Real Numbers Week 1 Topic 1

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, …  Real Numbers  Set of all irrational and rational numbers

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…}

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}

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

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}

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

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

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

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

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 = 64; 9 2 = 81; 10 2 = 100; 11 2 = 121; 12 2 = 144; 13 2 = 169