Lesson - The Real Number System
 There are 5 different classifications of numbersyou need to know: The Real Number         Systemnatural a.k.a counting numbers whole numbersintegersrational numbersirrational numbers The natural numbers are also known as the counting numbers. They begin with 1, 2, 3,...and they continue indefinitely.So, the number 254,673,843 is also a natural number.Natural Numbers The set of whole numbers includes all of the natural numbers and ONE other number:                          ZERO!So, if we wanted to list the whole numbersin ascending order we would start:0, 1, 2, 3, 4, 5, 6, 7...Whole Numbers The set of numbers called integers (this word comes from the same root as the word integrity) include all of the whole numbers (and, thus, allof the natural numbers), as well as,their opposites (negatives).So, we say that integers are all of the positiveand negative whole numbers and zero....-3, -2, -1, 0, 1, 2, 3,...Integers The root word of rational is ratio, so all rationalnumbers can be written as ratios (a.k.a. fractions).This set of numbers includes all integers, wholenumbers, and natural numbers as well as allnumbers that can be written as a fraction of twointegers, or a terminating (ending) or repeatingdecimal.Examples:  3/4     -8/2     0.342       -0.75    √64-15/3, -3.5, -1, 0, 1.2, 6/9, 32/8, 65/6Rational Numbers Irrational numbers are a set of numbers thatcannot be written as fractions or decimals thatterminate or repeat. They must be written usingspecial symbols because, if we tried to write a decimal equivalent, we would never be ableto stop writing.The most commonly known irrational number isπ (pi). All square roots of numbers that are notperfect squares are irrational (i.e. √7, √94, √2).Irrational Numbers -56Rational NumbersWhole Numbers-7.5 = -15/2The Real Number SystemNatural Numbers0.75 = 3/40.6 = 2/3Integers0103√9-√4Irrational Numbers√60.1010010001...√2√17π√5√3e Let's check what you know:How would you classify 1,345,752?IrrationalRational onlyRational and integer onlyRational, integer, and whole onlyRational, integer, whole, and natural 1,345,752 is rational, integer, whole, and naturalHow would you classify 1/3?IrrationalRational onlyRational and integer onlyRational, integer, and whole onlyRational, integer, whole, and natural 1/3 = 0.3 and is rational onlyHow would you classify 8/2?IrrationalRational onlyRational and integer onlyRational, integer, and whole onlyRational, integer, whole, and natural 8/2 = 4 is rational, integer, whole, and naturalHow would you classify -10?IrrationalRational onlyRational and integer onlyRational, integer, and whole onlyRational, integer, whole, and natural -10 is rational and integer onlyHow would you classify -2/4?IrrationalRational onlyRational and integer onlyRational, integer, and whole onlyRational, integer, whole, and natural -2/4 = -1/2 = -0.5 and is rational onlyHow would you classify √11?IrrationalRational onlyRational and integer onlyRational, integer, and whole onlyRational, integer, whole, and natural IrrationalRational onlyRational and integer onlyRational, integer, and whole onlyRational, integer, whole, and natural√11 is between 3 and 4 and can only beapproximated and is irrationalHow would you classify √81? √81 = 9 and is rational, integer, whole, and natural
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