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## Real Numbers and The Number Line

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**Real Numbers and The Number Line**Objectives • Classify numbers and graph them on number lines. • Tell which of two real numbers is less than the other. • Find the additive inverse of a real number. • Find the absolute value of a real number.**Square Root**A square root is one of two equal factors of a number. For example one square root of 64 is 8 since A number like 64, whose square root is a rational number is called a perfect square Example**Square Root**The symbol called a radical sign, is used to indicate the principal square root of the expression under the radical sign For example Note that is not the same as . is not a real number since no real number multiplied by itself is negative**Objective 1 Classify numbers and graph them on number lines**NATURAL NUMBERS {1, 2, 3,…} WHOLE NUMBERS {0, 1, 2, 3,…} INTEGERS {…-2, -1, 0, 1, 2,…} RATIONAL NUMBERS Any number that can be written in fraction form is a rational number. This includes integers, terminating decimals, and repeating decimals. Irrational numbers Numbers that can not be expressed as rational numbers.**Real Numbers**Rational Numbers Integers Irrational Numbers Whole Numbers Natural Numbers The set of Real Numbers consists of the set of rational numbers and the set of irrational numbers.**Examples of Rational numbers**5 0.3 - 7 0**EXAMPLES OF IRRATIONAL NUMBERS**the is a whole number, but the , since It lies between 5 and 6,must be irrational.**Name the sets of numbers to which belongs.**Name the sets of numbers to which belongs. lies between 2 and 3 so it is not a whole number. Example 2-1c Answer:irrational and real Answer:natural , whole , integer , rational, and real**Name the sets of numbers to which each number belongs.**a. b. c. d. Example 2-1f Answer:rational and real Answer:rational and real Answer:irrational and real Answer:natural , whole , integer rational and real (R)**Answer:rational and real**Answer:natural , whole , integer rational and real (R) Answer:irrational and real Answer: integer rational and real (R)**Completeness Property**Each point on the number line corresponds to exactly one real number Example: Graph: ( -4, -2, 0, ,4, )**Objective 2 Tell which of two real numbers is less than the**other Since the numbers are equal. Answer: Example 7-4a Replace the with <, >, or = to make the sentence true.**Objective 2 Tell which of two real numbers is less than the**other Answer: Example 7-4b Replace the with <, >, or = to make the sentence true.**Order Real numbers from least to greatest**From the least to the greatest**Objective 3 Find the additive inverse of a real number.**The opposite of 5 is The opposite of 5 is The opposite of -3 is When you add two opposite numbers , the sum is always 0.**Objective 4 Find the absolute value of a real number**The absolute value of any number n is its distance from zero on a number line and is represented as Example: and 3 units 3 units