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# Exp, Sci Not, Square Root

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### Exp, Sci Not, Square Root

1. 1. December 2009 Exponents Square Root Scientific Notation Maybe Rational/Irrational Numbers Quiz Tuesday - 12/8 Test Friday - 12/18
2. 2. Exponents <ul><li>Write the product as a power and describe it in words: </li></ul><ul><li>1.) 4*4*4*4*4*4 </li></ul><ul><li>4 6 , 4 to the sixth power </li></ul><ul><li>2.) R*R*R </li></ul><ul><li>R 3 , R to the third power or R cubed </li></ul><ul><li>3.)7*7*7*7*7*T*T*T*T </li></ul><ul><li>7 5 T 4 , 7 to the fifth power times T to </li></ul><ul><li>the fourth power </li></ul>
3. 3. Exponents <ul><li>Evaluate the Power: </li></ul><ul><li>4 squared </li></ul><ul><li>5 3 </li></ul><ul><li>1 19 </li></ul><ul><li>0 4 </li></ul><ul><li>3 5 </li></ul>
4. 4. Do Now 12/3 <ul><li>Write the product as a power and describe it in words: </li></ul><ul><li>1.) 8*8 </li></ul><ul><li>2.) L*L*L*L*L*L*L*L </li></ul><ul><li>Evaluate the Power: </li></ul><ul><li>3.) 6 4 4.) 11 1 5.) 2 5 </li></ul>
5. 5. Zero Exponents <ul><li>Zero Exponents- For any number a≠0 a 0 = 1 </li></ul><ul><li>Ex 1: 5 0 = </li></ul><ul><li>Ex 2: 32,543,325 0 = </li></ul><ul><li>Ex 3: (34xpr) 0 = </li></ul><ul><li>Be Careful!! </li></ul><ul><li>Ex 4: 14xy 0 = </li></ul>
6. 6. Negative Exponents <ul><li>Negative Exponents – for any integer n and any number a≠0: a -n = 1 </li></ul><ul><li> a n </li></ul><ul><li>Ex 1: 3 -2 = </li></ul><ul><li>EX 2: y -6 = </li></ul><ul><li>Ex 3: r 2 t -4 = </li></ul>1 3 2 1 y 6 r 2 t 4
7. 7. Negative and Zero Exponents <ul><li>Evaluate the Expressions: </li></ul><ul><li>6 -2 </li></ul><ul><li>(-2) -3 </li></ul><ul><li>(-5) 0 </li></ul><ul><li>(-3) -1 </li></ul><ul><li>4 -5 </li></ul>
8. 8. Negative and Zero Exponents <ul><li>Evaluate the Expressions: </li></ul><ul><li>6) (-4) -3 * (-4) 0 </li></ul><ul><li>7) (-5) 0 * (-5) -3 </li></ul><ul><li>8) 2 -2 * -2 </li></ul><ul><li>9) (-3) -6 * 3 2 </li></ul>
9. 9. Do Now 12/4 <ul><li>Evaluate the Expressions: </li></ul><ul><li>(-8) -3 </li></ul><ul><li>(-5) 0 </li></ul><ul><li>(-5) 0 * (-5) -3 </li></ul><ul><li>2 -2 * -2 </li></ul>
10. 10. Negative Exponents <ul><li>Simplify, write the expression using only positive exponents: </li></ul><ul><li>R -3 * R 6 </li></ul><ul><li>6m -3 </li></ul><ul><li>B 4 * B -3 * B -7 </li></ul><ul><li>X -2 </li></ul><ul><li>X 3 </li></ul>
11. 11. Do Now 12/7 <ul><li>Simplify, write the expression using only positive exponents: </li></ul><ul><li>R 9 * R -7 </li></ul><ul><li>-2m -4 rp -8 </li></ul><ul><li>B -7 * B 9 * B -6 </li></ul><ul><li>X -5 </li></ul><ul><li>X 2 </li></ul>
12. 12. Exponents <ul><li>Expand and Solve: </li></ul><ul><li>1. 10 3 </li></ul><ul><li>2. 10 -2 </li></ul><ul><li>3. 10 7 </li></ul><ul><li>4. 10 -6 </li></ul>
13. 13. Move the decimal to make the number greater than or equal to 1 and less than 10. <ul><li>1) 1589653.236 </li></ul><ul><li>2) 6523.4587 </li></ul><ul><li>3) 7865 </li></ul><ul><li>4) 0.000048 </li></ul><ul><li>5) 0.000000789 </li></ul>
14. 14. Do Now 12/9 <ul><li>Expand and Solve: </li></ul><ul><li>1) 10 4 </li></ul><ul><li>2) 10 -3 </li></ul><ul><li>Move the decimal to make the number greater than or equal to 1 and less than 10. </li></ul><ul><li>3) 486,000,000 </li></ul><ul><li>4) 0.00004789 </li></ul>
15. 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. 16. Scientific Notation <ul><li>Scientific Notation is written as: </li></ul><ul><li>The product of a number (less than 10 and greater than or equal to one) and a power of ten. </li></ul><ul><li>Ex: </li></ul><ul><li>Standard Notation Scientific Notation </li></ul><ul><li>4,320,000,000 = 4.32 * 10 9 </li></ul><ul><li>0.000056 = 5.6 * 10 -5 </li></ul>
17. 17. Scientific Notation <ul><li>To write a number in Scientific Notation: </li></ul><ul><li>1) Move decimal ≥ 1 and < 10. </li></ul><ul><li>2) Count how many spaces you moved </li></ul><ul><li>(exponent) </li></ul><ul><li>3) Re-write number using new decimal </li></ul><ul><li>4) Write * 10 (exponent =number of times you moved) </li></ul><ul><li>Pos exponent - If it was a large # </li></ul><ul><li>Neg exponent – If it was a small # </li></ul>
18. 18. Scientific Notation <ul><li>Write in Scientific Notation: </li></ul><ul><li>40,000,000 </li></ul><ul><li>765,000 </li></ul><ul><li>0.00086 </li></ul><ul><li>0.00000475 </li></ul>
19. 19. Do Now 12/11 <ul><li>Write in Scientific Notation: </li></ul><ul><li>4,206,000,000 </li></ul><ul><li>0.0000009058 </li></ul><ul><li>0.007 </li></ul><ul><li>487,500,000,000,000 </li></ul>
20. 20. Standard Notation <ul><li>Standard Notation- to write a number in standard notation move the decimal. </li></ul><ul><li>negative exponent move left (little) </li></ul><ul><li>positive exponent move right (big) </li></ul><ul><li>Ex: 2.304 * 10 8 </li></ul><ul><li>Positive exponent – make number bigger!! </li></ul><ul><li>= 230,400,000 </li></ul>
21. 21. Standard Notation <ul><li>Translate from Scientific Notation into Standard Note. </li></ul><ul><li>1. 4.65 * 10 -4 </li></ul><ul><li>2. 3.7 * 10 2 </li></ul><ul><li>3. 4 * 10 -5 </li></ul><ul><li>4. 9.6 * 10 11 </li></ul><ul><li>5. 4.005 * 10 -7 </li></ul>= 0.000465 = 370 = 0.00004 = 960,000,000,000 = 0.0000004005
22. 22. Square Root <ul><li>Square root : </li></ul><ul><li>-Every positive number has a positive </li></ul><ul><li>and negative square root. </li></ul><ul><li>√25 = 5 or -5 </li></ul><ul><li>√100 = 10 or -10 </li></ul><ul><li>Usually - √9= -3 </li></ul>
23. 23. Square Root <ul><li>Perfect Square- any number that has an integer square root. </li></ul><ul><li>Copy the chart from 1 to 15 </li></ul><ul><li>What is the square root of the following: </li></ul><ul><li>Ex 1: √225 </li></ul><ul><li>Ex 2: √16 </li></ul><ul><li>Ex 3: √49 </li></ul><ul><li>EXTRA CREDIT ON YOUR TEST – MEMORIZE PERFECT SQUARES FROM 1- 15 </li></ul>
24. 24. Square Root <ul><li>If its not a perfect square than you need to be able to tell which two whole numbers its in-between. </li></ul><ul><li>Ex 1: √115 </li></ul><ul><li>Ex 2: √43 </li></ul><ul><li>Ex 3: √8 </li></ul>
25. 25. Do Now 12/15 <ul><li>Find the Square root, If its not a perfect square tell which two integers its in-between: </li></ul><ul><li>1) √4 </li></ul><ul><li>2) √23 </li></ul><ul><li>3) -√36 </li></ul><ul><li>4) √81 </li></ul><ul><li>5) √41 </li></ul>
26. 26. Square Root – Using a Calculator <ul><li>Using a calculator find the square roots to the nearest tenth </li></ul><ul><li>1) √8 </li></ul><ul><li>2) √56.25 </li></ul><ul><li>3) -√1256 </li></ul><ul><li>4) √236 </li></ul><ul><li>5) √20.96 </li></ul>
27. 27. Do Now 12/16 <ul><li>Using a Calculator solve. Round to the nearest thousandth. </li></ul><ul><li>1) √1681 </li></ul><ul><li>2) -√48.5 </li></ul><ul><li>3) √1256 </li></ul><ul><li>4) -√6241 </li></ul>
28. 28. Solving an Equation using Square Root <ul><li>Use Inverse operations </li></ul><ul><li>Remember : +/– ; */÷ ; x 2 / √ </li></ul><ul><li>1) x 2 =64 </li></ul><ul><li>2) 144= y 2 </li></ul><ul><li>3) p 2 + 20 = 79 </li></ul>
29. 29. Do Now 12/17 <ul><li>1) p 2 = 1 </li></ul><ul><li>2) 230 = y 2 + 34 </li></ul><ul><li>3) x 2 – 18 = 103 </li></ul>