Classify numbers as Natural, Whole, Integers, Rational, Irrational and identify set elements belonging to these categories.

Question 1: Classify the following numbers.

• Natural Numbers (N): $\{1, 2, 3, ...\}$
• Whole Numbers (W): $\{0, 1, 2, 3, ...\}$
• Integers (Z): $\{..., -2, -1, 0, 1, 2, ...\}$
• Rational Numbers (Q): Can be written as $\frac{a}{b}$ (terminating or repeating decimals).
• Irrational Numbers (Q'): Cannot be written as $\frac{a}{b}$ (non-terminating, non-repeating decimals).

Here are the classifications for each number:

• 1: N, W, Z, Q
• 0: W, Z, Q
• 2.435435435...: This is a repeating decimal. Q
• 100: N, W, Z, Q
• $1/720012001200...$: This appears to be a typo in the question, likely intended as a repeating decimal or a fraction. Assuming it's a repeating decimal like 0.1200120012..., it would be Q. If it's literally 1 divided by a very long number, it's still a fraction, so Q.
• $\sqrt{7}$: This is a non-perfect square root. Q'
• 4.75: This is a terminating decimal. Q
• $-8$: Z, Q
• $-0.23874876967674...$: This is a non-terminating, non-repeating decimal. Q'
• 0.5: This is a terminating decimal. Q

Question 2: Find out which of the following elements of the set $M = \{-3, 2.5, \sqrt{16}, - \pi, 0, 23.6\}$ are:

First, simplify the elements of set M:
$M = \{-3, 2.5, 4, -\pi, 0, 23.6\}$

• a) Natural numbers: Numbers in N are positive integers.
  • Natural numbers: $\boxed{4}$
• b) Integers: Numbers in Z are whole numbers and their negatives.
  • Integers: $\boxed*{-3, 4, 0*}$
• c) Rational numbers: Numbers in Q can be expressed as a fraction.
  • Rational numbers: $\boxed*{-3, 2.5, 4, 0, 23.6*}$
• d) Irrational numbers: Numbers in Q' cannot be expressed as a fraction.
  • Irrational numbers: $\boxed*{-\pi*}$
• e) Real numbers: All numbers listed are real numbers.
  • Real numbers: $\boxed*{-3, 2.5, 4, -\pi, 0, 23.6*}$

Question 3: Classify the following numbers: $-5, 0, \sqrt{2}, \frac{1}{2}$ and 7.

• $-5$: Integer, Rational
• 0: Whole number, Integer, Rational
• $\sqrt{2}$: Irrational
• $\frac{1}{2}$: Rational
• 7: Natural number, Whole number, Integer, Rational

Question 4: Illustrate the content in the hunter's bag using a Venn diagram. Relate these within the real number system.

The hunter's bag contains a python and a bottle of water. The python contains a hawk, which contains a chicken, which contains a grain of corn.

Venn Diagram for Contents:
Let B = Hunter's Bag, P = Python, W = Bottle of Water, H = Hawk, C = Chicken, G = Grain of Corn.

\begin{tikzpicture} \draw (0,0) circle (3cm) node[above right] {B (Hunter's Bag)}; \draw (-1,0) circle (1.5cm) node[above right] {P (Python)}; \draw (1.5,0.5) circle (0.5cm) node[above right] {W (Bottle of Water)}; \draw (-1,0) circle (1cm) node[above right] {H (Hawk)}; \draw (-1,0) circle (0.5cm) node[above right] {C (Chicken)}; \node at (-1,0) {G (Grain of Corn)}; \end{tikzpicture}

Relation to the Real Number System:
Each distinct item (grain of corn, chicken, hawk, python, bottle of water) represents a count of 1. The number 1 is a natural number, a whole number, an integer, a rational number, and a real number.

Question 5: Convert the following decimals into fractions.

• a) 0.5 $$0.5 = \frac{5}{10} = \boxed*{\frac{1}{2}}$$
• b) 0.62 $$0.62 = \frac{62}{100} = \boxed*{\frac{31}{50}}$$
• c) 1.6 $$1.6 = 1\frac{6}{10} = 1\frac{3}{5} = \boxed*{\frac{8}{5}}$$
• d) 2.31 $$2.31 = 2\frac{31}{100} = \boxed*{\frac{231}{100}}$$