December 2009

ExponentsSquare RootScientific NotationMaybe Rational/Irrational Numbers

Quiz Tuesday - 12/8Test Friday - 12/18

ExponentsWrite the product as a power and describe it

in words:1.) 4*4*4*4*4*4

46, 4 to the sixth power2.) R*R*R

R3, R to the third power or R cubed3.)7*7*7*7*7*T*T*T*T

75T4, 7 to the fifth power times T to the fourth power

ExponentsEvaluate the Power:1) 4 squared

2) 53

3) 119

4) 04

5) 35

Do Now 12/3Write 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.) 64 4.) 111 5.) 25

Zero ExponentsZero Exponents- For any number a≠0

a0 = 1Ex 1: 50 =

Ex 2: 32,543,3250 =

Ex 3: (34xpr)0 =

Be Careful!!Ex 4: 14xy0 =

Negative ExponentsNegative Exponents – for any integer n and

any number a≠0: a-n = 1

an

Ex 1: 3-2 =

EX 2: y-6 =

Ex 3: r2t-4 =

1

32

1y6

r2

t4

Negative and Zero ExponentsEvaluate the Expressions:1) 6-2

2) (-2)-3

3) (-5)0

4) (-3)-1

5) 4-5

Negative and Zero ExponentsEvaluate the Expressions:6) (-4)-3 * (-4)0

7) (-5)0 * (-5)-3

8) 2-2 * -2

9) (-3)-6 * 32

Do Now 12/4Evaluate the Expressions:1) (-8)-3

2) (-5)0

3) (-5)0 * (-5)-3

4) 2-2 * -2

Negative ExponentsSimplify, write the expression using

only positive exponents:1) R-3 * R6

2) 6m-3

3) B4 * B-3 * B-7

4) X-2

X3

Do Now 12/7Simplify, write the expression using

only positive exponents:1) R9 * R-7

2) -2m-4rp-8

3) B-7 * B9 * B-6

4) X-5

X2

Exponents

Expand and Solve:1. 103

2. 10-2

3. 107

4. 10-6

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

Do Now 12/9

Expand and Solve:1) 104

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

Scientific NotationScientific Notation- Used to write very small numbers (the thickness of a soap bubble) or very large numbers (the number of stars in the galaxy.)

Scientific NotationScientific 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 * 109

0.000056 = 5.6 * 10-5

Scientific NotationTo 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 #

Scientific NotationWrite in Scientific Notation:

1) 40,000,000

2) 765,000

3) 0.00086

4) 0.00000475

Do Now 12/11Write in Scientific Notation:1) 4,206,000,000

2) 0.0000009058

3) 0.007

4) 487,500,000,000,000

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 * 108

Positive exponent – make number bigger!!

= 230,400,000

Standard Notation Translate from Scientific Notation into Standard Note.

1. 4.65 * 10-4

2. 3.7 * 102

3. 4 * 10-5

4. 9.6 * 1011

5. 4.005 * 10-7

= 0.000465

= 370

= 0.00004

= 960,000,000,000

= 0.0000004005

Square RootSquare root:

-Every positive number has a positive and negative square root.

√25 = 5 or -5√100 = 10 or -10

Usually - √9= -3

Square RootPerfect 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: √225Ex 2: √16Ex 3: √49EXTRA CREDIT ON YOUR TEST – MEMORIZE

PERFECT SQUARES FROM 1- 15

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

Do Now 12/15Find 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

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

Do Now 12/16

Using a Calculator solve. Round to the nearest thousandth.

1) √1681

2) -√48.5

3) √1256

4) -√6241

Solving an Equation using Square Root

Use Inverse operations

Remember : +/– ; */÷ ; x2/√1) x2=64

2) 144= y2

3) p2 + 20 = 79

Do Now 12/17

1) p2 = 1

2) 230 = y2 + 34

3) x2 – 18 = 103