1 / 21

Mastering Real Numbers: Classify, Graph, Compare & Simplify

Learn to classify, graph, compare real numbers, estimate square roots, and simplify expressions using square roots. Understand the properties of real numbers and subsets like natural, whole, integer, rational, and irrational numbers.

zachariahm
Download Presentation

Mastering Real Numbers: Classify, Graph, Compare & Simplify

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. 1-3 Real Numbers and the Number Line I Can: classify, graph, and compare real numbers . find and estimate square roots.

  2. Square Root • A number a is a square root of a number bif a2 = b • Example: 72 = 49, so 7 is the square root of 49. Vocabulary to Know

  3. You can use the definition of square root to find the exact square roots of some nonnegative numbers. • The radical symbol indicates a nonnegative square root, that is also called the principal square root. Square Root

  4. Radicand • The expression under the radical symbol is called the radicand. • x is the radicand in this case Vocabulary to Know

  5. Radical • Together, the radical symbol and radicand form a radical. Vocabulary to Know

  6. What is the simplified form of each expression? Simplifying Square Root Expressions

  7. Perfect Square • The square of an integer • For this class, you are required to memorize all perfect squares from 1-144. • Copy this list and study it. 12 = 1 72= 49 22= 4 82= 64 32= 9 92= 81 42 = 16 102 = 100 52= 25 112= 121 62 = 36 122 = 144 Vocabulary to Know

  8. Lobster eyes are made of tiny square regions. Under a microscope, the surface of the eye looks like graph paper. A scientist measured the area of one of the squares to be 386 square microns. What is the approximate side length of the square of the nearest micron? Estimating a Square Root

  9. Numbers can be classified by their characteristics. • Some can be represented on the number line. Types of Numbers

  10. Numbers are classified using sets. • Set- a well-defined collection of objects. • Each object is an element of the set. • Subset- consists of elements from the given set. Sets

  11. natural numbers {1,2,3,…} whole numbers {0,1,2,3,…} Integers {…,-2,-1,0,1,2,…} 0 0 0 Setsof Numbers

  12. Setsof Numbers 3 4 5 6 7 8 • Rational numbers can be written in the form where a and b are integers. They can also be written in decimal form. • Decimals must be terminating or repeating.

  13. Setsof Numbers 3 4 5 6 7 8 • Irrational numbers cannot be written in as a quotient of two integers. • Decimals are non-terminating • Ex: 0.1010010001…, 3.141592…

  14. #1 #2 What kind of number is -5? What kind of number is 42? natural, whole, integer, rational integer, rational

  15. #3 What kind of number is -4.5669? rational

  16. #4 Give an example of a whole number that isn’t positive.

  17. Rational numbers and irrational numbers form the set of real numbers. • Subsets of real numbers: • Natural • Whole • Integer • Rational • Irrational Real Numbers

  18. 8 -6 Inequalities An inequality is a mathematical sentence comparing the values of two expressions using an inequality symbol. -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 >

  19. Inequalities -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 -7 7 <

  20. #5 #6 -5 + 10 10 - 5 -7 10 < =

  21. ODDS ONLY • P.20 #19-31, 41-47, 53-55, 63 Assignment

More Related