the real number system. real numbers the set of all rational and the set of all irrational numbers...

11
The Real Number System

Upload: ashlie-hoover

Post on 27-Dec-2015

232 views

Category:

Documents


0 download

TRANSCRIPT

Page 1: The Real Number System. Real Numbers The set of all rational and the set of all irrational numbers together make up the set of real numbers. Any and all

The Real Number System

Page 2: The Real Number System. Real Numbers The set of all rational and the set of all irrational numbers together make up the set of real numbers. Any and all

Real Numbers

• The set of all rational and the set of all irrational numbers together make up the set of real numbers.

• Any and all kinds of numbers fall under real numbers.

Page 3: The Real Number System. Real Numbers The set of all rational and the set of all irrational numbers together make up the set of real numbers. Any and all

Rational Numbers

Rational numbers are numbers that can be written

as fractions. That is, the form a/b where a and b are

both integers and b ≠ 0.

Page 4: The Real Number System. Real Numbers The set of all rational and the set of all irrational numbers together make up the set of real numbers. Any and all

Examples of Rational Numbers

• -6

• 8 2/5

• .05

• -2.6

• 5.3333333

• -8.12121212…

• √16

Page 5: The Real Number System. Real Numbers The set of all rational and the set of all irrational numbers together make up the set of real numbers. Any and all

Irrational Numbers• Irrational Numbers – numbers that

are not repeating or terminating decimals.

• Examples:

• .01001000100001…• √2 = 1.414213562…• 3.14159…

Page 6: The Real Number System. Real Numbers The set of all rational and the set of all irrational numbers together make up the set of real numbers. Any and all

Whole Numbers, Natural Numbers, and Integers

• Whole Numbers include the following:• 0,1,2,3,4,5,6,7,8,9,10,…..

• Natural Numbers include the following:• 1,2,3,4,5,6,7,8,9,10,….. Does not

include 0.

• Integers include the following:• …-3,-2,-1,0,1,2,3,…

Page 7: The Real Number System. Real Numbers The set of all rational and the set of all irrational numbers together make up the set of real numbers. Any and all

Classifying Real Numbers

• Directions: Classify the following numbers as natural, whole, integer, rational, and/or irrational.

Page 8: The Real Number System. Real Numbers The set of all rational and the set of all irrational numbers together make up the set of real numbers. Any and all

• 8

• This number is a natural number, a whole number, an integer, and a rational number.

• 0.33333

• This repeating decimal is a rational number because it is equivalent to 1/3.

• √17

• √17 = 4.123105… It is not the square root of a perfect square so it is irrational.

Page 9: The Real Number System. Real Numbers The set of all rational and the set of all irrational numbers together make up the set of real numbers. Any and all

• -28/2

• Since -28/4 = -14, this number is an integer and a rational number.

• -√121

• Since -√121 = -11, this number is an integer and a rational number.

Page 10: The Real Number System. Real Numbers The set of all rational and the set of all irrational numbers together make up the set of real numbers. Any and all

Solving Equations

• a2 = 49

• To undo the square, take the square root of both sides. Then, you have this.

• √a2 = √49

• a = √49 or a = -√49

• a = 7 or a = -7

• Hence, the solutions are 7 and -7.

Page 11: The Real Number System. Real Numbers The set of all rational and the set of all irrational numbers together make up the set of real numbers. Any and all

• d2 = 55

• Take the square root of both sides.

• √d2 = √55

• d = √55 or d = - √55

• d = 7.41 or d = - 7.41

• Hence, the solutions are 7.41 and -7.41.