# Lesson 1.3 - Exploring Real Numbers

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### 1.3 Exploring Real Numbers :

1.3 Exploring Real Numbers

### Vocabulary :

Vocabulary 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

### More Vocabulary… :

More Vocabulary… If a number is rational, it could also be one of the following: 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… Whole Numbers: 0,1,2,3…. Only positive numbers and 0 (the word “whole” has an 0 in the middle!) Natural Numbers: 1,2,3,4…. Also called Counting Numbers - These are the numbers we naturally count with

### 1. Identifying Sets of Numbers :

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

### 2. 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?

### 3. Counterexamples :

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

### 4. Inequalities :

4. Inequalities Inequality: compares the value of two quantities, using <, >, =, or =. Write - , - , and - in order from least to greatest. Find the decimal approximation of each. - , - , -

### 4. Opposites and Absolute Value :

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