December 2009 Exponents Square Root Scientific Notation Maybe Rational/Irrational Numbers Quiz Tuesday - 12/8 Test Friday - 12/18
May 22, 2015
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