1. Real Numbers Types of Real Numbers Image source http://c.asstatic.com/images/sunnyrain43229-70600-real- numbers-rational-irrational-ecot-culver-math-education-ppt-powerpoint- 180_135.jpghttp://c.asstatic.com/images/sunnyrain43229-70600-real- numbers-rational-irrational-ecot-culver-math-education-ppt-powerpoint- 180_135.jpg

2. Real Numbers ✦ Two major groups - ✦ Rational ✦ & Irrational Image from http://2.bp.blogspot.com/_gWQaU40PH24/S4BfSLW_ONI/AAAAAAAAF wM/t3H-Sngze0A/s320/rational.gif Image source http://3.bp.blogspot.com/_r9OeV7enT6s/SctQz4 QiPLI/AAAAAAAAApM/aZVDaddjsmc/S220/321.j pg http://3.bp.blogspot.com/_r9OeV7enT6s/SctQz4 QiPLI/AAAAAAAAApM/aZVDaddjsmc/S220/321.j pg

3. Rational Numbers ✦ What does it mean to act rational? Hmmm.... ✦ Rational is something that makes sense. ✦ Rational numbers make sense because they are predictable. ✦ Rational numbers fall into 1 of 2 categories. Image from http://2.bp.blogspot.com/_gWQaU40PH24/S4BfSLW_ONI/AAAAAAAAF wM/t3H-Sngze0A/s320/rational.gif http://2.bp.blogspot.com/_gWQaU40PH24/S4BfSLW_ONI/AAAAAAAAF wM/t3H-Sngze0A/s320/rational.gif

4. Rational Numbers - Category 1 ✦ What do these numbers have in common? ✦ Notice they all stop or terminate. ✦ What about the fractions? Change them to decimals. ✦ Do they terminate now? ✦ Rational numbers are like the terminator because they terminate or end. ✦ The first category Rational Numbers can fall in is terminating numbers.

5. Rational Numbers - Category 2 ✦ What do these numbers have in common? ✦ Can you guess what the next number will be for each of these numbers? ✦ What about the fractions? ✦ Change them to decimals. Can you predict the next number? ✦ Notice they these numbers follow a predictable pattern. ✦ The second category Rational Number may fall in is following a predictable pattern.

6. Irrational Numbers ✦ What does it mean when a person is irrational? Hmm.... ✦ What do you notice about these numbers? ✦ Can you predict the next number? ✦ When do they end? (Put the square roots in a calculator to analyze their decimal equivalent.) ✦ Irrational numbers are unpredictable numbers just like an irrational person has unpredictable behavior. ✦ Irrational Numbers never end and the next number cannot be guessed because no pattern exists. Image from http://bulk2.destructoid.com/ul/181777-IrrationalMainImage.jpghttp://bulk2.destructoid.com/ul/181777-IrrationalMainImage.jpg

7. Types of Rational Numbers ✦ Natural Numbers (also called the Counting Numbers) ✦ What number do you naturally start with when you count? ✦ 1. ✦ The Natural Numbers are the numbers we count with beginning with 1. ✦ 1, 2, 3, 4,... ✦ Wh0le Numbers - The natural numbers plus zero ✦ 0, 1, 2, 3, 4,... ✦ Integers - All whole numbers and their opposites. In-other-words, all positive and negative numbers without decimals or fractions. ✦... -3, -2, -1, 0, 1, 2, 3,... ✦ Notice some numbers fall into more than one category.

8. Real Numbers Rational Irrational Integers Whole Natural

9. Be sure you can do the following... ✦ Describe the difference between an irrational and rational number. ✦ Describe the characteristics of a natural number. ✦ Describe the characteristics of a whole number. ✦ Describe the characteristics of a integer. ✦ Give a example of ✦ an irrational number. ✦ a rational number and one that is not an integer. ✦ an integer and one that is not a whole number. ✦ a whole number and one that is not a natural number. ✦ a natural number.