.29 → decimal ✘
- −3.30354... → non-terminating decimal ✘
- −2.319632... → same ✘
- 0.2 → decimal ✘
- −17 → integer ✔

So integers are: 34, −17

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Question 5: Choose the whole numbers.

Whole numbers: 0, 1, 2, 3, ... (non-negative integers)

List:
- −3.44 → negative decimal ✘
- √51 → approx 7.14, irrational ✘
- −3.9 → negative decimal ✘
- 4.874222... → repeating? Still decimal, not whole ✘
- −13/8 → negative fraction ✘
- 5√2 → approx 7.07, irrational ✘

None of these are whole numbers.

Wait — is that possible? Let me double-check.

√51 is about 7.1414… — not whole.
5√2 ≈ 5×1.414 = 7.07 — not whole.
All others are negative or fractional or decimal.

So actually, none of the options in Q5 are whole numbers.

But that seems odd for a worksheet. Did I miss something?

Look again:
Option 4: “4.874222...” — the ellipsis might indicate repeating? Even if it repeats, it’s still not a whole number unless it ends in .000...

No — whole numbers must be non-negative integers with no fractional part.

So yes — no correct answers in Q5? That can’t be right.

Wait — maybe “4.874222...” is meant to be terminating? But it has “...” which usually means continues.

Alternatively, perhaps it’s a trick question.

But let’s check Q6 first.

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Question 6: Choose the whole numbers.

List:
- 34 → whole number ✔
- 31 → whole number ✔
- 13 → whole number ✔
- −5/8 → negative fraction ✘
- 3/5 → positive fraction, not whole ✘
- 32 → whole number ✔

So whole numbers: 34, 31, 13, 32

That makes sense.

Back to Q5: Perhaps the intention was that none are whole numbers? Or maybe I misread.

Another thought: Is “4.874222...” meant to be 4.874222 (terminating)? But it has “...” which implies infinite continuation.

In math notation, “...” after decimals usually means non-terminating.

Moreover, √51 and 5√2 are definitely irrational.

So for Q5, there are no whole numbers among the choices.

But since the worksheet asks to “choose the whole numbers”, and provides options, perhaps it’s acceptable to select none — but radio buttons don’t allow that.

This suggests the worksheet may have a typo, or in context, we should go with what’s mathematically correct.

Perhaps “4.874222...” is intended to be a repeating decimal that equals a fraction, but still not a whole number.

I think we have to go with math: no whole numbers in Q5.

But let’s confirm definitions:

- Whole numbers: {0, 1, 2, 3, 4, ...} — non-negative integers.

None of the Q5 options fit.

So for Q5, no selections.

But since the format might require selecting something, and given that this is likely a mistake, I’ll note that.

Alternatively, maybe “4.874222...” is meant to be 4.874222 exactly? But even then, it’s not whole.

Unless it’s 4.000..., but it’s not.

I think we proceed with correctness.

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Now, compiling final answers based on mathematical accuracy:

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Final Answer:

1. Rational number, Integer, Whole number
2. Rational number, Integer, Whole number
3. −33, 30, 38, −3
4. 34, −17
5. (none)
6. 34, 31, 13, 32

But since the response format requires a concise final answer, and considering the worksheet likely expects selections per question, I'll format it as:

For questions 1 and 2: All three categories apply.
For 3 and 4: List the integers.
For 5 and 6: List the whole numbers.

Given the constraints, here's the clean final answer:

──────────────────────────────────────

Final Answer:
1. Rational number, Integer, Whole number
2. Rational number, Integer, Whole number
3. −33, 30, 38, −3
4. 34, −17
5. None
6. 34, 31, 13, 32