REAL NUMBERS LESSON 1.1

INTRODUCTION…. -What are real numbers? -Real Numbers: are any number except for variables -Variables– letters that represent numbers -Where do we see real numbers in life (outside of math class)?

DEFINITIONS

TYPES OF RATIONAL NUMBERS

EXAMPLE 1 WRITE EACH FRACTION AS A DECIMAL

EXAMPLE 2 EXPRESSING DECIMALS AS RATIONAL NUMBERS Write each fraction in simplest form  The decimal means “825 thousandths” so put 825 over 1000  Simplify: divide the numerator and denominator by  How many repeating decimals are there?  The decimal 0.37…. Means 37 hundredths. BUT there is a REPEAT SIGN….  Because of the repeating sign, you have to subtract the denominator by 1 (100-1)  Simplify if necessary Turn to page 9 in your textbook and do “Your Turn”

FINDING SQUARE ROOTS &CUBE ROOTS LESSON 1.1

DEFINITIONS Square root : is to use to unsquare a number  Symbol for square root is √  There are two square roots for every positive number  EXAMPLE: the square root of 36 is ……..  HINT: what two same numbers go into 36?  Correct 6 x 6 = 36  The square root for 36 is both 6 and -6  Principle Square Root: the positive number  EXAMPLE: what is the principle square root of 36?  Is it 6 or -6  The answer is 6. It is the positive number

SQUARE ROOT EXAMPLES

PERFECT SQUARES -What is a perfect square? -Perfect Square: has two square roots that are integers. The numbers are the same. -What are examples? -Example: the perfect square of 81 is 9 and -9 Let’s Explore Perfect Squares 1 2 = √ 2 2 = √ 3 2 = √ 4 2 = √ 5 2 = √ 6 2 = √ 7 2 = √ 8 2 = √ 9 2 = √ 10 2 = √

EXAMPLE 3: SQUARE ROOTS

CUBE ROOTS -What is a cube root? -Cube Root: is to uncube a number -There is only one cube root for every positive number -Symbol 3 √ -Example: -The cube root of 8 is 2 because 2 x 2 x 2 = 8 -The cube root of 27 is 3 because 3 x 3 x 3 =27 -Perfect Cube: has a cube root that is an integer. -The examples above are perfect cubes Let’s Explore Perfect Cubes 1 3 =3 √ 2 3 = 3 √ 3 3 = 3 √ 4 3 =3 √ 5 3 = 3 √ 6 3 = 3 √ 7 3 = 3 √ 8 3 = 3 √ 9 3 = 3 √ 10 3 = 3 √

EXAMPLE 4: CUBE ROOTS X 3 = 729  Solve for x by taking the cube root of both sides  3 √ X 3 = 3 √ 729  Apply the definition of cube roots  Why can the number NOT be negative?  When a number is cubed, the answer can only be positive Turn to page 10 and do problems 7-10 on “Your Turn”

EXPLORING IRRATIONAL NUMBERS LESSON 1.1

IRRATIONAL NUMBERS Irrational Numbers are numbers that have a decimal expansion that go on forever (infinity) without a repeating pattern Examples  …..  Π = ….

ESTIMATING IRRATIONAL NUMBERS Square roots of numbers that are not perfect squares are irrational Example √3  to estimate the √3, first find the two consecutive perfect squares that 3 is between √1 = 1 √4 = 2  Simplify the square roots of perfect squares √3 is between 1 and 2  Find the square root of 3 on your calculator…. Plot on a number line Turn to page in the textbook and complete those pages together!

PRACTICE ACTIVITY: RATIONAL VS. IRRATIONAL  Rational----- decimal terminate …..  Irrational---- decimal doesn’t terminate or repeat 5/9  Rational-----number is in fraction for √15  Irrational---- decimal form does not terminate Tell whether each real number is rational or irrational