Real Numbers Types of Real Numbers Image source numbers-rational-irrational-ecot-culver-math-education-ppt-powerpoint-

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

Real Numbers ✦ Two major groups - ✦ Rational ✦ & Irrational Image from wM/t3H-Sngze0A/s320/rational.gif Image source QiPLI/AAAAAAAAApM/aZVDaddjsmc/S220/321.j pg QiPLI/AAAAAAAAApM/aZVDaddjsmc/S220/321.j pg

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 wM/t3H-Sngze0A/s320/rational.gif wM/t3H-Sngze0A/s320/rational.gif

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.

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.

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

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.

Real Numbers Rational Irrational Integers Whole Natural

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.