1. **Problem:** Identify if the given statements about the rational number system are True or False, and correct the false ones. 2. **Formula/Rules:** - An integer is a rational number because it can be expressed as a fraction with denominator 1. - Real numbers include both rational and irrational numbers. - Rational numbers can be expressed as terminating or repeating decimals. - Irrational numbers cannot be expressed as fractions and have non-terminating, non-repeating decimals. - Natural numbers are positive integers starting from 1. - Whole numbers include all natural numbers and zero. 3. **Step-by-step answers:** 1. "If a number is an integer, then the number is also rational." This is **True** because every integer $n$ can be written as $\frac{n}{1}$. 2. "If a number is real, then it is also rational." This is **False**. Correction: "If a number is real, it can be rational or irrational." 3. "3.456 is an irrational number." This is **False**. Correction: "3.456 is a rational number" because it is a terminating decimal. 4. "$\sqrt{24}$ is a real number." This is **True** because square roots of positive numbers are real. 5. "Zero is a natural number." This is **False**. Correction: "Zero is a whole number but not a natural number." 6. "9 is an integer." This is **True**. 7. "If a number is natural, then it is also whole." This is **True** because natural numbers are a subset of whole numbers. **Final answers:** 1. True 2. False; Correction: Real numbers include rational and irrational numbers. 3. False; Correction: 3.456 is rational. 4. True 5. False; Correction: Zero is whole, not natural. 6. True 7. True