Presentation on theme: "Classification of the Real Number System"— Presentation transcript:
1 Classification of the Real Number System When you are ready to record start on slide 3! When you save your podcast as a video file, it will add these two slides automatically. Cool , huh?
2 RealNot RealRationalIrrationalRational - any number that can be written as the ratio of two integers, which consequently can be expressed as a terminating or repeating decimal.Irrational - numbers that cannot be written as a ratio of two integers.
3 RealRationalIrrationalIntegersIntegers are positive and negative whole numbers and zero such as … -4, -3, -2, -1, 0, 1, 2, 3, 4 and so on.Important TipIntegers do not have any fractional parts. So numbers such a ½, .3, 2 ¼ , 25% etc are not integers because they involve fractional parts.
4 Also …When determining if a number is rational the number must be able to be written in such a way that the numerator and denominator is a positive or negative whole number.Additionally …The numerator can be zero but not the denominator.
5 Examples of Rational Numbers Terminating decimalorNumberRatio of twointegersrepeating decimal5.000terminating.250terminating20%.20terminating=repeating-8-8.0terminating-2.5-2.50terminating-2=--6.0terminating0.0terminating
6 The set of rational numbers has subsets Some common subsets of rational numbers areNatural/counting numbersWhole numbersIntegersSome numbers fall into more than one category
7 RealNatural/counting numbers (N) are positive whole numbers beginning with 1. A way to remember natural / counting numbers is to think about what number you begin counting with So natural / counting numbers are numbers such as 1, 2, 3, 4, etc.Natural
8 RealWhole numbers (W) include ALL counting numbers and 0. So whole numbers are 0, 1, 2, 3, 4, etc.WholeNatural
9 Real Integers Whole Natural Integers (Z) were explained previously but to recall they include all natural/counting numbers and whole numbers. They are positive and negative whole numbers and 0 such as … -4, -3, -2, -1, 0, 1, 2, 3, 4 …RealIntegersWholeNatural
10 Real Rational Integers Whole Natural Rational Numbers (Q) recall that they are zero and all positive and negative numbers that can be expressed as a ratio of two integers (with no zero in the denominator), including integers, whole numbers, and natural/counting numbers.RationalIntegersWholeNatural
11 Real Rational Irrational Integers Whole Natural Irrational Numbers (I) recall that they are real numbers that are not rational and cannot be written as a ratio of integers.RationalIrrationalIntegersWholeNatural
12 Examples of Irrational Numbers 3 220Pi 𝞹… (and more)……Irrational numbers are considered real numbers.The real number system can be divided into two categories – rational and irrational. Many students tend to think that irrational numbers are not real.This is not true. Irrational numbers ARE real but just are expressed differently than rational numbers.
13 Basically in order to determine if a number is real, ask yourself if the numbers can be placed on a number line. If the number can be placed on a number line or be ordered, then the number is real.-1-2-3-4-5-6123456
20 𝒙 𝟐 = −𝟏 𝒙 𝟐 = −𝟏 𝒙 = −𝟏 Numbers Not Considered Real 𝟏𝟖 𝟎 𝟑 𝟎 −𝟕.𝟑 𝟎 𝒙 𝟐 = −𝟏𝟏𝟖 𝟎𝟑 𝟎−𝟕.𝟑 𝟎𝒙 𝟐 = −𝟏𝒙 = −𝟏These numbers are undefined because zero is in the denominator and cannot be considered a real number. They are not numbers at all.The square root of any negative number are numbers not considered real.
21 RationalNumbers Not Considered Real-5Integers−25-5-57 0− 2 3Whole18%− 67−2. 738 2Natural/Counting20 21 326Irrational0 20121 3
22 RationalNumbers Not Considered Real-5𝟕 𝟎Integers−25-5-57 0− 2 3Whole18%− 67−2. 738 2Natural/Counting20 21 326Irrational0 20121 3
23 RationalNumbers Not Considered Real-518%7 0Integers−25-5-57 0− 2 3Whole18%− 67−2. 738 2Natural/Counting20 21 326Irrational0 20121 3
24 Rational8 2Numbers Not Considered Real-518%7 0Integers−25-58 2-57 0− 2 3Whole18%8 2− 67−2. 738 2Natural/Counting20 21 38 226Irrational0 20121 3
25 Rational8 226Numbers Not Considered Real-518%7 0Integers26−25-58 2-57 0− 2 3Whole2618%8 2− 67−2. 738 2Natural/Counting20 21 38 22626Irrational0 20121 3