The document provides an overview of topics to be covered in exponents, scientific notation, square roots, and rational/irrational numbers. It includes examples and practice problems for exponents, zero exponents, negative exponents, scientific notation, standard notation, and square roots. A quiz will take place on Tuesday 12/8 and a test on Friday 12/18 covering this material.

1. December 2009 Exponents Square Root Scientific Notation Maybe Rational/Irrational Numbers Quiz Tuesday - 12/8 Test Friday - 12/18

2. Exponents Write the product as a power and describe it in words: 1.) 4*4*4*4*4*4 4 6 , 4 to the sixth power 2.) R*R*R R 3 , R to the third power or R cubed 3.)7*7*7*7*7*T*T*T*T 7 5 T 4 , 7 to the fifth power times T to the fourth power

3. Exponents Evaluate the Power: 4 squared 5 3 1 19 0 4 3 5

4. Do Now 12/3 Write the product as a power and describe it in words: 1.) 8*8 2.) L*L*L*L*L*L*L*L Evaluate the Power: 3.) 6 4 4.) 11 1 5.) 2 5

5. Zero Exponents Zero Exponents- For any number a≠0 a 0 = 1 Ex 1: 5 0 = Ex 2: 32,543,325 0 = Ex 3: (34xpr) 0 = Be Careful!! Ex 4: 14xy 0 =

6. Negative Exponents Negative Exponents – for any integer n and any number a≠0: a -n = 1 a n Ex 1: 3 -2 = EX 2: y -6 = Ex 3: r 2 t -4 = 1 3 2 1 y 6 r 2 t 4

7. Negative and Zero Exponents Evaluate the Expressions: 6 -2 (-2) -3 (-5) 0 (-3) -1 4 -5

8. Negative and Zero Exponents Evaluate the Expressions: 6) (-4) -3 * (-4) 0 7) (-5) 0 * (-5) -3 8) 2 -2 * -2 9) (-3) -6 * 3 2

9. Do Now 12/4 Evaluate the Expressions: (-8) -3 (-5) 0 (-5) 0 * (-5) -3 2 -2 * -2

10. Negative Exponents Simplify, write the expression using only positive exponents: R -3 * R 6 6m -3 B 4 * B -3 * B -7 X -2 X 3

11. Do Now 12/7 Simplify, write the expression using only positive exponents: R 9 * R -7 -2m -4 rp -8 B -7 * B 9 * B -6 X -5 X 2

12. Exponents Expand and Solve: 1. 10 3 2. 10 -2 3. 10 7 4. 10 -6

13. Move the decimal to make the number greater than or equal to 1 and less than 10. 1) 1589653.236 2) 6523.4587 3) 7865 4) 0.000048 5) 0.000000789

14. Do Now 12/9 Expand and Solve: 1) 10 4 2) 10 -3 Move the decimal to make the number greater than or equal to 1 and less than 10. 3) 486,000,000 4) 0.00004789

15. Scientific Notation S c i e n t i f i c N o t a t i o n- Used to write very small numbers (the thickness of a soap bubble) or very large numbers (the number of stars in the galaxy.)

16. Scientific Notation Scientific Notation is written as: The product of a number (less than 10 and greater than or equal to one) and a power of ten. Ex: Standard Notation Scientific Notation 4,320,000,000 = 4.32 * 10 9 0.000056 = 5.6 * 10 -5

17. Scientific Notation To write a number in Scientific Notation: 1) Move decimal ≥ 1 and < 10. 2) Count how many spaces you moved (exponent) 3) Re-write number using new decimal 4) Write * 10 (exponent =number of times you moved) Pos exponent - If it was a large # Neg exponent – If it was a small #

18. Scientific Notation Write in Scientific Notation: 40,000,000 765,000 0.00086 0.00000475

19. Do Now 12/11 Write in Scientific Notation: 4,206,000,000 0.0000009058 0.007 487,500,000,000,000

20. Standard Notation Standard Notation- to write a number in standard notation move the decimal. negative exponent move left (little) positive exponent move right (big) Ex: 2.304 * 10 8 Positive exponent – make number bigger!! = 230,400,000

21. Standard Notation Translate from Scientific Notation into Standard Note. 1. 4.65 * 10 -4 2. 3.7 * 10 2 3. 4 * 10 -5 4. 9.6 * 10 11 5. 4.005 * 10 -7 = 0.000465 = 370 = 0.00004 = 960,000,000,000 = 0.0000004005

22. Square Root Square root : -Every positive number has a positive and negative square root. √25 = 5 or -5 √100 = 10 or -10 Usually - √9= -3

23. Square Root Perfect Square- any number that has an integer square root. Copy the chart from 1 to 15 What is the square root of the following: Ex 1: √225 Ex 2: √16 Ex 3: √49 EXTRA CREDIT ON YOUR TEST – MEMORIZE PERFECT SQUARES FROM 1- 15

24. Square Root If its not a perfect square than you need to be able to tell which two whole numbers its in-between. Ex 1: √115 Ex 2: √43 Ex 3: √8

25. Do Now 12/15 Find the Square root, If its not a perfect square tell which two integers its in-between: 1) √4 2) √23 3) -√36 4) √81 5) √41

26. Square Root – Using a Calculator Using a calculator find the square roots to the nearest tenth 1) √8 2) √56.25 3) -√1256 4) √236 5) √20.96

27. Do Now 12/16 Using a Calculator solve. Round to the nearest thousandth. 1) √1681 2) -√48.5 3) √1256 4) -√6241

28. Solving an Equation using Square Root Use Inverse operations Remember : +/– ; */÷ ; x 2 / √ 1) x 2 =64 2) 144= y 2 3) p 2 + 20 = 79

29. Do Now 12/17 1) p 2 = 1 2) 230 = y 2 + 34 3) x 2 – 18 = 103