Grade 9 Chapter 1 Booklet 1 Numbers - 2024-2025 PDF

2024-2025 GRADE 9 2022-202 Booklet 1 – Chapter 1 Numbers NAME SURNAME  Learning Objectives: MAT 9.1.1. Discern the operations of exponents and radicals in real numbers. Prerequisites: Operating with decimals...

2024-2025 GRADE 9 2022-202 Booklet 1 – Chapter 1 Numbers NAME SURNAME  Learning Objectives: MAT 9.1.1. Discern the operations of exponents and radicals in real numbers. Prerequisites: Operating with decimals Determining the place value of a given decimal Calculating the exponent of a given rational number base to an integer power Determining the two integers that an irrational number is in between Graphing a real number interval on a number line Determining if the square root of a rational number is rational or irrational Operating with rational numbers and to know the addition and multiplication has the commutative, associative properties and to know the identity and null elements of those operations. Operating with the distribution property of multiplication over addition and subtraction. Vocabulary of the Unit exponent (power): üs base: taban exponential expression: üslü ifade principal root: pozitif kök radical: kök radical expression: köklü ifade radicand: kökün içindeki ifade index/degree of the root: kökün derecesi conjugate: eşlenik 1  Review: Work in pairs to solve the following questions. 1. Perform the operations given below. a) 0.19 + 2.01 2 20 !.#$%&!.!% b) #.$ 2 70 0.1 c) (−0.2)(0.1): 0.004 0 2 100 0 2 25 5 2. Write the given expressions as exponents. a) 2 ∙ 2 ∙ 2 ∙ 2 ∙ 2 ∙ 2 26 5 b) (−3) ∙ (−3) ∙ (−3) ∙ (−3) ∙ (−3) C 3 $ $ $ $ 4 c) ∙ ∙ ∙ ' ' ' ' f d) 011111121111113. ∙. ∙. ∙. ∙ …∙. ∙. ∙. 2100 $!! )*+ 3. Simplify the following radical expressions to their simplest form. a) √49 7 b) √1.69 1.32T 1 3 c) √0.04 V0.27 0.2 F ,- d) −6.$ 4. Graph each interval on a number line. a. (−3,3) 0 2  b. [4,9) 0 9 c. (−2,0] zero 0 d. [−8, −5] 0 5. For each radical number plot its location on a number line. nd cat ng the nearest ntegers a. √8 0 b. −√11 4 0 c. √29 0 g 6. Calculate the area and the perimeter of the given rectangle, square, and circle algebraically. 2< + = b a. D 2 20 6 20 2 49 8a 2< − = 29 6 20 6 A 49262 b. 3> c. F 2 T 4 D 4.39 4. 8TX 129 ? A T 4 32 A 3 32 2 167 9y 3  Exponents Read & Discuss: To increase the temperature of 1 gram of aluminum by 1 °C, 0.21 cal of heat must be added to the aluminum. The distance from Uranus to Earth, when Uranus is at its closest position to Earth, is approximately 2.57 × 10#% km. A neutron is a particle found in the atomic nucleus with a mass of 1.675 × 10&#- grams. For a square-shaped carpet with an area of 21 m², the length of one side is √21 meters. The world record for the 100 meters in athletics is 9.58 seconds, set by Usain Bolt. Now discuss your ideas with your classmates while thinking the probing questions below. 1. What are the advantages of using exponential and radical notation in real-life situations? 2. Provide examples of how exponential and radical notation is used in various scientific fields. 3. Why is decimal notation necessary for recording finish times in a 100-meter race? Exponential Notation of Real Numbers The approximate number of atoms in the human body can be expressed as a 29-digit number like 100 000...0. Archimedes used a 63-digit number like 800...0 to represent the number of grains of sand required to fill the entire universe. The approximate number of stars in the universe can be expressed as a 23-digit number like 10...0. The diameter of a hydrogen atom's nucleus is 0.00000000000000175 meters. Writing and reading such large or small numbers is quite difficult. Exponential notation provides a convenient way to write and work with very large or very small numbers. 4 For < ∈ ℝ and D ∈ ℝ, 01 < ∙ 1121 … ∙ < =