Powers of Ten (4-1#1) (PA) Power...What is another name for power?

Power or Expanded Form Standard Form Exponent Form 1 0 3 ~O.10.10 1 000 1 0 2 • 1 0 1 1 0

1 0 0 1 1 1 1 0 - 1 - 1 0 ~l

1 0 - 2 e 1 1 1 -e-e­ 1 0 - 3 1 0 1 0 1 0 "001

!Example! Write the in standard form. 10 3 10 10 10-2

IExample! Write the number as a power of 10. 10000 1 .0 0 1 .000 0 1 Scientific Notation (4-2#1) (PA) Scientific Notation is a shorthand way of writing numbers using powers of 10. You write a number in scientific notation as the product of two fa<:!or§. ... .' ,.. _ _- 6 l ,)00,000 = /.) 10 The 1st factor is greater than 0econd factor ~wer of 10. equal to 1, but less than 10. ~tandard Notation or Standard Forml ~cientific Notation Forma~ A regular number. --:. 3,000,000 ? . ? X 1 0

~tandard Notation to Scientific Notation!

7 2 0 ,0 0 0 = 7. 2::x~ 1 0 5 .0 °5 = 5. ° 1 0 - 3 IExample/ Write the number in scientific notation. 7,000,000 = .025 =

~cientific Notation to Standard Notation!

8.9 >( 105 = 890,000

8.9 x 10- 6 =.0000089

IExample! Write the number in standard form. 3.21 105 = 5.9 10-4

IExamplel 9,870,000,000 1.2 1 IFinding & Approximating Square Roots (4-4 #1)(PA) I KNumber Squared\ 22 = 3 2 = 4 2 = 52 = 6 2 = All of these answers are called Perfect Squares. [he Sign\ Square root sign or symbol" and the radical sign. ~quare Roots with Perfect Squares\ Square roots are squared in reverse. -J9 = -J32 = .J3· 3 = 3 .Jl6 = N = -J4 ·4 = 4 "'\./2; = ../; 2 = .J;. 5 =; - ..Ji5 = -..J52 = - -J; ·5 = -; Find two square roots of the number. 36 == ? & ? '\J!36 == ? &' ? \Example\ Simplify each square root. .J144 J64 ~81

...}1 2 = .J? ? = ? ..fiT = -J? ? = ? ..../? 2 = -J? ? = 1 \Estimate to the Nearest Integerl Approximate the square root to Between which two consecutive the nearest whole number. does the square root lie? ,/4 1 ~,/8 3 ~~ #~ ~ :J? ~ :J? ~ ,J? ')

Approximate the square root to\Example\Between which two consecutive the nearest whole number. integers does the square root lie?

.J146 .Jl4 Simplifying Square Roots (4-5 #1)(PA) IRememberl KNumber Squaredl 12 = 1 22 = 4 3 2 = 9 4 2 = 16 52 = 25 6 2 = 36 All of these answers are called Perfect Squares. ~quare Roots with Perfect Squaresl Square roots are squared in reverse . .,./9' = .J32 = J3' 3 = 3 J16 = J42 = J4 ·4 = 4 -J25 = ,/52 = -,/5 .5 = 5 - -J25 = - -J52 = - ,J5 .5 = - 5 What does this mean? Xi..' 21,xI 2x ~.

IProduct Property for Square Rootsl

--Jc;b = ,Ja·b = .../a. ~

~implifying Radical Expressionsl What do I do when the ~~_____ number is NOT J50 = A Perfect Square! I - r--. r-- = . Jr- = _~ -J250 = ~-'-= L"L= -"-L= _.J=

~implifying the Expressionsl -J5 ...jiO =J =)_.- =) .) =_. "\/- =-)

IExamplel -J8 ffi Fz .-J6 ~8 .J12 Simplifying Square Roots (4-5 #2)(PA) Quotient Property for Square Rootsl ~=1 ~implifying Radical Expressionsl 1100 _ ~~~ __ _ JI 7- ~~~ _""J 1J 4 - ~_ 9 - )_ IExamplel [15 1}64 rn C'~S5 N o ~ ,I:::a. Why Didn't Krok Like to Go Sailing With the

or@» Baseball Uniform Designer? JQ ...,G) ----~~ ~m Simplify each expression below and find your answer in the corresponding answer <=. OJ <'J]CD» column. Write the letter of the exercise in the box that contains the number of the answer. "1J §.~ .,.. g=i (rt•• ~I CD VB @70. ® 5v1a @6V7 0"1J :J­ • cnN N (D\i45 @5Vs I @ 3v28 @ 24\13 » N I N ®VsO @20. , ® 2V1000 ® 24Y2 CDvT2 0 50. I• ® V1,000,000 ® 15v2 @V98 @4\13 I @3V12a ® 16Vs ® V4a @ 2\13 j• ® 8Y27 @) 1000 @ V125 @ 3Vs I CD 4\180 @ 20vTO C:····,············,.·······,··········t,······,.·····••...•,•.•...... •..,..... ,.!) v20 30· , -3Vs4 @ -8% o ® ® • ® ~ ~ ® \172 CD 60. I ® - 7\140 @ 30\.13 ~~ CY) v63 (2) 100. I ® -8V121 @ -14\110 ~m , -w (J) @ vT44 40. 2VsOo @ 20Vs .....~I a. ® I ® ::J .. nJ-l <0 V32 @ 2v;G -4\1'24 @ 15V7 co(/) ® i CD ""0 -. co 3 4"0 @ V7s @ 12 : ® 3v17s ® -9V6 Q.-<­co= (J)(/) .0..0 ® v200 @ 5\13 c:~ © 5vTc)a @ -88 cC nJt\) coCO"""' .... roO 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 0 0 OU; ~2. -- - _ .. ""--- ..... Rational & Irrational Numbers (4-6 #1 )(PA) !Real Numbers! Rational Numbers irrational Numbers

IRational Numbe~ A rational number is a number that can be written as a a quotient b where a and b are integers and b can not be O. Every rational number can be written as a terminating or repeating decimal.

!Irrational NumbeQ An irrational number is a number that can not be written as a quotient of two numbers. Irrational numbers are non-repeating and non-terminating decimals. If a square root is a perfect square it's rational, If it's not a perfect square it's irrational.

IRational or I rrationall .02358489630... ~" ~ ,,/121

Complete the statement with <, >, or =. ,--­ -,-,5.. · .. (;5.- -J.9?9 5? v'lo -5?- ~25 6 ~'6