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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.

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Presentation on theme: "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."— Presentation transcript:

1 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.

2 Square Root A square root is one of two equal factors of a number. For example one square root of 64 is 8 since perfect square A number like 64, whose square root is a rational number is called a perfect square Example

3 Square Root radical sign, is used to indicate the principal square root of the expression under the radical sign 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

4 Find Square Roots

5 NATURAL NUMBERS {1, 2, 3,…} WHOLE NUMBERS {0, 1, 2, 3,…} INTEGERS {…-2, -1, 0, 1, 2,…} RATIONAL NUMBERS fraction integersterminating decimalsrepeating decimals 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. Objective 1 Classify numbers and graph them on number lines

6 Real Numbers Rational Numbers Irrational Numbers Natural Numbers Whole Numbers Integers The set of Real Numbers The set of Real Numbers consists of the set of rational numbers and the set of irrational numbers.

7 Examples of Rational numbers

8 EXAMPLES OF IRRATIONAL NUMBERS the is a whole number, but the, since It lies between 5 and 6,must be irrational.

9 Example 2-1c Answer:irrational and real Name the sets of numbers to which belongs. lies between 2 and 3 so it is not a whole number. Answer:natural, whole, integer, rational, and real Name the sets of numbers to which belongs.

10 Example 2-1f Name the sets of numbers to which each number belongs. a. b. c. d. Answer: rational and real Answer: irrational and real Answer: natural, whole, integer rational and real (R)

11 Answer: rational and real Answer: natural, whole, integer rational and real (R) Answer: irrational and real Answer: integer rational and real (R)

12 Example: Graph: ( -4, -2, 0,,4, ) Each point on the number line corresponds to exactly one real number Completeness Property

13 Example 7-4a Replace the with, or = to make the sentence true. Sincethe numbers are equal. Answer: Objective 2 Tell which of two real numbers is less than the other

14 Example 7-4b Replace the with, or = to make the sentence true. Answer: Objective 2 Tell which of two real numbers is less than the other

15 Objective 2 Order Real numbers from least to greatest

16 From the least to the greatest Order Real numbers from least to greatest

17 The opposite of 5 is The opposite of -3 is When you add two opposite numbers, the sum is always 0. Objective 3 Find the additive inverse of a real number. The opposite of 5 is

18 The absolute value of any number n is its distance from zero on a number line and is represented as Example : and 3 units Objective 4 Find the absolute value of a real number

19 END OF LESSON


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