Download 8.1 Symbols and Sets of Numbers

8.1
Symbols and Sets of Numbers Learning Objectives: 1. Define the meaning of the symbols: =, ≠, <, >, ≤ , and > . 2. Translate sentences into mathematical statements. 3. Identify integers, rational numbers, irrational numbers, and real numbers. 4. Find the absolute value of a real number. 1. Define the meaning of the symbols: =, ≠, <, >, ≤ , and > . Definitions: 1. Natural Numbers—are counting numbers. 2. Whole Numbers—are counting numbers and 0. Order Property for Real Numbers: For any two real numbers a and b, 1. a is less than b if a is to the left of b on the number line. 2. a is greater than b if a is to the right of b on the number line. Example 1. Insert <, >, or = in the space between the paired numbers to make each statement true. − 2.21 _________ − 2.12 Example 2. Determine whether each statement is true or false. 3.002 > 3.202 2. Translating sentences into mathematical statements Example 3. Translate each sentence into a mathematical statement. 1. Negative eleven is less than or equal to negative four. 2. Fourteen is greater than one. 3. Identify Integers, Rational Numbers, Irrational Numbers, and Real Numbers Definitions: 1. Integers—are positive, negative numbers and zero. ⎧a
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2. Rational Numbers—are any numbers that can be written as ⎨ a and b are interger and b ≠ 0⎬ . ⎩b
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3. Irrational Numbers—are nonrational numbers that correspond to points on the number line. 4. Real Numbers—are all numbers that correspond to points on the number line. 5. Absolute Value, a —is the distance between a and 0 on the number line. Example 4. Tell which set or sets each number belongs to: natural numbers, whole numbers, integers, rational numbers, irrational numbers, and real numbers. Real number Natural Whole Rational Irrational Integer number number number number number 5 8
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5 −2 0 4. Find the Absolute Value of a Real number Example 5. Find each absolute value. 2
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Example 6. Place the following numbers on the number line provided: ‐6 ‐5 ‐4 ‐3 ‐2 ‐1 0
1
2
3
4
5
13
1
7
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, − , − , 4
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2 10
6
7 8