Henry County Public Schools



SOL 8.2 The student will describe the relationships between the subsets of the real number system.THINGS TO KNOW:? Numbers can belong to more than one subset of the real number system.? Natural numbers are the counting numbers {1, 2, 3…}.? Whole numbers are zero and the counting numbers {0, 1, 2, 3…}.? Integers are the whole numbers, their opposites, and zero {…-2, -1, 0,1, 2…}.? Rational numbers are those numbers that can be written as fractions.? Rational numbers written in decimal form include terminating and repeating decimals.? Irrational numbers cannot be written as fractions. When written in decimal form that are nonterminating, nonrepeating decimals.HINTS/TRICKY FACTS? DECIMALS!? Ending = Rational? Repeating = Rational?NOT ending, NOT repeating = Irrational? Rational + Rational = Rational? Rational × Rational = Rational? Rational + Irrational = Irrational?(non-zero) Rational × Irrational = Irrational?One subset can be partially or totally included in another subset.? ALL natural numbers arewhole.?Only SOME whole numbers are natural.VISUAL MODEL EXAMPLES1). Identify each value that can be represented as an integer.2).50.75?9?243? 225 8.0Identify the relationships between the subsets of the real number system by placing the correct subset name in each shaded box.Integers Irrational NumbersNatural Numbers Rational NumbersWhole Numbers3). Select all real number subsets to which the numbers in this set belong.?12 , ?256,200%?? ?? 3 ?Integers IrrationalNumbersRationalNumbersNaturalNumbersWholeNumbers4). Which of the following is a rational number?A. 3.2871...B. 2.36 C. 30 D. π5). Sort the numbers into the correct column.6). Sort the numbers into the correct column.??2.1, 3 , 3 ,5, ?2,1.00?{2.6,1.72...,3.375,9, ?55, π}? ?? 1 5 ?Rational IrrationalInteger Not an integer7). Which of the Venn Diagrams below does NOT correctly show a relationship between subsets of the real number system?8). Place the numbers in the correct location in the Venn Diagram.?6 ,?8,9, ? 2?? ??3 1?9). All of the following statements are true except:A. Repeating decimal numbers are rational numbers.B. Some integers are natural numbers.C. No whole numbers are rational numbers. D. All natural numbers are real numbers.10). Which statement is true?A. All square roots are rational.B. Some integers are irrational numbers. C. The sum of two rational numbers isirrational.D. The smallest natural number is 1.Questions/comments about this activity?Contact: Kelly Johnson – kpjohnson@henrico.k12.va.us

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