TechMathII - 1.1 - The Set of Real Numbers
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The document defines and provides examples of different types of numerical sets: - Natural numbers are counting numbers like 1, 2, 3, etc. - Whole numbers include natural numbers and 0. - Integers include all whole numbers and their negatives. - Rational numbers are numbers that can be written as fractions like a/b where a and b are integers. - Irrational numbers cannot be written as fractions and include numbers like the square root of numbers and pi. - Real numbers include all numbers, both rational and irrational.
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TechMathII - 1.1 - The Set of Real Numbers
- 1. Vocabulary Natural Numbers : or “counting numbers” : 1, 2, 3, … Whole Numbers : “counting numbers AND 0” : 0, 1, 2, 3, … Integers : All whole numbers, both positive and negative. : …, -3, -2, -1, 0, 1, 2, …
- 2. Vocabulary Rational Numbers : any number you can write as a/b, where a and b are integers and b ≠0 : fractions : decimals that terminate or stop Irrational Numbers : no fractions, no whole numbers, no integers : 1.10002111101… : √91 : pi
- 3. Vocabulary Real Numbers : everything is always a real number! :all numbers!
- 4. Examples Name the set(s) of numbers to which each number belongs. 1) 35.99 2) 5/6 3) 0 4) 5 1/8 5) √5 6) -80
- 5. You try! Name the set(s) of numbers to which each number belongs. 1) -32 2) 4/2 3) √1.6 4) 5/8
- 6. Inequality A mathematical sentence that compares the value of two expressions using an inequality symbol such as < or >. a ≥ b Greater than or equal to a ≠ b Is not equal to a ≤ b Less than or equal to a > b Greater than a = b Is equal to a < b Less than
- 7. Examples Write in order from least to greatest. 1) -3/8, -1/2, -5/12 2) -8/9, -7/8, -22/25 3) 1/12, -2/3, -5/8 Step 1: Write as a decimal. Step 2: Write from least to greatest using a number line.
- 8. You try! Write in order from least to greatest. 1) -3/4, -7/12, -5/8 2) -1/3, -2/9, -3/8 3) 1/8, 1/15, 3/16
- 9. Absolute Value -the distance away from 0 on a number line Find each absolute value. |12| |-2/3| |0| |-2.9| |5/8|
- 10. Homework Real Numbers WS