1.3 Exploring Real Numbers

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1.3 Exploring Real Numbers

*All numbers are either Rational or Irrational* Real Numbers: The set of numbers containing both rational and irrational numbers All the numbers we deal with are REAL  *All numbers are either Rational or Irrational* Rational Numbers: Any number you can write as a fraction Any decimal that either ends or repeats with a pattern Irrational Numbers: Any number that cannot be written as a fraction Non-terminating, non-repeating wacky decimals Examples? If a number is irrational, it cannot belong to any other set Vocabulary

If a number is rational, it could also be one of the following: Natural Numbers: 1,2,3,4…. Also called Counting Numbers - These are the numbers we naturally count with Whole Numbers: 0,1,2,3…. Only positive numbers and 0 (the word “whole” has an 0 in the middle!) Integers: Negatives and positive numbers and 0 No fractions or decimals All the numbers you see on my number line -2, -1, 0, 1, 2… More Vocabulary…

1. Identifying Sets of Numbers a) -13 Rational numbers Integers b) 3.28 c) d) 42 Natural numbers Whole Numbers 1. Identifying Sets of Numbers

2. Identifying Sets of Numbers a) outdoor temperatures Integers or Rational Numbers b) the number of beans in a bag Whole Numbers Why not Natural Numbers? 2. Identifying Sets of Numbers

A counterexample is an example that proves a statement false. True or False: All negative numbers are integers. False Counterexample? 3. Counterexamples

Inequality: compares the value of two quantities, using <, >, ≤, or ≥. Compare the following fractions: 4 4 18 24/7 13 15 7 4. Inequalities

Write - , - , and - in order from least to greatest. Find the decimal approximation of each. - , - , - 5. Order fractions

4. Opposites and Absolute Value Opposites are on opposites sides of zero and are the same distance away from zero. Examples? -2 and 2, -6 and 6, etc. Absolute Value is the distance a number is from zero. a) l-2.5l 2.5 b) l7l 7 4. Opposites and Absolute Value

Wednesday, August 24 Keep your assignment out. We are going to grade. Please bring a pen to class to use. Remember, no stars, just a mark if the answer is wrong. Wednesday, August 24

Answers for 1-18 Integers, rational Rational Irrational Answers vary Natural, whole, integers, rational Whole Whole, integers, rational Integers Answers for 1-18

20. False 22. True 24. > 26. > 28. 2.001, 2.01, 2.1 30. -5/6, -1/2, 2/3 32. 0.63, 0.636, 7/11 34. 4 36. 9/14 38. 3/5 40. 1295 Answers for 20-40 even