1. **Problem Statement:** This worksheet covers understanding real numbers and their subsets through examples, definitions, true/false questions, multiple choice, and classification tasks. 2. **Q1: Examples of Number Types** a. Rational Number: A number that can be expressed as a fraction of two integers, e.g., $\frac{3}{4}$. b. Irrational Number: A number that cannot be expressed as a fraction, e.g., $\sqrt{2}$. c. Integer: Whole numbers including negatives, zero, and positives, e.g., $-5$. d. Fraction: A number expressed as $\frac{p}{q}$ where $p,q$ are integers and $q \neq 0$, e.g., $\frac{7}{8}$. e. Recurring Decimal Number: A decimal number with repeating digits, e.g., $0.333...$. f. Natural Number: Positive integers starting from 1, e.g., $1, 2, 3$. 3. **Q2: Fill in the blanks** a. The lowest whole number is **0**. b. Natural numbers start with **1**. c. $\pi$ is an **Irrational** number. d. A non-terminating non-repeating decimal is called an **Irrational** number. e. A rational number can be expressed as **$\frac{p}{q}$** form, where $p$ and $q$ are integers and $q \neq 0$. 4. **Q3: True or False** a. $\sqrt{9} = 3$, which is a rational number. **True**. b. All whole numbers are integers. **True** because whole numbers are a subset of integers. c. Every fraction can be expressed as a decimal number. **True**; fractions convert to terminating or repeating decimals. 5. **Q4: Multiple Choice** a. Integer: Options are 3.5, $\pi$, -3, 1/2. Correct: **-3** (an integer). b. Irrational number: Options 0.444..., 3$\pi$, -9, 1/5. Correct: **3$\pi$** (irrational). c. Whole number: Options 0, -3, -10, 5 2/3. Correct: **0** (whole number). d. Natural number: Options 3.121212..., 0, -3, 5. Correct: **5** (natural number). 6. **Q5: Identify Rational and Irrational Numbers** List: -3, 2.5, $\sqrt{5}$, 1.333..., $\frac{2}{3}$, -3.14, 2$\pi$, 1.287631..., $\sqrt{4}$, 2 1/5 - Rational: -3, 2.5, 1.333..., $\frac{2}{3}$, -3.14, 1.287631..., $\sqrt{4} = 2$, 2 1/5 (which is $\frac{11}{5}$) - Irrational: $\sqrt{5}$, 2$\pi$ 7. **Q6: Identify Integers and Non-Integers** List: 3.7, 0, -7, $\frac{1}{2}$, 0.333..., $\sqrt{25}$, -5, -1.3, 100 - Integers: 0, -7, $\sqrt{25} = 5$, -5, 100 - Non-Integers: 3.7, $\frac{1}{2}$, 0.333..., -1.3 8. **Q7: Arrange numbers in boxes** List: -3, 2.5, $\sqrt{5}$, 1.333..., $\frac{2}{3}$, 50, -3.14, 2$\pi$, 1.287631..., $\sqrt{4}$, 2 1/5 - Rational numbers: -3, 2.5, 1.333..., $\frac{2}{3}$, 50, -3.14, 1.287631..., $\sqrt{4} = 2$, 2 1/5 - Irrational Numbers: $\sqrt{5}$, 2$\pi$ - Integers: -3, 50, $\sqrt{4} = 2$ - Non Integers: 2.5, 1.333..., $\frac{2}{3}$, -3.14, 1.287631..., 2 1/5 **Final notes:** - Rational numbers include integers, fractions, and decimals that terminate or repeat. - Irrational numbers cannot be expressed as fractions and have non-repeating, non-terminating decimals. - Integers are whole numbers including negatives and zero. - Natural numbers start from 1 upwards.