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1-3 Real Numbers and the Number Line

1-3 Real Numbers and the Number Line. I Can: classify, graph, and compare real numbers . find and estimate square roots. Square Root A number a is a square root of a number b if a 2 = b Example: 7 2 = 49, so 7 is the square root of 49. Vocabulary to Know.

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1-3 Real Numbers and the Number Line

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  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

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