real numbers quiz grade 9

📚 Quick Study Guide

• 🔢 Real Numbers: Real numbers include all rational and irrational numbers.
• ➕ Rational Numbers: Numbers that can be expressed as a fraction $\frac{p}{q}$, where p and q are integers and q ≠ 0.
• ➗ Integers: Whole numbers (positive, negative, and zero). Examples: -3, -2, -1, 0, 1, 2, 3.
• ♾️ Irrational Numbers: Numbers that cannot be expressed as a fraction. They have non-repeating, non-terminating decimal representations. Examples: $\pi$, $\sqrt{2}$.
• 💯 Perfect Squares: Numbers that are squares of integers. The square root of a perfect square is always a rational number.
• 📝 Decimal Representation: Rational numbers have either terminating or repeating decimal representations. Irrational numbers have non-terminating and non-repeating decimal representations.
• 💡 Key Properties: Real numbers follow commutative, associative, and distributive properties.

📝 Practice Quiz

1. Which of the following is an irrational number?
   1. A. 0.75
   2. B. $\sqrt{16}$
   3. C. $\frac{2}{3}$
   4. D. $\sqrt{5}$
2. Which of the following is a rational number?
   1. A. $\pi$
   2. B. $\sqrt{3}$
   3. C. $\sqrt{9}$
   4. D. 3.14159265...
3. Which of the following numbers is an integer?
   1. A. 2.5
   2. B. -7
   3. C. $\frac{1}{2}$
   4. D. $\sqrt{2}$
4. Which statement is true about rational numbers?
   1. A. They cannot be expressed as a fraction.
   2. B. They have non-repeating, non-terminating decimal representations.
   3. C. They can be expressed as a fraction $\frac{p}{q}$, where p and q are integers and q ≠ 0.
   4. D. They are always positive.
5. Which of the following is a perfect square?
   1. A. 5
   2. B. 10
   3. C. 16
   4. D. 20
6. Which number has a non-terminating and non-repeating decimal representation?
   1. A. $\frac{1}{4}$
   2. B. $\frac{1}{3}$
   3. C. $\sqrt{4}$
   4. D. $\sqrt{7}$
7. Which property applies to all real numbers?
   1. A. Closure under division
   2. B. Commutative property of addition
   3. C. Existence of multiplicative inverse for all numbers
   4. D. Associative property of subtraction