Lesson - The Real Number System

There are 5 different classifications of numbersyou need to know: The Real Number System natural a.k.a counting numbers whole numbers integers rational numbers irrational 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 numbers in 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, 65/6 Rational 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 -56 Rational Numbers Whole Numbers -7.5 = -15/2 The Real Number System Natural Numbers 0.75 = 3/4 0.6 = 2/3 Integers 0 103 √9 -√4 Irrational Numbers √6 0.1010010001... √2 √17 π √5 √3 e Let's check what you know: How would you classify 1,345,752? Irrational Rational only Rational and integer only Rational, integer, and whole only Rational, integer, whole, and natural 1,345,752 is rational, integer, whole, and natural How would you classify 1/3? Irrational Rational only Rational and integer only Rational, integer, and whole only Rational, integer, whole, and natural 1/3 = 0.3 and is rational only How would you classify 8/2? Irrational Rational only Rational and integer only Rational, integer, and whole only Rational, integer, whole, and natural 8/2 = 4 is rational, integer, whole, and natural How would you classify -10? Irrational Rational only Rational and integer only Rational, integer, and whole only Rational, integer, whole, and natural -10 is rational and integer only How would you classify -2/4? Irrational Rational only Rational and integer only Rational, integer, and whole only Rational, integer, whole, and natural -2/4 = -1/2 = -0.5 and is rational only How would you classify √11? Irrational Rational only Rational and integer only Rational, integer, and whole only Rational, integer, whole, and natural Irrational Rational only Rational and integer only Rational, integer, and whole only Rational, integer, whole, and natural √11 is between 3 and 4 and can only beapproximated and is irrational How would you classify √81? √81 = 9 and is rational, integer, whole, and natural |

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