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Real Numbers Week 1 Topic 1

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Real Numbers Irrational Numbers Numbers that cannot be written as a fraction √2, π Rational Numbers Numbers that can be written as a fraction Decimals that repeat Decimals that stop √25, ½, 5, 0.123, 0.333333… Real Numbers Set of all irrational and rational numbers

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Real Numbers Integers Positive and negative counting numbers (plus 0) {…-3, -2, -1, 0, 1, 2, 3…) Whole Numbers Counting numbers starting at 0 {0, 1, 2, 3…} Natural Numbers Counting numbers starting at 1 {1, 2, 3…}

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Real Numbers Infinite sets- not countable Whole numbers greater than 8 {3, 4, 5 …} Finite sets- countable Integers between 2 and 17 {2, 5, 7, 19, 23}

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Real Numbers Estimating the value of an irrational number Compare perfect square values List perfect squares close to your value √67 √49 = 7; √64 = 8; √81 = 9 67 is between 64 and 81 so √67 is between 8 and 9 8 < √67 < 9

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Real Numbers 1.Which of the following represents an infinite set of numbers? a.{1/2, 1/3, ¼, 1/5} b.{Negative integers} c.{-3, -1, 0, 1, 3} d.{Natural numbers between 5 and 20}

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Real Numbers 1.Which of the following represents an infinite set of numbers? a.{1/2, 1/3, ¼, 1/5} This set has a clear start and stop, we see exactly 4 values in the set so it is countable or finite b.{Negative integers} integers go off to infinite so this set is not countable c. {-3, -1, 0, 1, 3} We can count the 5 values in this set. d.{Natural numbers between 5 and 20} We can list and count the values in this set. 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20

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Real Numbers 2.Which of the following is an irrational number? a. √5 b. √9 c.7 d.3.78

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Real Numbers 2.Which of the following is an irrational number? a. √5 b. √9 = 3 whole numbers are rational c.7 = 7/1 whole numbers are rational d.3.78 = 378/100 decimals that stop are rational

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Real Numbers 3. Between which two consecutive integers is √113 ? a. 12 and 13 b. 8 and 9 c. 10 and 11 d. 11 and 12

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Real Numbers 3. Between which two consecutive integers is √113 ? a. 12 and 13 b. 8 and 9 c. 10 and 11 d. 11 and 12 8 2 = 64; 9 2 = 81; 10 2 = 100; 11 2 = 121; 12 2 = 144; 13 2 = 169

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